Classification and Pixel Change Detection of Brain Tumor Using Adam Kookaburra Optimization-Based Shepard Convolutional Neural Network

The uncommon growth of cells in the brain is termed as brain tumor. To identify chronic nerve problems, like strokes, brain tumors, multiple sclerosis, and dementia, brain magnetic resonance imaging (MRI) is normally utilized. Identifying the tumor on early stage can improve the patient's survival rate. However, it is difficult to identify the exact tumor region with less computational complexity. Also, the tumors can vary significantly in shape, size, and appearance, which complicates the task of correctly classifying tumor types and detecting subtle pixel changes over time. Hence, an Adam kookaburra optimization-based Shepard convolutional neural network (AKO-based Shepard CNN) is established in this study for the classification and pixel change detection of brain tumor. The Adam kookaburra optimization (AKO) is established by integrating the kookaburra optimization algorithm (KOA) and Adam. Here, the pre- and post-operative MRIs are pre-processed and then segmented by U-Net++. The tuning of U-Net++ is done by the bald Border collie firefly optimization algorithm (BBCFO). The bald eagle search (BES), firefly algorithm (FA), and Border collie optimization (BCO) are combined to form the BBCFO. The next operation is the feature extraction and the classification is conducted at last using ShCNN. The AKO is utilized to tune the ShCNN for obtaining effective classification results. Unlike conventional optimization algorithms, AKO offers faster convergence and higher accuracy in classification. The highest negative predictive value (NPV), true negative rate (TNR), true positive rate (TPR), positive predictive value (PPV), and accuracy produced by the AKO-based ShCNN are 89.91%, 92.26%, 93.78%, and 93.60%, respectively, using Brain Images of Tumors for Evaluation database (BITE).

Deep unfolding network with spatial alignment for multi-modal MRI reconstruction

Multi-modal Magnetic Resonance Imaging (MRI) offers complementary diagnostic information, but some modalities are limited by the long scanning time. To accelerate the whole acquisition process, MRI reconstruction of one modality from highly under-sampled k-space data with another fully-sampled reference modality is an efficient solution. However, the misalignment between modalities, which is common in clinic practice, can negatively affect reconstruction quality. Existing deep learning-based methods that account for inter-modality misalignment perform better, but still share two main common limitations: (1) The spatial alignment task is not adaptively integrated with the reconstruction process, resulting in insufficient complementarity between the two tasks; (2) the entire framework has weak interpretability. In this paper, we construct a novel Deep Unfolding Network with Spatial Alignment, termed DUN-SA, to appropriately embed the spatial alignment task into the reconstruction process. Concretely, we derive a novel joint alignment-reconstruction model with a specially designed aligned cross-modal prior term. By relaxing the model into cross-modal spatial alignment and multi-modal reconstruction tasks, we propose an effective algorithm to solve this model alternatively. Then, we unfold the iterative stages of the proposed algorithm and design corresponding network modules to build DUN-SA with interpretability. Through end-to-end training, we effectively compensate for spatial misalignment using only reconstruction loss, and utilize the progressively aligned reference modality to provide inter-modality prior to improve the reconstruction of the target modality. Comprehensive experiments on four real datasets demonstrate that our method exhibits superior reconstruction performance compared to state-of-the-art methods.

ISRSL0: compressed sensing MRI with image smoothness regularized-smoothed [Formula: see text] norm

The reconstruction of MR images has always been a challenging inverse problem in medical imaging. Acceleration of MR scanning is of great importance for clinical research and cutting-edge applications. One of the primary efforts to achieve this is using compressed sensing (CS) theory. The CS aims to reconstruct MR images using a small number of sampled data in k-space. The CS-MRI techniques face challenges, including the potential loss of fine structure and increased computational complexity. We introduce a novel framework based on a regularized sparse recovery problem and a sharpening step to improve the CS-MRI approaches regarding fine structure loss under high acceleration factors. This problem is solved via the Half Quadratic Splitting (HQS) approach. The inverse problem for reconstructing MR images is converted into two distinct sub-problems, each of which can be solved separately. One key feature of the proposed approach is the replacement of one sub-problem with a denoiser. This regularization assists the optimization of the Smoothed [Formula: see text] (SL0) norm in escaping local minimums and enhances its precision. The proposed method consists of smoothing, feature modification, and Smoothed [Formula: see text] cost function optimization. The proposed approach improves the SL0 algorithm for MRI reconstruction without complicating it. The convergence of the proposed approach is illustrated analytically. The experimental results show an acceptable performance of the proposed method compared to the network-based approaches.

AliasNet: Alias artefact suppression network for accelerated phase-encode MRI

Sparse reconstruction is an important aspect of MRI, helping to reduce acquisition time and improve spatial-temporal resolution. Popular methods are based mostly on compressed sensing (CS), which relies on the random sampling of k-space to produce incoherent (noise-like) artefacts. Due to hardware constraints, 1D Cartesian phase-encode under-sampling schemes are popular for 2D CS-MRI. However, 1D under-sampling limits 2D incoherence between measurements, yielding structured aliasing artefacts (ghosts) that may be difficult to remove assuming a 2D sparsity model. Reconstruction algorithms typically deploy direction-insensitive 2D regularisation for these direction-associated artefacts. Recognising that phase-encode artefacts can be separated into contiguous 1D signals, we develop two decoupling techniques that enable explicit 1D regularisation and leverage the excellent 1D incoherence characteristics. We also derive a combined 1D + 2D reconstruction technique that takes advantage of spatial relationships within the image. Experiments conducted on retrospectively under-sampled brain and knee data demonstrate that combination of the proposed 1D AliasNet modules with existing 2D deep learned (DL) recovery techniques leads to an improvement in image quality. We also find AliasNet enables a superior scaling of performance compared to increasing the size of the original 2D network layers. AliasNet therefore improves the regularisation of aliasing artefacts arising from phase-encode under-sampling, by tailoring the network architecture to account for their expected appearance. The proposed 1D + 2D approach is compatible with any existing 2D DL recovery technique deployed for this application.

A generalized dual-domain generative framework with hierarchical consistency for medical image reconstruction and synthesis

Medical image reconstruction and synthesis are critical for imaging quality, disease diagnosis and treatment. Most of the existing generative models ignore the fact that medical imaging usually occurs in the acquisition domain, which is different from, but associated with, the image domain. Such methods exploit either single-domain or dual-domain information and suffer from inefficient information coupling across domains. Moreover, these models are usually designed specifically and not general enough for different tasks. Here we present a generalized dual-domain generative framework to facilitate the connections within and across domains by elaborately-designed hierarchical consistency constraints. A multi-stage learning strategy is proposed to construct hierarchical constraints effectively and stably. We conducted experiments for representative generative tasks including low-dose PET/CT reconstruction, CT metal artifact reduction, fast MRI reconstruction, and PET/CT synthesis. All these tasks share the same framework and achieve better performance, which validates the effectiveness of our framework. This technology is expected to be applied in clinical imaging to increase diagnosis efficiency and accuracy.

A framework applicable in different imaging modalities can facilitate the medical imaging reconstruction efficiency but hindered by inefficient information communication across the data acquisition and imaging domains. Here, Jiadong Zhang and coworkers report a dual-domain generative framework to explore the underlying patterns across domains and apply their method to routine imaging modalities (computed tomography, positron emission tomography, magnetic resonance imaging) under one framework.

Hybrid Optimization Algorithm Enabled Deep Learning Approach Brain Tumor Segmentation and Classification Using MRI

The unnatural and uncontrolled increase of brain cells is called brain tumors, leading to human health danger. Magnetic resonance imaging (MRI) is widely applied for classifying and detecting brain tumors, due to its better resolution. In general, medical specialists require more details regarding the size, type, and changes in small lesions for effective classification. The timely and exact diagnosis plays a major role in the efficient treatment of patients. Therefore, in this research, an efficient hybrid optimization algorithm is implemented for brain tumor segmentation and classification. The convolutional neural network (CNN) features are extracted to perform a better classification. The classification is performed by considering the extracted features as the input of the deep residual network (DRN), in which the training is performed using the proposed chronological Jaya honey badger algorithm (CJHBA). The proposed CJHBA is the integration of the Jaya algorithm, honey badger algorithm (HBA), and chronological concept. The performance is evaluated using the BRATS 2018 and Figshare datasets, in which the maximum accuracy, sensitivity, and specificity are attained using the BRATS dataset with values 0.9210, 0.9313, and 0.9284, respectively.

A convergence analysis for projected fast iterative soft-thresholding algorithm under radial sampling MRI

Radial sampling is a fast magnetic resonance imaging technique. Further imaging acceleration can be achieved with undersampling but how to reconstruct a clear image with fast algorithm is still challenging. Previous work has shown the advantage of removing undersampling image artifacts using the tight-frame sparse reconstruction model. This model was further solved with a projected fast iterative soft-thresholding algorithm (pFISTA). However, the convergence of this algorithm under radial sampling has not been clearly set up. In this work, the authors derived a theoretical convergence condition for this algorithm. This condition was approximated by estimating the maximal eigenvalue of reconstruction operators through the power iteration. Based on the condition, an optimal step size was further suggested to allow the fastest convergence. Verifications were made on the prospective in vivo data of static brain imaging and dynamic contrast-enhanced liver imaging, demonstrating that the recommended parameter allowed fast convergence in radial MRI.

Deep compressed sensing MRI via a gradient-enhanced fusion model

BACKGROUND

Compressed sensing has been employed to accelerate magnetic resonance imaging by sampling fewer measurements. However, conventional iterative optimization-based CS-MRI are time-consuming for iterative calculations and often share poor generalization ability on multicontrast datasets. Most deep-learning-based CS-MRI focus on learning an end-to-end mapping while ignoring some prior knowledge existed in MR images.

PURPOSE

We propose an iterative fusion model to integrate the image and gradient-based priors into reconstruction via convolutional neural network models while maintaining high quality and preserving the detailed information as well.

METHODS

We propose a gradient-enhanced fusion network (GFN) for fast and accurate MRI reconstruction, in which dense blocks with dilated convolution and dense residual learnings are used to capture abundant features with fewer parameters. Meanwhile, decomposed gradient maps containing obvious structural information are introduced into the network to enhance the reconstructed images. Besides this, gradient-based priors along directions X and Y are exploited to learn adaptive tight frames for reconstructing the desired image contrast and edges by respective gradient fusion networks. After that, both image and gradient priors are fused in the proposed optimization model, in which we employ the l₂ -norm to promote the sparsity of gradient priors. The proposed fusion model can effectively help to capture edge structures in the gradient images and to preserve more detailed information of MR images.

RESULTS

Experimental results demonstrate that the proposed method outperforms several CS-MRI methods in terms of peak signal-to-noise (PSNR), the structural similarity index (SSIM), and visualizations on three sampling masks with different rates. Noteworthy, to evaluate the generalization ability, the proposed model conducts cross-center training and testing experiments for all three modalities and shares more stable performance compared than other approaches. In addition, the proposed fusion model is applied to other comparable deep learning methods. The quantitative results show that the reconstruction results of these methods are obviously improved.

CONCLUSIONS

The gradient-based priors reconstructed from GFNs can effectively enhance the edges and details of under-sampled data. The proposed fusion model integrates image and gradient priors using l₂ -norm can effectively improve the generalization ability on multicontrast datasets reconstruction.

One-Dimensional Deep Low-Rank and Sparse Network for Accelerated MRI

Deep learning has shown astonishing performance in accelerated magnetic resonance imaging (MRI). Most state-of-the-art deep learning reconstructions adopt the powerful convolutional neural network and perform 2D convolution since many magnetic resonance images or their corresponding k-space are in 2D. In this work, we present a new approach that explores the 1D convolution, making the deep network much easier to be trained and generalized. We further integrate the 1D convolution into the proposed deep network, named as One-dimensional Deep Low-rank and Sparse network (ODLS), which unrolls the iteration procedure of a low-rank and sparse reconstruction model. Extensive results on in vivo knee and brain datasets demonstrate that, the proposed ODLS is very suitable for the case of limited training subjects and provides improved reconstruction performance than state-of-the-art methods both visually and quantitatively. Additionally, ODLS also shows nice robustness to different undersampling scenarios and some mismatches between the training and test data. In summary, our work demonstrates that the 1D deep learning scheme is memory-efficient and robust in fast MRI.

A unified model for reconstruction and R2* mapping of accelerated 7T data using the quantitative recurrent inference machine

Quantitative MRI (qMRI) acquired at the ultra-high field of 7 Tesla has been used in visualizing and analyzing subcortical structures. qMRI relies on the acquisition of multiple images with different scan settings, leading to extended scanning times. Data redundancy and prior information from the relaxometry model can be exploited by deep learning to accelerate the imaging process. We propose the quantitative Recurrent Inference Machine (qRIM), with a unified forward model for joint reconstruction and R₂^*-mapping from sparse data, embedded in a Recurrent Inference Machine (RIM), an iterative inverse problem-solving network. To study the dependency of the proposed extension of the unified forward model to network architecture, we implemented and compared a quantitative End-to-End Variational Network (qE2EVN). Experiments were performed with high-resolution multi-echo gradient echo data of the brain at 7T of a cohort study covering the entire adult life span. The error in reconstructed R₂^* from undersampled data relative to reference data significantly decreased for the unified model compared to sequential image reconstruction and parameter fitting using the RIM. With increasing acceleration factor, an increasing reduction in the reconstruction error was observed, pointing to a larger benefit for sparser data. Qualitatively, this was following an observed reduction of image blurriness in R₂^*-maps. In contrast, when using the U-Net as network architecture, a negative bias in R₂^* in selected regions of interest was observed. Compressed Sensing rendered accurate, but less precise estimates of R₂^*. The qE2EVN showed slightly inferior reconstruction quality compared to the qRIM but better quality than the U-Net and Compressed Sensing. Subcortical maturation over age measured by a linearly increasing interquartile range of R₂^* in the striatum was preserved up to an acceleration factor of 9. With the integrated prior of the unified forward model, the proposed qRIM can exploit the redundancy among repeated measurements and shared information between tasks, facilitating relaxometry in accelerated MRI.

A cascade of preconditioned conjugate gradient networks for accelerated magnetic resonance imaging

BACKGROUND AND OBJECTIVE

Recent unfolding based compressed sensing magnetic resonance imaging (CS-MRI) methods only reinterpret conventional CS-MRI optimization algorithms and, consequently, inherit the weaknesses of the alternating optimization strategy. In order to avoid the structural complexity of the alternating optimization strategy and achieve better reconstruction performance, we propose to directly optimize the ℓ₁ regularized convex optimization problem using a deep learning approach.

METHOD

In order to achieve direct optimization, a system of equations solving the ℓ₁ regularized optimization problem is constructed from the optimality conditions of a novel primal-dual form proposed for the effective training of the sparsifying transform. The optimal solution is obtained by a cascade of unfolding networks of the preconditioned conjugate gradient (PCG) algorithm trained to minimize the mean element-wise absolute difference (ℓ₁ loss) between the terminal output and ground truth image in an end-to-end manner. The performance of the proposed method was compared with that of U-Net, PD-Net, ISTA-Net+, and the recently proposed projection-based cascaded U-Net, using single-coil knee MR images of the fastMRI dataset.

RESULTS

In our experiment, the proposed network outperformed existing unfolding-based networks and the complex version of U-Net in several subsampling scenarios. In particular, when using the random Cartesian subsampling mask with 25 % sampling rate, the proposed model outperformed PD-Net by 0.76 dB, ISTA-Net+ by 0.43 dB, and U-Net by 1.21 dB on the positron density without suppression (PD) dataset in term of peak signal to noise ratio. In comparison with the projection-based cascade U-Net, the proposed algorithm achieved approximately the same performance when the sampling rate was 25% with only 1.62% number of network parameters at the cost of a longer reconstruction time (approximately twice).

CONCLUSION

A cascade of unfolding networks of the PCG algorithm was proposed to directly optimize the ℓ₁ regularized CS-MRI optimization problem. The proposed network achieved improved reconstruction performance compared with U-Net, PD-Net, and ISTA-Net+, and achieved approximately the same performance as the projection-based cascaded U-Net while using significantly fewer network parameters.

Jointly estimating bias field and reconstructing uniform MRI image by deep learning

Bias field is one of the main artifacts that degrade the quality of magnetic resonance images. It introduces intensity inhomogeneity and affects image analysis such as segmentation. In this work, we proposed a deep learning approach to jointly estimate bias field and reconstruct uniform image. By modeling the quality degradation process as the product of a spatially varying field and a uniform image, the network was trained on 800 images with true bias fields from 12 healthy subjects. A network structure of bias field estimation and uniform image reconstruction was designed to compensate for the intensity loss. To further evaluate the benefit of bias field correction, a quantitative analysis was made on image segmentation. Experimental results show that the proposed BFCNet improves the image uniformity by 8.3% and 10.1%, the segmentation accuracy by 4.1% and 6.8% on white and grey matter in T2-weighted brain images. Moreover, BFCNet outperforms the state-of-the-art traditional methods and deep learning methods on estimating bias field and preserving image structure, and BFCNet is robust to different levels of bias field and noise.

Accelerated MRI Reconstruction With Separable and Enhanced Low-Rank Hankel Regularization

Magnetic resonance imaging serves as an essential tool for clinical diagnosis, however, suffers from a long acquisition time. Sparse sampling effectively saves this time but images need to be faithfully reconstructed from undersampled data. Among the existing reconstruction methods, the structured low-rank methods have advantages in robustness to the sampling patterns and lower error. However, the structured low-rank methods use the 2D or higher dimension k-space data to build a huge block Hankel matrix, leading to considerable time and memory consumption. To reduce the size of the Hankel matrix, we proposed to separably construct multiple small Hankel matrices from rows and columns of the k-space and then constrain the low-rankness on these small matrices. This separable model can significantly reduce the computational time but ignores the correlation existed in inter- and intra-row or column, resulting in increased reconstruction error. To improve the reconstructed image without obviously increasing the computation, we further introduced the self-consistency of k-space and virtual coil prior. Besides, the proposed separable model can be extended into other imaging scenarios which hold exponential characteristics in the parameter dimension. The in vivo experimental results demonstrated that the proposed method permits the lowest reconstruction error with a fast reconstruction. The proposed approach requires only 4% of the state-of-the-art STDLR-SPIRiT runtime for parallel imaging reconstruction, and achieves the fastest computational speed in parameter imaging reconstruction.

MRI Reconstruction with Separate Magnitude and Phase Priors Based on Dual-Tree Complex Wavelet Transform

The methods of compressed sensing magnetic resonance imaging (CS-MRI) can be divided into two categories roughly based on the number of target variables. One group devotes to estimating the complex-valued MRI image. And the other calculates the magnitude and phase parts of the complex-valued MRI image, respectively, by enforcing separate penalties on them. We propose a new CS-based method based on dual-tree complex wavelet (DT CWT) sparsity, which is under the frame of the second class of CS-MRI. Owing to the separate regularization frame, this method reduces the impact of the phase jumps (that means the jumps or discontinuities of phase values) on magnitude reconstruction. Moreover, by virtue of the excellent features of DT CWT, such as nonoscillating envelope of coefficients and multidirectional selectivity, the proposed method is capable of capturing more details in the magnitude and phase images. The experimental results show that the proposed method recovers the image contour and edges information well and can eliminate the artifacts in magnitude results caused by phase jumps.

Task-adaptive eigenvector-based projection (EBP) transform for compressed sensing: A case study of spectroscopic profiling sensor

The compressed sensing (CS) theory requires the signal to be sparse under some transform. For most signals (e.g., speech and photos), the non-adaptive transform bases, such as discrete cosine transform (DCT), discrete Fourier transform (DFT), and Walsh-Hadamard transform (WHT), can meet this requirement and perform quite well. However, one limitation of these non-adaptive transforms is that we cannot leverage domain-specific knowledge to improve CS efficiency. This study presents a task-adaptive eigenvector-based projection (EBP) transform. The EBP basis has an equivalent effect of the principal component loading matrix and can generate a sparse representation in the latent space. In a Raman spectroscopic profiling case study, EBP demonstrates better performance than its non-adaptive counterparts. At the 1% CS sampling ratio (k), the reconstruction relative mean square errors of DCT, DFT, WHT and EBP are 0.33, 0.68, 0.32, and 0.00, respectively. At a fixed k, EBP achieves much better reconstruction quality than the non-adaptive counterparts. For specific domain tasks, EBP can significantly lower the CS sampling ratio and reduce the overall measurement cost.

Task-Oriented Convex Bilevel Optimization With Latent Feasibility

This paper firstly proposes a convex bilevel optimization paradigm to formulate and optimize popular learning and vision problems in real-world scenarios. Different from conventional approaches, which directly design their iteration schemes based on given problem formulation, we introduce a task-oriented energy as our latent constraint which integrates richer task information. By explicitly re- characterizing the feasibility, we establish an efficient and flexible algorithmic framework to tackle convex models with both shrunken solution space and powerful auxiliary (based on domain knowledge and data distribution of the task). In theory, we present the convergence analysis of our latent feasibility re- characterization based numerical strategy. We also analyze the stability of the theoretical convergence under computational error perturbation. Extensive numerical experiments are conducted to verify our theoretical findings and evaluate the practical performance of our method on different applications.

Synthetic Aperture Radar Image Despeckling Based on Multi-Weighted Sparse Coding

Synthetic aperture radar (SAR) images are inherently degraded by speckle noise caused by coherent imaging, which may affect the performance of the subsequent image analysis task. To resolve this problem, this article proposes an integrated SAR image despeckling model based on dictionary learning and multi-weighted sparse coding. First, the dictionary is trained by groups composed of similar image patches, which have the same structural features. An effective orthogonal dictionary with high sparse representation ability is realized by introducing a properly tight frame. Furthermore, the data-fidelity term and regularization terms are constrained by weighting factors. The weighted sparse representation model not only fully utilizes the interblock relevance but also reflects the importance of various structural groups in despeckling processing. The proposed model is implemented with fast and effective solving steps that simultaneously perform orthogonal dictionary learning, weight parameter updating, sparse coding, and image reconstruction. The solving steps are designed using the alternative minimization method. Finally, the speckles are further suppressed by iterative regularization methods. In a comparison study with existing methods, our method demonstrated state-of-the-art performance in suppressing speckle noise and protecting the image texture details.

A review on deep learning MRI reconstruction without fully sampled k-space

BACKGROUND

Magnetic resonance imaging (MRI) is an effective auxiliary diagnostic method in clinical medicine, but it has always suffered from the problem of long acquisition time. Compressed sensing and parallel imaging are two common techniques to accelerate MRI reconstruction. Recently, deep learning provides a new direction for MRI, while most of them require a large number of data pairs for training. However, there are many scenarios where fully sampled k-space data cannot be obtained, which will seriously hinder the application of supervised learning. Therefore, deep learning without fully sampled data is indispensable.

MAIN TEXT

In this review, we first introduce the forward model of MRI as a classic inverse problem, and briefly discuss the connection of traditional iterative methods to deep learning. Next, we will explain how to train reconstruction network without fully sampled data from the perspective of obtaining prior information.

CONCLUSION

Although the reviewed methods are used for MRI reconstruction, they can also be extended to other areas where ground-truth is not available. Furthermore, we may anticipate that the combination of traditional methods and deep learning will produce better reconstruction results.

Accelerated image reconstruction with separable Hankel regularization in parallel MRI

Magnetic resonance imaging has been widely adopted in clinical diagnose, however, it suffers from relatively long data acquisition time. Sparse sampling with reconstruction can speed up the data acquisition duration. As the state-of-the-art magnetic resonance imaging methods, the structured low rank reconstruction approaches embrace the advantage of holding low reconstruction errors and permit flexible undersampling patterns. However, this type of method demands intensive computations and high memory consumptions, thereby resulting in a lengthy reconstruction time. In this work, we proposed a separable Hankel low rank reconstruction method to explore the low rankness of each row and each column. Furthermore, we utilized the self-consistence and conjugate symmetry property of k-space data. The experimental results demonstrated that the proposed method outperforms the state-of-the-art approaches in terms of lower reconstruction errors and better detail preservation. Besides, the proposed method requires much less computation and memory consumption.Clinical Relevance- Parallel imaging, image reconstruction, Hankel low-rank.

XCloud-pFISTA: A Medical Intelligence Cloud for Accelerated MRI

Machine learning and artificial intelligence have shown remarkable performance in accelerated magnetic resonance imaging (MRI). Cloud computing technologies have great advantages in building an easily accessible platform to deploy advanced algorithms. In this work, we develop an open-access, easy-to-use and high-performance medical intelligence cloud computing platform (XCloud-pFISTA) to reconstruct MRI images from undersampled k-space data. Two state-of-the-art approaches of the Projected Fast Iterative Soft-Thresholding Algorithm (pFISTA) family have been successfully implemented on the cloud. This work can be considered as a good example of cloud-based medical image reconstruction and may benefit the future development of integrated reconstruction and online diagnosis system.

Investigating Customization Strategies and Convergence Behaviors of Task-Specific ADMM

Alternating Direction Method of Multiplier (ADMM) has been a popular algorithmic framework for separable optimization problems with linear constraints. For numerical ADMM fail to exploit the particular structure of the problem at hand nor the input data information, leveraging task-specific modules (e.g., neural networks and other data-driven architectures) to extend ADMM is a significant but challenging task. This work focuses on designing a flexible algorithmic framework to incorporate various task-specific modules (with no additional constraints) to improve the performance of ADMM in real-world applications. Specifically, we propose Guidance from Optimality (GO), a new customization strategy, to embed task-specific modules into ADMM (GO-ADMM). By introducing an optimality-based criterion to guide the propagation, GO-ADMM establishes an updating scheme agnostic to the choice of additional modules. The existing task-specific methods just plug their task-specific modules into the numerical iterations in a straightforward manner. Even with some restrictive constraints on the plug-in modules, they can only obtain some relatively weaker convergence properties for the resulted ADMM iterations. Fortunately, without any restrictions on the embedded modules, we prove the convergence of GO-ADMM regarding objective values and constraint violations, and derive the worst-case convergence rate measured by iteration complexity. Extensive experiments are conducted to verify the theoretical results and demonstrate the efficiency of GO-ADMM.

Systematic Analysis and Review of Magnetic Resonance Imaging (MRI) Reconstruction Techniques

BACKGROUND

Magnetic Resonance Imaging (MRI) plays an important role in the field of medical diagnostic imaging as it poses non-invasive acquisition and high soft-tissue contrast. However, a huge time is needed for the MRI scanning process that results in motion artifacts, degrades image quality, misinterprets the data, and may cause discomfort to the patient. Thus, the main goal of MRI research is to accelerate data acquisition processing without affecting the quality of the image.

INTRODUCTION

This paper presents a survey based on distinct conventional MRI reconstruction methodologies. In addition, a novel MRI reconstruction strategy is proposed based on weighted Compressive Sensing (CS), Penalty-aided minimization function, and Meta-heuristic optimization technique.

METHODS

An illustrative analysis is done concerning adapted methods, datasets used, execution tools, performance measures, and values of evaluation metrics. Moreover, the issues of existing methods and the research gaps considering conventional MRI reconstruction schemes are elaborated to obtain improved contribution for devising significant MRI reconstruction techniques.

RESULTS

The proposed method will reduce conventional aliasing artifact problems, may attain lower Mean Square Error (MSE), higher Peak Signal-to-Noise Ratio (PSNR), and Structural SIMilarity (SSIM) index.

CONCLUSION

The issues of existing methods and the research gaps considering conventional MRI reconstruction schemes are elaborated to devising an improved significant MRI reconstruction technique.

Deep Multi-Scale 3D Convolutional Neural Network (CNN) for MRI Gliomas Brain Tumor Classification

Accurate and fully automatic brain tumor grading from volumetric 3D magnetic resonance imaging (MRI) is an essential procedure in the field of medical imaging analysis for full assistance of neuroradiology during clinical diagnosis. We propose, in this paper, an efficient and fully automatic deep multi-scale three-dimensional convolutional neural network (3D CNN) architecture for glioma brain tumor classification into low-grade gliomas (LGG) and high-grade gliomas (HGG) using the whole volumetric T1-Gado MRI sequence. Based on a 3D convolutional layer and a deep network, via small kernels, the proposed architecture has the potential to merge both the local and global contextual information with reduced weights. To overcome the data heterogeneity, we proposed a preprocessing technique based on intensity normalization and adaptive contrast enhancement of MRI data. Furthermore, for an effective training of such a deep 3D network, we used a data augmentation technique. The paper studied the impact of the proposed preprocessing and data augmentation on classification accuracy.Quantitative evaluations, over the well-known benchmark (Brats-2018), attest that the proposed architecture generates the most discriminative feature map to distinguish between LG and HG gliomas compared with 2D CNN variant. The proposed approach offers promising results outperforming the recently supervised and unsupervised state-of-the-art approaches by achieving an overall accuracy of 96.49% using the validation dataset. The obtained experimental results confirm that adequate MRI's preprocessing and data augmentation could lead to an accurate classification when exploiting CNN-based approaches.

Optimizing multicontrast MRI reconstruction with shareable feature aggregation and selection

This paper proposes a new method for optimizing feature sharing in deep neural network-based, rapid, multicontrast magnetic resonance imaging (MC-MRI). Using the shareable information of MC images for accelerated MC-MRI reconstruction, current algorithms stack the MC images or features without optimizing the sharing protocols, leading to suboptimal reconstruction results. In this paper, we propose a novel feature aggregation and selection scheme in a deep neural network to better leverage the MC features and improve the reconstruction results. First, we propose to extract and use the shareable information by mapping the MC images into multiresolution feature maps with multilevel layers of the neural network. In this way, the extracted features capture complementary image properties, including local patterns from the shallow layers and semantic information from the deep layers. Then, an explicit selection module is designed to compile the extracted features optimally. That is, larger weights are learned to incorporate the constructive, shareable features; and smaller weights are assigned to the unshareable information. We conduct comparative studies on publicly available T2-weighted and T2-weighted fluid attenuated inversion recovery brain images, and the results show that the proposed network consistently outperforms existing algorithms. In addition, the proposed method can recover the images with high fidelity under 16 times acceleration. The ablation studies are conducted to evaluate the effectiveness of the proposed feature aggregation and selection mechanism. The results and the visualization of the weighted features show that the proposed method does effectively improve the usage of the useful features and suppress useless information, leading to overall enhanced reconstruction results. Additionally, the selection module can zero-out repeated and redundant features and improve network efficiency.

Spatiotemporal Flexible Sparse Reconstruction for Rapid Dynamic Contrast-enhanced MRI

Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) is a tissue perfusion imaging technique. Some versatile free-breathing DCE-MRI techniques combining compressed sensing (CS) and parallel imaging with golden-angle radial sampling have been developed to improve motion robustness with high spatial and temporal resolution. These methods have demonstrated good diagnostic performance in clinical setting, but the reconstruction quality will degrade at high acceleration rates and overall reconstruction time remains long. In this paper, we proposed a new parallel CS reconstruction model for DCE-MRI that enforces flexible weighted sparse constraint along both spatial and temporal dimensions. Weights were introduced to flexibly adjust the importance of time and space sparsity, and we derived a fast-thresholding algorithm which was proven to be simple and efficient for solving the proposed reconstruction model. Results on both the brain tumor DCE and liver DCE show that, at relatively high acceleration factor of fast sampling, lowest reconstruction error and highest image structural similarity are obtained by the proposed method. Besides, the proposed method achieves faster reconstruction for liver datasets and better physiological measures are also obtained on tumor images.

A dual-task dual-domain model for blind MRI reconstruction

MRI reconstruction is the key technology to accelerate MR acquisition. Recent cascade models have gained satisfactory results, however, they deeply rely on the known sample mask, which we call it mask prior. To restore the MR image without mask prior, we designed an auxiliary network to estimate the mask from sampled k-space data. Experimentally, the sample mask can be completely estimated by the proposed network and be used to input to the cascade models. Moreover, we rethink the MRI reconstruction model as a k-space inpainting task. A dual-domain cascade network, which utilized partial convolutional layers to inpaint features in k-space, was presented to restore the MR image. Without the mask prior, our blind reconstruction model demonstrates the best reconstruction ability in both 4x acceleration and 8x acceleration.

SR-Net: A sequence offset fusion net and refine net for undersampled multislice MR image reconstruction

BACKGROUND AND OBJECTIVE

The study of deep learning-based fast magnetic resonance imaging (MRI) reconstruction methods has become popular in recent years. However, there is still a challenge when MRI results undersample large acceleration factors. The objective of this study was to improve the reconstruction quality of undersampled MR images by exploring data redundancy among slices.

METHODS

There are two aspects of redundancy in multislice MR images including correlations inside a single slice and correlations among slices. Thus, we built two subnets for the two kinds of redundancy. For correlations among slices, we built a bidirectional recurrent convolutional neural network, named Sequence Offset Fusion Net (S-Net). In S-Net, we used a deformable convolution module to construct a neighbor slice feature extractor. For the correlation inside a single slice, we built a Refine Net (R-Net), which has 5 layers of 2D convolutions. In addition, we used a data consistency (DC) operation to maintain data fidelity in k-space. Finally, we treated the reconstruction task as a dealiasing problem in the image domain, and S-Net and R-Net are applied alternately and iteratively to generate the final reconstructions.

RESULTS

The proposed algorithm was evaluated using two online public MRI datasets. Compared with several state-of-the-art methods, the proposed method achieved better reconstruction results in terms of dealiasing and restoring tissue structure. Moreover, with over 14 slices per second reconstruction speed on 256x256 pixel images, the proposed method can meet the need for real-time processing.

CONCLUSION

With spatial correlation among slices as additional prior information, the proposed method dramatically improves the reconstruction quality of undersampled MR images.

Differential Deep Convolutional Neural Network Model for Brain Tumor Classification

The classification of brain tumors is a difficult task in the field of medical image analysis. Improving algorithms and machine learning technology helps radiologists to easily diagnose the tumor without surgical intervention. In recent years, deep learning techniques have made excellent progress in the field of medical image processing and analysis. However, there are many difficulties in classifying brain tumors using magnetic resonance imaging; first, the difficulty of brain structure and the intertwining of tissues in it; and secondly, the difficulty of classifying brain tumors due to the high density nature of the brain. We propose a differential deep convolutional neural network model (differential deep-CNN) to classify different types of brain tumor, including abnormal and normal magnetic resonance (MR) images. Using differential operators in the differential deep-CNN architecture, we derived the additional differential feature maps in the original CNN feature maps. The derivation process led to an improvement in the performance of the proposed approach in accordance with the results of the evaluation parameters used. The advantage of the differential deep-CNN model is an analysis of a pixel directional pattern of images using contrast calculations and its high ability to classify a large database of images with high accuracy and without technical problems. Therefore, the proposed approach gives an excellent overall performance. To test and train the performance of this model, we used a dataset consisting of 25,000 brain magnetic resonance imaging (MRI) images, which includes abnormal and normal images. The experimental results showed that the proposed model achieved an accuracy of 99.25%. This study demonstrates that the proposed differential deep-CNN model can be used to facilitate the automatic classification of brain tumors.

A guaranteed convergence analysis for the projected fast iterative soft-thresholding algorithm in parallel MRI

Sparse sampling and parallel imaging techniques are two effective approaches to alleviate the lengthy magnetic resonance imaging (MRI) data acquisition problem. Promising data recoveries can be obtained from a few MRI samples with the help of sparse reconstruction models. To solve the optimization models, proper algorithms are indispensable. The pFISTA, a simple and efficient algorithm, has been successfully extended to parallel imaging. However, its convergence criterion is still an open question. Besides, the existing convergence criterion of single-coil pFISTA cannot be applied to the parallel imaging pFISTA, which, therefore, imposes confusions and difficulties on users about determining the only parameter - step size. In this work, we provide the guaranteed convergence analysis of the parallel imaging version pFISTA to solve the two well-known parallel imaging reconstruction models, SENSE and SPIRiT. Along with the convergence analysis, we provide recommended step size values for SENSE and SPIRiT reconstructions to obtain fast and promising reconstructions. Experiments on in vivo brain images demonstrate the validity of the convergence criterion.

Reference-Driven Undersampled MR Image Reconstruction Using Wavelet Sparsity-Constrained Deep Image Prior

Deep learning has shown potential in significantly improving performance for undersampled magnetic resonance (MR) image reconstruction. However, one challenge for the application of deep learning to clinical scenarios is the requirement of large, high-quality patient-based datasets for network training. In this paper, we propose a novel deep learning-based method for undersampled MR image reconstruction that does not require pre-training procedure and pre-training datasets. The proposed reference-driven method using wavelet sparsity-constrained deep image prior (RWS-DIP) is based on the DIP framework and thereby reduces the dependence on datasets. Moreover, RWS-DIP explores and introduces structure and sparsity priors into network learning to improve the efficiency of learning. By employing a high-resolution reference image as the network input, RWS-DIP incorporates structural information into network. RWS-DIP also uses the wavelet sparsity to further enrich the implicit regularization of traditional DIP by formulating the training of network parameters as a constrained optimization problem, which is solved using the alternating direction method of multipliers (ADMM) algorithm. Experiments on in vivo MR scans have demonstrated that the RWS-DIP method can reconstruct MR images more accurately and preserve features and textures from undersampled k-space measurements.

Stability of conventional and machine learning-based tumor auto-segmentation techniques using undersampled dynamic radial bSSFP acquisitions on a 0.35 T hybrid MR-linac system

PURPOSE

Hybrid MRI-linear accelerator systems (MR-linacs) allow for the incorporation of MR images with high soft-tissue contrast into the radiation therapy procedure prior to, during, or post irradiation. This allows not only for the optimization of the treatment planning, but also for real-time monitoring of the tumor position using cine MRI, from which intrafractional motion can be compensated. Fast imaging and accurate tumor tracking are crucial for effective compensation. This study investigates the application of cine MRI with a radial acquisition scheme on a low-field MR-linac to accelerate the acquisition rate and evaluates the effect on tracking accuracy.

METHODS

An MR sequence using tiny golden-angle radial k-space sampling was developed and applied to cine imaging on patients with liver tumors on a 0.35 T MR-linac. Tumor tracking was assessed for accuracy and stability from the cine images with increasing k-space undersampling factors. Tracking was achieved using two different auto-segmentation algorithms: a deformable image registration B-spline similar to that implemented on the MR-linac and a convolutional neural network approach known as U-Net.

RESULTS

Radial imaging allows for increased temporal resolution with reliable tumor tracking, although tracking robustness decreases as temporal resolution increases. Additional acquisition-based artifacts can be avoided by reducing the angle increment using tiny golden-angles. The U-net algorithm was found to have superior auto-segmentation metrics compared to B-spline. U-net was able to track two well-defined tumors, imaged with just 30 spokes per image (10.6 frames per second), with an average Dice coefficient ≥ 83%, Hausdorff distance ≤ 1.4 pixel, and mean contour distance ≤ 0.5 pixel.

CONCLUSIONS

Radial acquisitions are commonplace in dynamic imaging; however, in MR-guided radiotherapy, robust tumor tracking is also required. This study demonstrates the in vivo feasibility of tumor tracking from radially acquired images on a low-field MR-linac. Radial imaging allows for decreased image acquisition times while maintaining robust tracking. The U-net algorithm can track a tumor with higher accuracy in images with undersampling artifacts than a conventional deformable B-spline algorithm and is a promising tool for tracking in MR-guided radiation therapy.

High quality and fast compressed sensing MRI reconstruction via edge-enhanced dual discriminator generative adversarial network

Generative adversarial networks (GAN) are widely used for fast compressed sensing magnetic resonance imaging (CSMRI) reconstruction. However, most existing methods are difficult to make an effective trade-off between abstract global high-level features and edge features. It easily causes problems, such as significant remaining aliasing artifacts and clearly over-smoothed reconstruction details. To tackle these issues, we propose a novel edge-enhanced dual discriminator generative adversarial network architecture called EDDGAN for CSMRI reconstruction with high quality. In this model, we extract effective edge features by fusing edge information from different depths. Then, leveraging the relationship between abstract global high-level features and edge features, a three-player game is introduced to control the hallucination of details and stabilize the training process. The resulting EDDGAN can offer more focus on edge restoration and de-aliasing. Extensive experimental results demonstrate that our method consistently outperforms state-of-the-art methods and obtains reconstructed images with rich edge details. In addition, our method also shows remarkable generalization, and its time consumption for each 256 × 256 image reconstruction is approximately 8.39 ms.

On the regularization of feature fusion and mapping for fast MR multi-contrast imaging via iterative networks

Multi-contrast (MC) Magnetic Resonance Imaging (MRI) of the same patient usually requires long scanning times, despite the images sharing redundant information. In this work, we propose a new iterative network that utilizes the sharable information among MC images for MRI acceleration. The proposed network has reinforced data fidelity control and anatomy guidance through an iterative optimization procedure of Gradient Descent, leading to reduced uncertainties and improved reconstruction results. Through a convolutional network, the new method incorporates a learnable regularization unit that is capable of extracting, fusing, and mapping shareable information among different contrasts. Specifically, a dilated inception block is proposed to promote multi-scale feature extractions and increase the receptive field diversity for contextual information incorporation. Lastly, an optimal MC information feeding protocol is built through the design of a complementary feature extractor block. Comprehensive experiments demonstrated the superiority of the proposed network, both qualitatively and quantitatively.

A Deep Framework Assembling Principled Modules for CS-MRI: Unrolling Perspective, Convergence Behaviors, and Practical Modeling

Compressed Sensing Magnetic Resonance Imaging (CS-MRI) significantly accelerates MR acquisition at a sampling rate much lower than the Nyquist criterion. A major challenge for CS-MRI lies in solving the severely ill-posed inverse problem to reconstruct aliasing-free MR images from the sparse k -space data. Conventional methods typically optimize an energy function, producing restoration of high quality, but their iterative numerical solvers unavoidably bring extremely large time consumption. Recent deep techniques provide fast restoration by either learning direct prediction to final reconstruction or plugging learned modules into the energy optimizer. Nevertheless, these data-driven predictors cannot guarantee the reconstruction following principled constraints underlying the domain knowledge so that the reliability of their reconstruction process is questionable. In this paper, we propose a deep framework assembling principled modules for CS-MRI that fuses learning strategy with the iterative solver of a conventional reconstruction energy. This framework embeds an optimal condition checking mechanism, fostering efficient and reliable reconstruction. We also apply the framework to three practical tasks, i.e., complex-valued data reconstruction, parallel imaging and reconstruction with Rician noise. Extensive experiments on both benchmark and manufacturer-testing images demonstrate that the proposed method reliably converges to the optimal solution more efficiently and accurately than the state-of-the-art in various scenarios.

Deep Convolutional Encoder-Decoder algorithm for MRI brain reconstruction

Compressed Sensing Magnetic Resonance Imaging (CS-MRI) could be considered a challenged task since it could be designed as an efficient technique for fast MRI acquisition which could be highly beneficial for several clinical routines. In fact, it could grant better scan quality by reducing motion artifacts amount as well as the contrast washout effect. It offers also the possibility to reduce the exploration cost and the patient's anxiety. Recently, Deep Learning Neuronal Network (DL) has been suggested in order to reconstruct MRI scans with conserving the structural details and improving parallel imaging-based fast MRI. In this paper, we propose Deep Convolutional Encoder-Decoder architecture for CS-MRI reconstruction. Such architecture bridges the gap between the non-learning techniques, using data from only one image, and approaches using large training data. The proposed approach is based on autoencoder architecture divided into two parts: an encoder and a decoder. The encoder as well as the decoder has essentially three convolutional blocks. The proposed architecture has been evaluated through two databases: Hammersmith dataset (for the normal scans) and MICCAI 2018 (for pathological MRI). Moreover, we extend our model to cope with noisy pathological MRI scans. The normalized mean square error (NMSE), the peak-to-noise ratio (PSNR), and the structural similarity index (SSIM) have been adopted as evaluation metrics in order to evaluate the proposed architecture performance and to make a comparative study with the state-of-the-art reconstruction algorithms. The higher PSNR and SSIM values as well as the lowest NMSE values could attest that the proposed architecture offers better reconstruction and preserves textural image details. Furthermore, the running time is about 0.8 s, which is suitable for real-time processing. Such results could encourage the neurologist to adopt it in their clinical routines. Graphical abstract.

Dense Recurrent Neural Networks for Accelerated MRI: History-Cognizant Unrolling of Optimization Algorithms

Inverse problems for accelerated MRI typically incorporate domain-specific knowledge about the forward encoding operator in a regularized reconstruction framework. Recently physics-driven deep learning (DL) methods have been proposed to use neural networks for data-driven regularization. These methods unroll iterative optimization algorithms to solve the inverse problem objective function, by alternating between domain-specific data consistency and data-driven regularization via neural networks. The whole unrolled network is then trained end-to-end to learn the parameters of the network. Due to simplicity of data consistency updates with gradient descent steps, proximal gradient descent (PGD) is a common approach to unroll physics-driven DL reconstruction methods. However, PGD methods have slow convergence rates, necessitating a higher number of unrolled iterations, leading to memory issues in training and slower reconstruction times in testing. Inspired by efficient variants of PGD methods that use a history of the previous iterates, we propose a history-cognizant unrolling of the optimization algorithm with dense connections across iterations for improved performance. In our approach, the gradient descent steps are calculated at a trainable combination of the outputs of all the previous regularization units. We also apply this idea to unrolling variable splitting methods with quadratic relaxation. Our results in reconstruction of the fastMRI knee dataset show that the proposed history-cognizant approach reduces residual aliasing artifacts compared to its conventional unrolled counterpart without requiring extra computational power or increasing reconstruction time.

pFISTA-SENSE-ResNet for parallel MRI reconstruction

Magnetic resonance imaging has been widely applied in clinical diagnosis. However, it is limited by its long data acquisition time. Although the imaging can be accelerated by sparse sampling and parallel imaging, achieving promising reconstructed images with a fast computation speed remains a challenge. Recently, deep learning methods have attracted a lot of attention for encouraging reconstruction results, but they are lack of proper interpretability for neural networks. In this work, in order to enable high-quality image reconstruction for the parallel magnetic resonance imaging, we design the network structure from the perspective of sparse iterative reconstruction and enhance it with the residual structure. Experimental results on a public knee dataset indicate that, as compared with the state-of-the-art deep learning-based and optimization-based methods, the proposed network achieves lower error in reconstruction and is more robust under different samplings.

High-dimensional embedding network derived prior for compressive sensing MRI reconstruction

Although recent deep learning methodology has shown promising performance in fast imaging, the network needs to be retrained for specific sampling patterns and ratios. Therefore, how to explore the network as a general prior and leverage it into the observation constraint flexibly is urgent. In this work, we present a multi-channel enhanced Deep Mean-Shift Prior (MEDMSP) to address the highly under-sampled magnetic resonance imaging reconstruction problem. By extending the naive DMSP via integration of multi-model aggregation and multi-channel network learning, a high-dimensional embedding network derived prior is formed. Then, we apply the learned prior to single-channel image reconstruction via variable augmentation technique. The resulting model is tackled by proximal gradient descent and alternative iteration. Experimental results under various sampling trajectories and acceleration factors consistently demonstrated the superiority of the proposed prior.

Compressed MRI reconstruction exploiting a rotation-invariant total variation discretization

Inspired by the first-order method of Malitsky and Pock, we propose a new variational framework for compressed MR image reconstruction which introduces the application of a rotation-invariant discretization of total variation functional into MR imaging while exploiting BM3D frame as a sparsifying transform. In the first step, we provide theoretical and numerical analysis establishing the exceptional rotation-invariance property of this total variation functional and observe its superiority over other well-known variational regularization terms in both upright and rotated imaging setups. Thereupon, the proposed MRI reconstruction model is presented as a constrained optimization problem, however, we do not use conventional ADMM-type algorithms designed for constrained problems to obtain a solution, but rather we tailor the linesearch-equipped method of Malitsky and Pock to our model, which was originally proposed for unconstrained problems. As attested by numerical experiments, this framework significantly outperforms various state-of-the-art algorithms from variational methods to adaptive and learning approaches and in particular, it eliminates the stagnating behavior of a previous work on BM3D-MRI which compromised the solution beyond a certain iteration.

Coupled Dictionary Learning for Multi-Contrast MRI Reconstruction

Magnetic resonance (MR) imaging tasks often involve multiple contrasts, such as T1-weighted, T2-weighted and fluid-attenuated inversion recovery (FLAIR) data. These contrasts capture information associated with the same underlying anatomy and thus exhibit similarities in either structure level or gray level. In this paper, we propose a coupled dictionary learning based multi-contrast MRI reconstruction (CDLMRI) approach to leverage the dependency correlation between different contrasts for guided or joint reconstruction from their under-sampled k -space data. Our approach iterates between three stages: coupled dictionary learning, coupled sparse denoising, and enforcing k -space consistency. The first stage learns a set of dictionaries that not only are adaptive to the contrasts, but also capture correlations among multiple contrasts in a sparse transform domain. By capitalizing on the learned dictionaries, the second stage performs coupled sparse coding to remove the aliasing and noise in the corrupted contrasts. The third stage enforces consistency between the denoised contrasts and the measurements in the k -space domain. Numerical experiments, consisting of retrospective under-sampling of various MRI contrasts with a variety of sampling schemes, demonstrate that CDLMRI is capable of capturing structural dependencies between different contrasts. The learned priors indicate notable advantages in multi-contrast MR imaging and promising applications in quantitative MR imaging such as MR fingerprinting.

ADMM-CSNet: A Deep Learning Approach for Image Compressive Sensing

Compressive sensing (CS) is an effective technique for reconstructing image from a small amount of sampled data. It has been widely applied in medical imaging, remote sensing, image compression, etc. In this paper, we propose two versions of a novel deep learning architecture, dubbed as ADMM-CSNet, by combining the traditional model-based CS method and data-driven deep learning method for image reconstruction from sparsely sampled measurements. We first consider a generalized CS model for image reconstruction with undetermined regularizations in undetermined transform domains, and then two efficient solvers using Alternating Direction Method of Multipliers (ADMM) algorithm for optimizing the model are proposed. We further unroll and generalize the ADMM algorithm to be two deep architectures, in which all parameters of the CS model and the ADMM algorithm are discriminatively learned by end-to-end training. For both applications of fast CS complex-valued MR imaging and CS imaging of real-valued natural images, the proposed ADMM-CSNet achieved favorable reconstruction accuracy in fast computational speed compared with the traditional and the other deep learning methods.