Efficient directionality-driven dictionary learning for compressive sensing magnetic resonance imaging reconstruction

Compressed sensing is an acquisition strategy that possesses great potential to accelerate magnetic resonance imaging (MRI) within the ambit of existing hardware, by enforcing sparsity on MR image slices. Compared to traditional reconstruction methods, dictionary learning-based reconstruction algorithms, which locally sparsify image patches, have been found to boost the reconstruction quality. However, due to the learning complexity, they have to be independently employed on successive MR undersampled slices one at a time. This causes them to forfeit prior knowledge of the anatomical structure of the region of interest. An MR reconstruction algorithm is proposed that employs the double sparsity model coupled with online sparse dictionary learning to learn directional features of the region under observation from existing prior knowledge. This is found to enhance the capability of sparsely representing directional features in an MR image and results in better reconstructions. The proposed framework is shown to have superior performance compared to state-of-art MRI reconstruction algorithms under noiseless and noisy conditions for various undersampling percentages and distinct scanning strategies.

Reference-Driven Compressed Sensing MR Image Reconstruction Using Deep Convolutional Neural Networks without Pre-Training

Deep learning has proven itself to be able to reduce the scanning time of Magnetic Resonance Imaging (MRI) and to improve the image reconstruction quality since it was introduced into Compressed Sensing MRI (CS-MRI). However, the requirement of using large, high-quality, and patient-based datasets for network training procedures is always a challenge in clinical applications. In this paper, we propose a novel deep learning based compressed sensing MR image reconstruction method that does not require any pre-training procedure or training dataset, thereby largely reducing clinician dependence on patient-based datasets. The proposed method is based on the Deep Image Prior (DIP) framework and uses a high-resolution reference MR image as the input of the convolutional neural network in order to induce the structural prior in the learning procedure. This reference-driven strategy improves the efficiency and effect of network learning. We then add the k-space data correction step to enforce the consistency of the k-space data with the measurements, which further improve the image reconstruction accuracy. Experiments on in vivo MR datasets showed that the proposed method can achieve more accurate reconstruction results from undersampled k-space data.

Image Reconstruction: From Sparsity to Data-adaptive Methods and Machine Learning

The field of medical image reconstruction has seen roughly four types of methods. The first type tended to be analytical methods, such as filtered back-projection (FBP) for X-ray computed tomography (CT) and the inverse Fourier transform for magnetic resonance imaging (MRI), based on simple mathematical models for the imaging systems. These methods are typically fast, but have suboptimal properties such as poor resolution-noise trade-off for CT. A second type is iterative reconstruction methods based on more complete models for the imaging system physics and, where appropriate, models for the sensor statistics. These iterative methods improved image quality by reducing noise and artifacts. The FDA-approved methods among these have been based on relatively simple regularization models. A third type of methods has been designed to accommodate modified data acquisition methods, such as reduced sampling in MRI and CT to reduce scan time or radiation dose. These methods typically involve mathematical image models involving assumptions such as sparsity or low-rank. A fourth type of methods replaces mathematically designed models of signals and systems with data-driven or adaptive models inspired by the field of machine learning. This paper focuses on the two most recent trends in medical image reconstruction: methods based on sparsity or low-rank models, and data-driven methods based on machine learning techniques.

CS-MRI reconstruction based on analysis dictionary learning and manifold structure regularization

Compressed sensing (CS) significantly accelerates magnetic resonance imaging (MRI) by allowing the exact reconstruction of image from highly undersampling k-space data. In this process, the high sparsity obtained by the learned dictionary and exploitation of correlation among patches are essential to the reconstructed image quality. In this paper, by a use of these two aspects, we propose a novel CS-MRI model based on analysis dictionary learning and manifold structure regularization (ADMS). Furthermore, a proper tight frame constraint is used to obtain an effective overcomplete analysis dictionary with a high sparsifying capacity. The constructed manifold structure regularization nonuniformly enforces the correlation of each group formed by similar patches, which is more consistent with the diverse nonlocal similarity in realistic images. The proposed model is efficiently solved by the alternating direction method of multipliers (ADMM), in which the fast algorithm for each sub-problem is separately developed. The experimental results demonstrate that main components in the proposed method contribute to the final reconstruction performance and the effectiveness of the proposed model.

A Deep Information Sharing Network for Multi-Contrast Compressed Sensing MRI Reconstruction

Compressed sensing (CS) theory can accelerate multi-contrast magnetic resonance imaging (MRI) by sampling fewer measurements within each contrast. However, conventional optimization-based reconstruction models suffer several limitations, including a strict assumption of shared sparse support, time-consuming optimization, and "shallow" models with difficulties in encoding the patterns contained in massive MRI data. In this paper, we propose the first deep learning model for multi-contrast CS-MRI reconstruction. We achieve information sharing through feature sharing units, which significantly reduces the number of model parameters. The feature sharing unit combines with a data fidelity unit to comprise an inference block, which are then cascaded with dense connections, allowing for efficient information transmission across different depths of the network. Experiments on various multi-contrast MRI datasets show that the proposed model outperforms both state-of-the-art single-contrast and multi-contrast MRI methods in accuracy and efficiency. We demonstrate that improved reconstruction quality can bring benefits to subsequent medical image analysis. Furthermore, the robustness of the proposed model to misregistration shows its potential in real MRI applications.

A cosparse analysis model with combined redundant systems for MRI reconstruction

PURPOSE

Magnetic resonance imaging (MRI) is widely used due to its noninvasive and nonionizing properties. However, MRI requires a long scanning time. In this paper, our goal is to reconstruct a high-quality MR image from its sampled k-space data to accelerate the data acquisition in MRI.

METHODS

We propose a cosparse analysis model with combined redundant systems to fully exploit the sparsity of MR images. Two fixed redundant systems are used to characterize different structures, namely, the wavelet tight frame and Gabor frame. An alternating iteration scheme is used for reconstruction with simple implementation and good performance.

RESULTS

The proposed method is tested on two MR images under three sampling patterns with sampling ratios ranging from 10% to 60%. The results show that the proposed method outperforms other state-of-the-art MRI reconstruction methods in terms of both subjective visual quality and objective quantitative measurement. For instance, for brain images under random sampling with a ratio of 10%, compared to the other three methods, the proposed method improves the peak signal-to-noise ratio (PSNR) by more than 9 dB.

CONCLUSIONS

To better characterize different sparsities of different structures of MRI, a cosparse analysis model combining the wavelet tight frame and Gabor frame is proposed. A partial ℓ 2 norm regularization is leveraged to obtain the optimal solution in a lower dimension. Compared to other state-of-the-art MRI reconstruction methods, the proposed method improves the reconstruction quality of MRI, especially highly undersampled MRI.

MR Image Reconstruction Using Deep Density Priors

Algorithms for magnetic resonance (MR) image reconstruction from undersampled measurements exploit prior information to compensate for missing k-space data. Deep learning (DL) provides a powerful framework for extracting such information from existing image datasets, through learning, and then using it for reconstruction. Leveraging this, recent methods employed DL to learn mappings from undersampled to fully sampled images using paired datasets, including undersampled and corresponding fully sampled images, integrating prior knowledge implicitly. In this letter, we propose an alternative approach that learns the probability distribution of fully sampled MR images using unsupervised DL, specifically variational autoencoders (VAE), and use this as an explicit prior term in reconstruction, completely decoupling the encoding operation from the prior. The resulting reconstruction algorithm enjoys a powerful image prior to compensate for missing k-space data without requiring paired datasets for training nor being prone to associated sensitivities, such as deviations in undersampling patterns used in training and test time or coil settings. We evaluated the proposed method with T1 weighted images from a publicly available dataset, multi-coil complex images acquired from healthy volunteers ( N=8 ), and images with white matter lesions. The proposed algorithm, using the VAE prior, produced visually high quality reconstructions and achieved low RMSE values, outperforming most of the alternative methods on the same dataset. On multi-coil complex data, the algorithm yielded accurate magnitude and phase reconstruction results. In the experiments on images with white matter lesions, the method faithfully reconstructed the lesions.

Orthogonal tensor dictionary learning for accelerated dynamic MRI

A direct application of the compressed sensing (CS) theory to dynamic magnetic resonance imaging (MRI) reconstruction needs vectorization or matricization of the dynamic MRI data, which is composed of a stack of 2D images and can be naturally regarded as a tensor. This 1D/2D model may destroy the inherent spatial structure property of the data. An alternative way to exploit the multidimensional structure in dynamic MRI is to employ tensor decomposition for dictionary learning, that is, learning multiple dictionaries along each dimension (mode) and sparsely representing the multidimensional data with respect to the Kronecker product of these dictionaries. In this work, we introduce a novel tensor dictionary learning method under an orthonormal constraint on the elementary matrix of the tensor dictionary for dynamic MRI reconstruction. The proposed algorithm alternates sparse coding, tensor dictionary learning, and updating reconstruction, and each corresponding subproblem is efficiently solved by a closed-form solution. Numerical experiments on phantom and synthetic data show significant improvements in reconstruction accuracy and computational efficiency obtained by the proposed scheme over the existing method that uses the 1D/2D model with overcomplete dictionary learning. Graphical abstract Fig. 1 Comparison between (a) the traditional method and (b) the proposed method based on dictionary learning for dynamic MRI reconstruction.

Cartesian MR fingerprinting in the eye at 7T using compressed sensing and matrix completion-based reconstructions

PURPOSE

To explore the feasibility of MR Fingerprinting (MRF) to rapidly quantify relaxation times in the human eye at 7T, and to provide a data acquisition and processing framework for future tissue characterization in eye tumor patients.

METHODS

In this single-element receive coil MRF approach with Cartesian sampling, undersampling is used to shorten scan time and, therefore, to reduce the degree of motion artifacts. For reconstruction, approaches based on compressed sensing (CS) and matrix completion (MC) were used, while their effects on the quality of the MRF parameter maps were studied in simulations and experiments. Average relaxation times in the eye were measured in 6 healthy volunteers. One uveal melanoma patient was included to show the feasibility of MRF in a clinical context.

RESULTS

Simulation results showed that an MC-based reconstruction enables large undersampling factors and also results in more accurate parameter maps compared with using CS. Experiments in 6 healthy volunteers used a reduction in scan time from 7:02 to 1:16 min, producing images without visible loss of detail in the parameter maps when using the MC-based reconstruction. Relaxation times from 6 healthy volunteers are in agreement with values obtained from fully sampled scans and values in literature, and parameter maps in a uveal melanoma patient show clear difference in relaxation times between tumor and healthy tissue.

CONCLUSION

Cartesian-based MRF is feasible in the eye at 7T. High undersampling factors can be achieved by means of MC, significantly shortening scan time and increasing patient comfort, while also mitigating the risk of motion artifacts.

Robustly reconstructing magnetic resonance images via structure decomposition

In magnetic resonance (MR) imaging, for highly under-sampled k-space data, it is typically difficult to reconstruct images and preserve their original texture simultaneously. The high-degree total variation (HDTV) regularization handles staircase effects but still blurs textures. On the other hand, the non-local TV (NLTV) regularization can preserve textures, but will introduce additional artifacts for highly-noised images. In this paper, we propose a reconstruction model derived from HDTV and NLTV for robust MRI reconstruction. First, an MR image is decomposed into a smooth component and a texture component. Second, for the smooth component with sharp edges, isotropic second-order TV is used to reduce staircase effects. For the texture component with piecewise constant background, NLTV and contourlet-based sparsity regularizations are employed to recover textures. The piecewise constant background in the texture component contributes to accurately detect non-local similar image patches and avoid artifacts introduced by NLTV. Finally, the proposed reconstruction model is solved through an alternating minimization scheme. The experimental results demonstrate that the proposed reconstruction model can effectively achieve satisfied quality of reconstruction for highly under-sampled k-space data.

VIDOSAT: High-Dimensional Sparsifying Transform Learning for Online Video Denoising

Techniques exploiting the sparsity of images in a transform domain are effective for various applications in image and video processing. In particular, transform learning methods involve cheap computations and have been demonstrated to perform well in applications, such as image denoising and medical image reconstruction. Recently, we proposed methods for online learning of sparsifying transforms from streaming signals, which enjoy good convergence guarantees and involve lower computational costs than online synthesis dictionary learning. In this paper, we apply online transform learning to video denoising. We present a novel framework for online video denoising based on high-dimensional sparsifying transform learning for spatio-temporal patches. The patches are constructed either from corresponding 2D patches in successive frames or using an online block matching technique. The proposed online video denoising requires little memory and offers efficient processing. Numerical experiments evaluate the performance of the proposed video denoising algorithms on multiple video data sets. The proposed methods outperform several related and recent techniques, including denoising with 3D DCT, prior schemes based on dictionary learning, non-local means, background separation, and deep learning, as well as the popular VBM3D and VBM4D.

Salt and Pepper Noise Removal with Multi-Class Dictionary Learning and L0 Norm Regularizations

Images may be corrupted by salt and pepper impulse noise during image acquisitions or transmissions. Although promising denoising performances have been recently obtained with sparse representations, how to restore high-quality images remains challenging and open. In this work, image sparsity is enhanced with a fast multiclass dictionary learning, and then both the sparsity regularization and robust data fidelity are formulated as minimizations of L0-L0 norms for salt and pepper impulse noise removal. Additionally, a numerical algorithm of modified alternating direction minimization is derived to solve the proposed denoising model. Experimental results demonstrate that the proposed method outperforms the compared state-of-the-art ones on preserving image details and achieving higher objective evaluation criteria.

DAGAN: Deep De-Aliasing Generative Adversarial Networks for Fast Compressed Sensing MRI Reconstruction

Compressed sensing magnetic resonance imaging (CS-MRI) enables fast acquisition, which is highly desirable for numerous clinical applications. This can not only reduce the scanning cost and ease patient burden, but also potentially reduce motion artefacts and the effect of contrast washout, thus yielding better image quality. Different from parallel imaging-based fast MRI, which utilizes multiple coils to simultaneously receive MR signals, CS-MRI breaks the Nyquist-Shannon sampling barrier to reconstruct MRI images with much less required raw data. This paper provides a deep learning-based strategy for reconstruction of CS-MRI, and bridges a substantial gap between conventional non-learning methods working only on data from a single image, and prior knowledge from large training data sets. In particular, a novel conditional Generative Adversarial Networks-based model (DAGAN)-based model is proposed to reconstruct CS-MRI. In our DAGAN architecture, we have designed a refinement learning method to stabilize our U-Net based generator, which provides an end-to-end network to reduce aliasing artefacts. To better preserve texture and edges in the reconstruction, we have coupled the adversarial loss with an innovative content loss. In addition, we incorporate frequency-domain information to enforce similarity in both the image and frequency domains. We have performed comprehensive comparison studies with both conventional CS-MRI reconstruction methods and newly investigated deep learning approaches. Compared with these methods, our DAGAN method provides superior reconstruction with preserved perceptual image details. Furthermore, each image is reconstructed in about 5 ms, which is suitable for real-time processing.

Joint sparse reconstruction of multi-contrast MRI images with graph based redundant wavelet transform

Background

Multi-contrast images in magnetic resonance imaging (MRI) provide abundant contrast information reflecting the characteristics of the internal tissues of human bodies, and thus have been widely utilized in clinical diagnosis. However, long acquisition time limits the application of multi-contrast MRI. One efficient way to accelerate data acquisition is to under-sample the k-space data and then reconstruct images with sparsity constraint. However, images are compromised at high acceleration factor if images are reconstructed individually. We aim to improve the images with a jointly sparse reconstruction and Graph-based redundant wavelet transform (GBRWT).

Methods

First, a sparsifying transform, GBRWT, is trained to reflect the similarity of tissue structures in multi-contrast images. Second, joint multi-contrast image reconstruction is formulated as a ℓ_{2, 1} norm optimization problem under GBRWT representations. Third, the optimization problem is numerically solved using a derived alternating direction method.

Results

Experimental results in synthetic and in vivo MRI data demonstrate that the proposed joint reconstruction method can achieve lower reconstruction errors and better preserve image structures than the compared joint reconstruction methods. Besides, the proposed method outperforms single image reconstruction with joint sparsity constraint of multi-contrast images.

Conclusions

The proposed method explores the joint sparsity of multi-contrast MRI images under graph-based redundant wavelet transform and realizes joint sparse reconstruction of multi-contrast images. Experiment demonstrate that the proposed method outperforms the compared joint reconstruction methods as well as individual reconstructions. With this high quality image reconstruction method, it is possible to achieve the high acceleration factors by exploring the complementary information provided by multi-contrast MRI.

Efficient Sum of Outer Products Dictionary Learning (SOUP-DIL) and Its Application to Inverse Problems

The sparsity of signals in a transform domain or dictionary has been exploited in applications such as compression, denoising and inverse problems. More recently, data-driven adaptation of synthesis dictionaries has shown promise compared to analytical dictionary models. However, dictionary learning problems are typically non-convex and NP-hard, and the usual alternating minimization approaches for these problems are often computationally expensive, with the computations dominated by the NP-hard synthesis sparse coding step. This paper exploits the ideas that drive algorithms such as K-SVD, and investigates in detail efficient methods for aggregate sparsity penalized dictionary learning by first approximating the data with a sum of sparse rank-one matrices (outer products) and then using a block coordinate descent approach to estimate the unknowns. The resulting block coordinate descent algorithms involve efficient closed-form solutions. Furthermore, we consider the problem of dictionary-blind image reconstruction, and propose novel and efficient algorithms for adaptive image reconstruction using block coordinate descent and sum of outer products methodologies. We provide a convergence study of the algorithms for dictionary learning and dictionary-blind image reconstruction. Our numerical experiments show the promising performance and speedups provided by the proposed methods over previous schemes in sparse data representation and compressed sensing-based image reconstruction.

A low rank Hankel matrix reconstruction method for ultrafast magnetic resonance spectroscopy

Magnetic resonance spectroscopy has many important applications in bio-engineering while acquiring high dimensional spectroscopy is usually time consuming. Non-uniformly sampling can speed up the data acquisition but the missing data points have to be restored with proper signal models. In this work, a specific two dimensional (2D) magnetic resonance signal, in which the first dimension lies in frequency domain while the second dimension lies in time domain, is reconstructed with a proposed low rank Hankel-matrix method. This method explores two general properties: 1) the rank of a structured matrix, converted from a 2D exponential signal, is equal to the number of 2D spectral peaks; 2) this rank is small if the spectrum is sparse. Results on real magnetic resonance spectroscopy show that proposed method outperforms the state-of-compressed sensing method on recovering low-intensity spectral peaks.

Accelerated magnetic resonance spectroscopy with Vandermonde factorization

Multi-dimensional magnetic resonance spectroscopy is an important tool for studying molecular structures, interactions and dynamics in bio-engineering. The data acquisition time, however, is relatively long and non-uniform sampling can be applied to reduce this time. To obtain the full spectrum,a reconstruction method with Vandermonde factorization is proposed. This method explores the general signal property in magnetic resonance spectroscopy: Its time domain signal is approximated by a sum of a few exponentials. Results on synthetic and realistic data show that the new approach can achieve faithful spectrum reconstruction and outperforms state-of-the-art low rank Hankel matrix method.

Low Rank Enhanced Matrix Recovery of Hybrid Time and Frequency Data in Fast Magnetic Resonance Spectroscopy

GOAL

The two dimensional magnetic resonance spectroscopy (MRS) possesses many important applications in bioengineering but suffers from long acquisition duration. Non-uniform sampling has been applied to the spatiotemporally encoded ultrafast MRS, but results in missing data in the hybrid time and frequency plane. An approach is proposed to recover this missing signal, of which enables high quality spectrum reconstruction. M ethods: The natural exponential characteristic of MRS is exploited to recover the hybrid time and frequency signal. The reconstruction issue is formulated as a low rank enhanced Hankel matrix completion problem and is solved by a fast numerical algorithm.

RESULTS

Experiments on synthetic and real MRS data show that the proposed method provides faithful spectrum reconstruction, and outperforms the state-of-the-art compressed sensing approach on recovering low-intensity spectral peaks and robustness to different sampling patterns. C onclusion: The exponential signal property serves as an useful tool to model the time-domain MRS signals and even allows missing data recovery. The proposed method has been shown to reconstruct high quality MRS spectra from non-uniformly sampled data in the hybrid time and frequency plane.

SIGNIFICANCE

Low-intensity signal reconstruction is generally challenging in biological MRS and we provide a solution to this problem. The proposed method may be extended to recover signals that generally can be modeled as a sum of exponential functions in biomedical engineering applications, e.g., signal enhancement, feature extraction, and fast sampling.

Multi-contrast brain magnetic resonance image super-resolution using the local weight similarity

Background

Low-resolution images may be acquired in magnetic resonance imaging (MRI) due to limited data acquisition time or other physical constraints, and their resolutions can be improved with super-resolution methods. Since MRI can offer images of an object with different contrasts, e.g., T1-weighted or T2-weighted, the shared information between inter-contrast images can be used to benefit super-resolution.

Methods

In this study, an MRI image super-resolution approach to enhance in-plane resolution is proposed by exploring the statistical information estimated from another contrast MRI image that shares similar anatomical structures. We assume some edge structures are shown both in T1-weighted and T2-weighted MRI brain images acquired of the same subject, and the proposed approach aims to recover such kind of structures to generate a high-resolution image from its low-resolution counterpart.

Results

The statistical information produces a local weight of image that are found to be nearly invariant to the image contrast and thus this weight can be used to transfer the shared information from one contrast to another. We analyze this property with comprehensive mathematics as well as numerical experiments.

Conclusion

Experimental results demonstrate that the image quality of low-resolution images can be remarkably improved with the proposed method if this weight is borrowed from a high resolution image with another contrast.

Graphical Abstract

Multi-contrast MRI Image Super-resolution with Contrast-invariant Regression Weights

Electronic supplementary material

The online version of this article (doi:10.1186/s12880-016-0176-2) contains supplementary material, which is available to authorized users.

Highly undersampled MR image reconstruction using an improved dual-dictionary learning method with self-adaptive dictionaries

Dual-dictionary learning (Dual-DL) method utilizes both a low-resolution dictionary and a high-resolution dictionary, which are co-trained for sparse coding and image updating, respectively. It can effectively exploit a priori knowledge regarding the typical structures, specific features, and local details of training sets images. The prior knowledge helps to improve the reconstruction quality greatly. This method has been successfully applied in magnetic resonance (MR) image reconstruction. However, it relies heavily on the training sets, and dictionaries are fixed and nonadaptive. In this research, we improve Dual-DL by using self-adaptive dictionaries. The low- and high-resolution dictionaries are updated correspondingly along with the image updating stage to ensure their self-adaptivity. The updated dictionaries incorporate both the prior information of the training sets and the test image directly. Both dictionaries feature improved adaptability. Experimental results demonstrate that the proposed method can efficiently and significantly improve the quality and robustness of MR image reconstruction.