KerNL: Kernel-Based Nonlinear Approach to Parallel MRI Reconstruction

Dual-domain faster Fourier convolution based network for MR image reconstruction

Deep learning methods for fast MRI have shown promise in reconstructing high-quality images from undersampled multi-coil k-space data, leading to reduced scan duration. However, existing methods encounter challenges related to limited receptive fields in dual-domain (k-space and image domains) reconstruction networks, rigid data consistency operations, and suboptimal refinement structures, which collectively restrict overall reconstruction performance. This study introduces a comprehensive framework that addresses these challenges and enhances MR image reconstruction quality. Firstly, we propose Faster Inverse Fourier Convolution (FasterIFC), a frequency domain convolutional operator that significantly expands the receptive field of k-space domain reconstruction networks. Expanding the information extraction range to the entire frequency spectrum according to the spectral convolution theorem in Fourier theory enables the network to easily utilize richer redundant long-range information from adjacent, symmetrical, and diagonal locations of multi-coil k-space data. Secondly, we introduce a novel softer Data Consistency (softerDC) layer, which achieves an enhanced balance between data consistency and smoothness. This layer facilitates the implementation of diverse data consistency strategies across distinct frequency positions, addressing the inflexibility observed in current methods. Finally, we present the Dual-Domain Faster Fourier Convolution Based Network (D2F2), which features a centrosymmetric dual-domain parallel structure based on FasterIFC. This architecture optimally leverages dual-domain data characteristics while substantially expanding the receptive field in both domains. Coupled with the softerDC layer, D2F2 demonstrates superior performance on the NYU fastMRI dataset at multiple acceleration factors, surpassing state-of-the-art methods in both quantitative and qualitative evaluations.

Image Reconstruction for Accelerated MR Scan With Faster Fourier Convolutional Neural Networks

High quality image reconstruction from undersampled k -space data is key to accelerating MR scanning. Current deep learning methods are limited by the small receptive fields in reconstruction networks, which restrict the exploitation of long-range information, and impede the mitigation of full-image artifacts, particularly in 3D reconstruction tasks. Additionally, the substantial computational demands of 3D reconstruction considerably hinder advancements in related fields. To tackle these challenges, we propose the following: 1) A novel convolution operator named Faster Fourier Convolution (FasterFC), aims at providing an adaptable broad receptive field for spatial domain reconstruction networks with fast computational speed. 2) A split-slice strategy that substantially reduces the computational load of 3D reconstruction, enabling high-resolution, multi-coil, 3D MR image reconstruction while fully utilizing inter-layer and intra-layer information. 3) A single-to-group algorithm that efficiently utilizes scan-specific and data-driven priors to enhance k -space interpolation effects. 4) A multi-stage, multi-coil, 3D fast MRI method, called the faster Fourier convolution based single-to-group network (FAS-Net), comprising a single-to-group k -space interpolation algorithm and a FasterFC-based image domain reconstruction module, significantly minimizes the computational demands of 3D reconstruction through split-slice strategy. Experimental evaluations conducted on the NYU fastMRI and Stanford MRI Data datasets reveal that the FasterFC significantly enhances the quality of both 2D and 3D reconstruction results. Moreover, FAS-Net, characterized as a method that can achieve high-resolution (320, 320, 256), multi-coil, (8 coils), 3D fast MRI, exhibits superior reconstruction performance compared to other state-of-the-art 2D and 3D methods.

Recent advances in highly accelerated 3D MRI

Three-dimensional MRI has gained increasing popularity in various clinical applications due to its improved through-plane spatial resolution, which enhances the detection of subtle abnormalities and provides valuable clinical information. However, the long data acquisition time and high computational cost pose significant challenges for 3D MRI. In this comprehensive review article, we aim to summarize the latest advancements in accelerated 3D MR techniques. Covering over 200 remarkable research studies conducted over the past 20 years, we explore the development of MR signal excitation and encoding, advancements in reconstruction algorithms, and potential clinical applications. We hope that this survey serves as a valuable resource, providing insights into the current state of the field and serving as a guide for future research in accelerated 3D MRI.

Virtual Conjugate Coil for Improving KerNL Reconstruction

Ker NL is a general kernel-based framework for auto calibrated reconstruction method, which does not need any explicit formulas of the kernel function for characterizing nonlinear relationships between acquired and unacquired k-space data. It is non-iterative without requiring a large amount of computational costs. Since the limited autocalibration signals (ACS) are acquired to perform KerNL calibration and the calibration suffers from the overfitting problem, more training data can improve the kernel model accuracy. In this work, virtual conjugate coil data are incorporated into the KerNL calibration and estimation process for enhancing reconstruction performance. Experimental results show that the proposed method can further suppress noise and aliasing artifacts with fewer ACS data and higher acceleration factors. Computation efficiency is still retained to keep fast reconstruction with the random projection.

Accelerating MR Parameter Mapping Using Nonlinear Compressive Manifold Learning and Regularized Pre-Imaging

In this study, we presented a novel method to reconstruct the MR parametric maps from highly undersampled k-space data. Specifically, we utilized a nonlinear model to sparsely represent the unknown MR parameter-weighted images in high-dimensional feature space. Each image at a specific time point is assumed to belong to a low-dimensional manifold which is learned from training images created based on the parametric model. The final reconstruction is carried out by venturing the sparse representation of the images in the feature space back to the input space, using the pre-imaging technique. Particularly, among an infinite number of solutions that satisfy the data consistency, the one that is closest to the manifold is selected as the desired solution. The underlying optimization problem is solved using kernel trick, sparse coding, and split Bregman iteration algorithm. In addition, both spatial and temporal regularizations were utilized to further improve the reconstruction quality. The proposed method was validated on both phantom and in vivo human brain T2 mapping data. Results showed the proposed method was superior to the conventional linear model-based reconstruction methods, in terms of artifact removal and quantitative estimate accuracy. The proposed method could be potentially beneficial for quantitative MR applications.

On the shape of convolution kernels in MRI reconstruction: Rectangles versus ellipsoids

PURPOSE

Many MRI reconstruction methods (including GRAPPA, SPIRiT, ESPIRiT, LORAKS, and convolutional neural network [CNN] methods) involve shift-invariant convolution models. Rectangular convolution kernel shapes are often chosen by default, although ellipsoidal kernel shapes have potentially appealing theoretical characteristics. In this work, we systematically investigate the differences between different kernel shape choices in several contexts.

THEORY

It is well-understood that a rectangular region of k-space is associated with anisotropic spatial resolution, while ellipsoidal regions can be associated with more isotropic resolution. Further, for a fixed spatial resolution, ellipsoidal kernels are associated with substantially fewer parameters than rectangular kernels. These characteristics suggest that ellipsoidal kernels may have certain advantages over rectangular kernels.

METHODS

We used real retrospectively undersampled k-space data to empirically study the characteristics of rectangular and ellipsoidal kernels in the context of seven methods (GRAPPA, SPIRiT, ESPIRiT, SAKE, LORAKS, AC-LORAKS, and CNN-based reconstructions).

RESULTS

Empirical results suggest that both kernel shapes can produce reconstructed images with similar error metrics, although the ellipsoidal shape can often achieve this with reduced computation time and memory usage and/or fewer model parameters.

CONCLUSION

Ellipsoidal kernel shapes may offer advantages over rectangular kernel shapes in various MRI applications.

Group feature selection for enhancing information gain in MRI reconstruction

Magnetic resonance imaging (MRI) has revolutionized the radiology. As a leading medical imaging modality, MRI not only visualizes the structures inside body, but also produces functional imaging. However, due to the slow imaging speed constrained by the MR physics, MRI cost is expensive, and patient may feel not comfortable in a scanner for a long time. Parallel MRI has accelerated the imaging speed through the sub-Nyquist sampling strategy and the missing data are interpolated by the multiple coil data acquired. Kernel learning has been used in the parallel MRI reconstruction to learn the interpolation weights and re-construct the undersampled data. However, noise and aliasing artifacts still exist in the reconstructed image and a large number of auto-calibration signal lines are needed. To further improve the kernel learning-based MRI reconstruction and accelerate the speed, this paper proposes a group feature selection strategy to improve the learning performance and enhance the reconstruction quality. An explicit kernel mapping is used for selecting a subset of features which contribute most to estimate the missing k-space data. The experimental results show that the learning behaviours can be better predicted and therefore the reconstructed image quality is improved.

Fusion of 3D lung CT and serum biomarkers for diagnosis of multiple pathological types on pulmonary nodules

BACKGROUND AND OBJECTIVE

Current researches on pulmonary nodules mainly focused on the binary-classification of benign and malignant pulmonary nodules. However, in clinical applications, it is not enough to judge whether pulmonary nodules are benign or malignant. In this paper, we proposed a fusion model based on the Lung Information Dataset Containing 3D CT Images and Serum Biomarkers (LIDCCISB) we constructed to accurately diagnose the types of pulmonary nodules in squamous cell carcinoma, adenocarcinoma, inflammation and other benign diseases.

METHODS

Using single modal information of lung 3D CT images and single modal information of Lung Tumor Biomarkers (LTBs) in LIDCCISB, a Multi-resolution 3D Multi-classification deep learning model (Mr-Mc) and a Multi-Layer Perceptron machine learning model (MLP) were constructed for diagnosing multiple pathological types of pulmonary nodules, respectively. To comprehensively use the double modal information of CT images and LTBs, we used transfer learning to fuse Mr-Mc and MLP, and constructed a multimodal information fusion model that could classify multiple pathological types of benign and malignant pulmonary nodules.

RESULTS

Experiments showed that the constructed Mr-Mc model can achieve an average accuracy of 0.805 and MLP model can achieve an average accuracy of 0.887. The fusion model was verified on a dataset containing 64 samples, and achieved an average accuracy of 0.906.

CONCLUSIONS

This is the first study to simultaneously use CT images and LTBs to diagnose multiple pathological types of benign and malignant pulmonary nodules, and experiments showed that our research was more advanced and more suitable for practical clinical applications.

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.

Improved parallel magnetic resonance imaging reconstruction with multiple variable density sampling

Generalized auto-calibrating partially parallel acquisitions (GRAPPA) and other parallel Magnetic Resonance Imaging (pMRI) methods restore the unacquired data in k-space by linearly calculating the undersampled data around the missing points. In order to obtain the weight of the linear calculation, a small number of auto-calibration signal (ACS) lines need to be sampled at the center of the k-space. Therefore, the sampling pattern used in this type of method is to full sample data in the middle area and undersample in the outer k-space with nominal reduction factors. In this paper, we propose a novel reconstruction method with a multiple variable density sampling (MVDS) that is different from traditional sampling patterns. Our method can significantly improve the image quality using multiple reduction factors with fewer ACS lines. Specifically, the traditional sampling pattern only uses a single reduction factor to uniformly undersample data in the region outside the ACS, but we use multiple reduction factors. When sampling the k-space data, we keep the ACS lines unchanged, use a smaller reduction factor for undersampling data near the ACS lines and a larger reduction factor for the outermost part of k-space. The error is lower after reconstruction of this region by undersampled data with a smaller reduction factor. The experimental results show that with the same amount of data sampled, using NL-GRAPPA to reconstruct the k-space data sampled by our method can result in lower noise and fewer artifacts than traditional methods. In particular, our method is extremely effective when the number of ACS lines is small.

SURE-based automatic parameter selection for ESPIRiT calibration

PURPOSE

ESPIRiT is a parallel imaging method that estimates coil sensitivity maps from the auto-calibration region (ACS). This requires choosing several parameters for the optimal map estimation. While fairly robust to these parameter choices, occasionally, poor selection can result in reduced performance. The purpose of this work is to automatically select parameters in ESPIRiT for more robust and consistent performance across a variety of exams.

METHODS

By viewing ESPIRiT as a denoiser, Stein's unbiased risk estimate (SURE) is leveraged to automatically optimize parameter selection in a data-driven manner. The optimum parameters corresponding to the minimum true squared error, minimum SURE as derived from densely sampled, high-resolution, and non-accelerated data and minimum SURE as derived from ACS are compared using simulation experiments. To avoid optimizing the rank of ESPIRiT's auto-calibrating matrix (one of the parameters), a heuristic derived from SURE-based singular value thresholding is also proposed.

RESULTS

Simulations show SURE derived from the densely sampled, high-resolution, and non-accelerated data to be an accurate estimator of the true mean squared error, enabling automatic parameter selection. The parameters that minimize SURE as derived from ACS correspond well to the optimal parameters. The soft-threshold heuristic improves computational efficiency while providing similar results to an exhaustive search. In-vivo experiments verify the reliability of this method.

CONCLUSIONS

Using SURE to determine ESPIRiT parameters allows for automatic parameter selections. In-vivo results are consistent with simulation and theoretical results.

Broad Learning Enhanced 1H-MRS for Early Diagnosis of Neuropsychiatric Systemic Lupus Erythematosus

In this paper, we explore the potential of using the multivoxel proton magnetic resonance spectroscopy (¹H-MRS) to diagnose neuropsychiatric systemic lupus erythematosus (NPSLE) with the assistance of a support vector machine broad learning system (BL-SVM). We retrospectively analysed 23 confirmed patients and 16 healthy controls, who underwent a 3.0 T magnetic resonance imaging (MRI) sequence with multivoxel ¹H-MRS in our hospitals. One hundred and seventeen metabolic features were extracted from the multivoxel ¹H-MRS image. Thirty-three metabolic features selected by the Mann-Whitney U test were considered to have a statistically significant difference (p < 0.05). However, the best accuracy achieved by conventional statistical methods using these 33 metabolic features was only 77%. We turned to develop a support vector machine broad learning system (BL-SVM) to quantitatively analyse the metabolic features from ¹H-MRS. Although not all the individual features manifested statistics significantly, the BL-SVM could still learn to distinguish the NPSLE from the healthy controls. The area under the receiver operating characteristic curve (AUC), the sensitivity, and the specificity of our BL-SVM in predicting NPSLE were 95%, 95.8%, and 93%, respectively, by 3-fold cross-validation. We consequently conclude that the proposed system effectively and efficiently working on limited and noisy samples may brighten a noinvasive in vivo instrument for early diagnosis of NPSLE.