A Generalized Structured Low-Rank Matrix Completion Algorithm for MR Image Recovery

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.

Artificial Intelligence Algorithm-Based MRI for Differentiation Diagnosis of Prostate Cancer

The rapid increase in prostate cancer (PCa) patients is similar to that of benign prostatic hyperplasia (BPH) patients, but the treatments are quite different. In this research, magnetic resonance imaging (MRI) images under the weighted low-rank matrix restoration algorithm (RLRE) were utilized to differentiate PCa from BPH. The diagnostic effects of different sequences of MRI images were evaluated to provide a more effective examination method for the clinical differential diagnosis of PCa and BPH. 150 patients with suspected PCa were taken as the research objects. Pathological examination revealed that 137 patients had PCa and 13 patients had BPH. The pathological results were the gold standard and were compared with the MRI results of different sequences. Therefore, the accuracy of the MRI results was evaluated. The results showed that with the rise of Gaussian noise, the peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) of all three algorithms gradually decreased, but the PSNR and SSIM of the RLRE algorithm were always higher than those of the RL and BM3D algorithms (P < 0.05). The sensitivity (97.08%), specificity (92.31%), accuracy (96.67%), and consistency (0.678) of the dynamic contrast enhancement (DCE) sequence were higher than those of the plain scan (86.13%, 69.23%, 84.67%, and 0.469, respectively). In conclusion, the RLRE algorithm could promote the resolution of MRI images and improve the display effect. DCE could better differentiate PCa from BPH, had great clinical application value, and was worthy of clinical promotion.

High-Quality MR Fingerprinting Reconstruction Using Structured Low-Rank Matrix Completion and Subspace Projection

Due to the capability of fast multiparametric quantitative imaging, magnetic resonance fingerprinting (MRF) is becoming a promising quantitative magnetic resonance imaging approach. However, the artifacts caused by the highly undersampled data acquisition lead to inaccurate estimation of the tissue parameter maps. Based on the assumption that the 3-D MRF data can be modeled as a piecewise smooth signal, with the discontinuities localized to the zero sets of a bandlimited function, we exploit the low-rank property of the structured Toeplitz matrix constructed from the Fourier measurements. In addition, we adopt the subspace projection scheme to improve the accuracy of parameter estimation. In order to efficiently solve the regularized problem, we propose an iterative two-stage algorithm, which alternately updates the k -space data and projects the space-time matrix into the dictionary space. Numerical experiments demonstrate that the proposed algorithm shows significant improvement in MRF time-series images reconstruction and can provide more accurate parameter maps over the state-of-the-art algorithms.

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.

Structured Low-Rank Algorithms: Theory, Magnetic Resonance Applications, and Links to Machine Learning

In this survey, we provide a detailed review of recent advances in the recovery of continuous domain multidimensional signals from their few non-uniform (multichannel) measurements using structured low-rank matrix completion formulation. This framework is centered on the fundamental duality between the compactness (e.g., sparsity) of the continuous signal and the rank of a structured matrix, whose entries are functions of the signal. This property enables the reformulation of the signal recovery as a low-rank structured matrix completion, which comes with performance guarantees. We will also review fast algorithms that are comparable in complexity to current compressed sensing methods, which enables the application of the framework to large-scale magnetic resonance (MR) recovery problems. The remarkable flexibility of the formulation can be used to exploit signal properties that are difficult to capture by current sparse and low-rank optimization strategies. We demonstrate the utility of the framework in a wide range of MR imaging (MRI) applications, including highly accelerated imaging, calibration-free acquisition, MR artifact correction, and ungated dynamic MRI.

Improved MUSSELS reconstruction for high-resolution multi-shot diffusion weighted imaging

PURPOSE

MUSSELS is a one-step iterative reconstruction method for multishot diffusion weighted (msDW) imaging. The current work presents an efficient implementation, termed IRLS MUSSELS, that enables faster reconstruction to enhance its utility for high-resolution diffusion MRI studies.

METHODS

The recently proposed MUSSELS reconstruction belongs to a new class of parallel imaging-based methods that recover artifact-free DWIs from msDW data without needing phase compensation. The reconstruction is achieved via structured low-rank matrix completion algorithms, which are computationally demanding due to the large size of the Hankel matrices and their associated computations involving singular value decompositions. Because of this, computational demands of the MUSSELS reconstruction scales as the matrix size and the number of shots increases, which hinders its practical utility for high-resolution applications. In this work, we derive a computationally efficient MUSSELS formulation by modifying the iterative reweighted least squares (IRLS) method that were proposed earlier to solve such problems. Using whole-brain in vivo data, we show the utility of the IRLS MUSSELS for routine high-resolution studies with reduced computational burden.

RESULTS

IRLS MUSSELS provides about five times faster reconstruction for matrix sizes 192 × 192 and 256 × 256 compared to the earlier MUSSELS implementation. The widely employed conjugate symmetry priors can also be incorporated into IRLS MUSSELS to reduce blurring of the partial Fourier acquisitions, without incurring much computational burden.

CONCLUSIONS

The proposed method is observed to be computationally efficient to enable routine high-resolution studies. The computational complexity matches the traditional msDWI reconstruction methods and provides improved reconstruction results with the additional constraints.

Reconstruction of Binary Shapes from Blurred Images via Hankel-structured Low-rank Matrix Recovery

With the dominance of digital imaging systems, we are often dealing with discrete-domain samples of an analog image. Due to physical limitations, all imaging devices apply a blurring kernel on the input image before taking samples to form the output pixels. In this paper, we focus on the reconstruction of binary shape images from few blurred samples. This problem has applications in medical imaging, shape processing, and image segmentation. Our method relies on representing the analog shape image in a discrete grid much finer than the sampling grid. We formulate the problem as the recovery of a rank r matrix that is formed by a Hankel structure on the pixels. We further propose efficient ADMM-based algorithms to recover the low-rank matrix in both noiseless and noisy settings. We also analytically investigate the number of required samples for successful recovery in the noiseless case. For this purpose, we study the problem in the random sampling framework, and show that with O(r log4(n1n2)) random samples (where the size of the image is assumed to be n1 x n2) we can guarantee the perfect reconstruction with high probability under mild conditions. We further prove the robustness of the proposed recovery in the noisy setting by showing that the reconstruction error in the noisy case is bounded when the input noise is bounded. Simulation results confirm that our proposed method outperform the conventional total variation minimization in the noiseless settings.