Deep Low-rank Prior in Dynamic MR Imaging

The deep learning methods have achieved attractive performance in dynamic MR cine imaging. However, all of these methods are only driven by the sparse prior of MR images, while the important low-rank (LR) prior of dynamic MR cine images is not explored, which limits the further improvements on dynamic MR reconstruction. In this paper, a learned singular value thresholding (Learned-SVT) operation is proposed to explore deep low-rank prior in dynamic MR imaging for obtaining improved reconstruction results. In particular, we come up with two novel and distinct schemes to introduce the learnable low-rank prior into deep network architectures in an unrolling manner and a plug-and-play manner respectively. In the unrolling manner, we put forward a model-based unrolling sparse and low-rank network for dynamic MR imaging, dubbed SLR-Net. The SLR-Net is defined over a deep network flow graph, which is unrolled from the iterative procedures in the Iterative Shrinkage-Thresholding Algorithm (ISTA) for optimizing a sparse and low-rank based dynamic MRI model. In the plug-and-play manner, we present a plug-and-play LR network module that can be easily embedded into any other dynamic MR neural networks without changing the network paradigm. Experimental results show that both schemes can further improve the state-of-the-art CS methods, such as k-t SLR, and sparsity-driven deep learning-based methods, such as DC-CNN and CRNN, both qualitatively and quantitatively.

[1]  Dong Liang,et al.  Deep Magnetic Resonance Image Reconstruction: Inverse Problems Meet Neural Networks , 2020, IEEE Signal Processing Magazine.

[2]  Taeseong Kim,et al.  KIKI‐net: cross‐domain convolutional neural networks for reconstructing undersampled magnetic resonance images , 2018, Magnetic resonance in medicine.

[3]  Mathews Jacob,et al.  MoDL: Model-Based Deep Learning Architecture for Inverse Problems , 2017, IEEE Transactions on Medical Imaging.

[4]  Leon Axel,et al.  Combination of Compressed Sensing and Parallel Imaging for Highly-Accelerated 3 D First-Pass Cardiac Perfusion MRI , 2009 .

[5]  John W. Paisley,et al.  A Deep Information Sharing Network for Multi-Contrast Compressed Sensing MRI Reconstruction , 2018, IEEE Transactions on Image Processing.

[6]  HyunWook Park,et al.  A parallel MR imaging method using multilayer perceptron , 2017, Medical physics.

[7]  Leslie Ying,et al.  Compressed Sensing Dynamic Cardiac Cine MRI Using Learned Spatiotemporal Dictionary , 2014, IEEE Transactions on Biomedical Engineering.

[8]  Emmanuel J. Candès,et al.  Exact Matrix Completion via Convex Optimization , 2008, Found. Comput. Math..

[9]  Bernard Ghanem,et al.  ISTA-Net: Interpretable Optimization-Inspired Deep Network for Image Compressive Sensing , 2017, 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition.

[10]  Richard G. Baraniuk,et al.  From Denoising to Compressed Sensing , 2014, IEEE Transactions on Information Theory.

[11]  Won-Ki Jeong,et al.  Compressed Sensing MRI Reconstruction Using a Generative Adversarial Network With a Cyclic Loss , 2017, IEEE Transactions on Medical Imaging.

[12]  John W. Paisley,et al.  Compressed Sensing MRI Using a Recursive Dilated Network , 2018, AAAI.

[13]  Justin P. Haldar,et al.  Spatiotemporal imaging with partially separable functions: A matrix recovery approach , 2010, 2010 IEEE International Symposium on Biomedical Imaging: From Nano to Macro.

[14]  Jian Sun,et al.  Deep ADMM-Net for Compressive Sensing MRI , 2016, NIPS.

[15]  Justin P. Haldar,et al.  Image Reconstruction From Highly Undersampled $( {\bf k}, {t})$-Space Data With Joint Partial Separability and Sparsity Constraints , 2012, IEEE Transactions on Medical Imaging.

[16]  Dong Liang,et al.  k‐t ISD: Dynamic cardiac MR imaging using compressed sensing with iterative support detection , 2012, Magnetic resonance in medicine.

[17]  Daniel Rueckert,et al.  A Deep Cascade of Convolutional Neural Networks for Dynamic MR Image Reconstruction , 2017, IEEE Transactions on Medical Imaging.

[18]  Daniel Rueckert,et al.  Convolutional Recurrent Neural Networks for Dynamic MR Image Reconstruction , 2017, IEEE Transactions on Medical Imaging.

[19]  Eero P. Simoncelli,et al.  Image quality assessment: from error visibility to structural similarity , 2004, IEEE Transactions on Image Processing.

[20]  Brendt Wohlberg,et al.  Plug-and-Play priors for model based reconstruction , 2013, 2013 IEEE Global Conference on Signal and Information Processing.

[21]  Jong Chul Ye,et al.  Deep learning with domain adaptation for accelerated projection‐reconstruction MR , 2018, Magnetic resonance in medicine.

[22]  Guigang Zhang,et al.  Deep Learning , 2016, Int. J. Semantic Comput..

[23]  Matthew D. Zeiler ADADELTA: An Adaptive Learning Rate Method , 2012, ArXiv.

[24]  Jimmy Ba,et al.  Adam: A Method for Stochastic Optimization , 2014, ICLR.

[25]  Daniel Rueckert,et al.  Dictionary Learning and Time Sparsity for Dynamic MR Data Reconstruction , 2014, IEEE Transactions on Medical Imaging.

[26]  D. O. Walsh,et al.  Adaptive reconstruction of phased array MR imagery , 2000, Magnetic resonance in medicine.

[27]  Dong Liang,et al.  Model Learning: Primal Dual Networks for Fast MR imaging , 2019, MICCAI.

[28]  Hong Jiang,et al.  Dynamic imaging by model estimation , 2002, 5th IEEE EMBS International Summer School on Biomedical Imaging, 2002..

[29]  Marc Teboulle,et al.  A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems , 2009, SIAM J. Imaging Sci..

[30]  Junfeng Yang,et al.  A Fast Alternating Direction Method for TVL1-L2 Signal Reconstruction From Partial Fourier Data , 2010, IEEE Journal of Selected Topics in Signal Processing.

[31]  Jong Chul Ye,et al.  ${k}$ -Space Deep Learning for Accelerated MRI , 2020, IEEE Transactions on Medical Imaging.

[32]  Bruce R. Rosen,et al.  Image reconstruction by domain-transform manifold learning , 2017, Nature.

[33]  Emmanuel J. Candès,et al.  Exact Matrix Completion via Convex Optimization , 2009, Found. Comput. Math..

[34]  Dong Liang,et al.  DeepcomplexMRI: Exploiting deep residual network for fast parallel MR imaging with complex convolution. , 2020, Magnetic resonance imaging.

[35]  Zhi-Pei Liang,et al.  Real-time cardiac MRI without triggering, gating, or breath holding , 2008, 2008 30th Annual International Conference of the IEEE Engineering in Medicine and Biology Society.

[36]  D. Donoho,et al.  Sparse MRI: The application of compressed sensing for rapid MR imaging , 2007, Magnetic resonance in medicine.

[37]  Thomas Pock,et al.  Learning a variational network for reconstruction of accelerated MRI data , 2017, Magnetic resonance in medicine.

[38]  Leslie Ying,et al.  A Kernel-Based Low-Rank (KLR) Model for Low-Dimensional Manifold Recovery in Highly Accelerated Dynamic MRI , 2017, IEEE Transactions on Medical Imaging.

[39]  Bruno Madore Using UNFOLD to remove artifacts in parallel imaging and in partial‐Fourier imaging , 2002, Magnetic resonance in medicine.

[40]  Jian Sun,et al.  Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification , 2015, 2015 IEEE International Conference on Computer Vision (ICCV).

[41]  Yoshua Bengio,et al.  Deep Sparse Rectifier Neural Networks , 2011, AISTATS.

[42]  Leslie Ying,et al.  Bi-Linear Modeling of Data Manifolds for Dynamic-MRI Recovery , 2018, IEEE Transactions on Medical Imaging.

[43]  Dong Liang,et al.  DIMENSION: Dynamic MR imaging with both k‐space and spatial prior knowledge obtained via multi‐supervised network training , 2018, NMR in biomedicine.

[44]  Yoram Bresler,et al.  ADMiRA: Atomic Decomposition for Minimum Rank Approximation , 2009, IEEE Transactions on Information Theory.

[45]  Leslie Ying,et al.  Accelerating magnetic resonance imaging via deep learning , 2016, 2016 IEEE 13th International Symposium on Biomedical Imaging (ISBI).

[46]  Zhi-Pei Liang,et al.  SPATIOTEMPORAL IMAGINGWITH PARTIALLY SEPARABLE FUNCTIONS , 2007, 2007 4th IEEE International Symposium on Biomedical Imaging: From Nano to Macro.

[47]  Emmanuel J. Candès,et al.  A Singular Value Thresholding Algorithm for Matrix Completion , 2008, SIAM J. Optim..

[48]  José M. Bioucas-Dias,et al.  An Augmented Lagrangian Approach to the Constrained Optimization Formulation of Imaging Inverse Problems , 2009, IEEE Transactions on Image Processing.

[49]  Zhi-Pei Liang,et al.  Spatiotemporal Imaging with Partially Separable Functions , 2007, 2007 Joint Meeting of the 6th International Symposium on Noninvasive Functional Source Imaging of the Brain and Heart and the International Conference on Functional Biomedical Imaging.

[50]  R. Rockafellar Monotone Operators and the Proximal Point Algorithm , 1976 .

[51]  Steen Moeller,et al.  Scan‐specific robust artificial‐neural‐networks for k‐space interpolation (RAKI) reconstruction: Database‐free deep learning for fast imaging , 2018, Magnetic resonance in medicine.

[52]  Michael Lustig,et al.  k-t SPARSE: High frame rate dynamic MRI exploiting spatio-temporal sparsity , 2006 .

[53]  Mathews Jacob,et al.  Accelerated Dynamic MRI Exploiting Sparsity and Low-Rank Structure: k-t SLR , 2011, IEEE Transactions on Medical Imaging.

[54]  Jong Chul Ye,et al.  Improved k–t BLAST and k–t SENSE using FOCUSS , 2007, Physics in medicine and biology.

[55]  Daniel K Sodickson,et al.  Low‐rank plus sparse matrix decomposition for accelerated dynamic MRI with separation of background and dynamic components , 2015, Magnetic resonance in medicine.

[56]  Yuan Yu,et al.  TensorFlow: A system for large-scale machine learning , 2016, OSDI.

[57]  S. Frick,et al.  Compressed Sensing , 2014, Computer Vision, A Reference Guide.

[58]  Jaejun Yoo,et al.  Deep Residual Learning for Accelerated MRI Using Magnitude and Phase Networks , 2018, IEEE Transactions on Biomedical Engineering.

[59]  Mathews Jacob,et al.  Dynamic MRI Using SmooThness Regularization on Manifolds (SToRM) , 2016, IEEE Transactions on Medical Imaging.

[60]  Peter Boesiger,et al.  k‐t BLAST and k‐t SENSE: Dynamic MRI with high frame rate exploiting spatiotemporal correlations , 2003, Magnetic resonance in medicine.