MRI Image Recovery using Damped Denoising Vector AMP

Motivated by image recovery in magnetic resonance imaging (MRI), we propose a new approach to solving linear inverse problems based on iteratively calling a deep neural-network, sometimes referred to as plug-and-play recovery. Our approach is based on the vector approximate message passing (VAMP) algorithm, which is known for mean-squared error (MSE)-optimal recovery under certain conditions. The forward operator in MRI, however, does not satisfy these conditions, and thus we design new damping and initialization schemes to help VAMP. The resulting DD-VAMP++ algorithm is shown to outperform existing algorithms in convergence speed and accuracy when recovering images from the fastMRI database for the practical case of Cartesian sampling.

[1]  Jeffrey A. Fessler,et al.  Optimization Methods for Magnetic Resonance Image Reconstruction: Key Models and Optimization Algorithms , 2020, IEEE Signal Processing Magazine.

[2]  Andrea Montanari,et al.  Message passing algorithms for compressed sensing: I. motivation and construction , 2009, 2010 IEEE Information Theory Workshop on Information Theory (ITW 2010, Cairo).

[3]  M. Lustig,et al.  Compressed Sensing MRI , 2008, IEEE Signal Processing Magazine.

[4]  Ender M. Eksioglu,et al.  Denoising AMP for MRI Reconstruction: BM3D-AMP-MRI , 2018, SIAM J. Imaging Sci..

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

[6]  Pascal Vincent,et al.  fastMRI: An Open Dataset and Benchmarks for Accelerated MRI , 2018, ArXiv.

[7]  Charles A. Bouman,et al.  Plug and play methods for magnetic resonance imaging , 2019, ArXiv.

[8]  Thierry Blu,et al.  Monte-Carlo Sure: A Black-Box Optimization of Regularization Parameters for General Denoising Algorithms , 2008, IEEE Transactions on Image Processing.

[9]  Michael Unser,et al.  Deep Convolutional Neural Network for Inverse Problems in Imaging , 2016, IEEE Transactions on Image Processing.

[10]  Lei Zhang,et al.  Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising , 2016, IEEE Transactions on Image Processing.

[11]  D. Gabay.  Applications of the method of multipliers to variational inequalities , 1983 .

[12]  Sundeep Rangan,et al.  Expectation consistent approximate inference: Generalizations and convergence , 2016, 2016 IEEE International Symposium on Information Theory (ISIT).

[13]  Andrea Montanari,et al.  State Evolution for Approximate Message Passing with Non-Separable Functions , 2017, Information and Inference: A Journal of the IMA.

[14]  Andrea Montanari,et al.  The dynamics of message passing on dense graphs, with applications to compressed sensing , 2010, 2010 IEEE International Symposium on Information Theory.

[15]  Stephen P. Boyd,et al.  Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers , 2011, Found. Trends Mach. Learn..

[16]  Andrea Montanari,et al.  Message-passing algorithms for compressed sensing , 2009, Proceedings of the National Academy of Sciences.

[17]  Sundeep Rangan,et al.  Vector approximate message passing , 2017, 2017 IEEE International Symposium on Information Theory (ISIT).

[18]  Yong Cheng,et al.  Comments on "Image Denoising by Sparse 3-D Transform-Domain Collaborative Filtering" , 2011, IEEE Trans. Image Process..

[19]  Sundeep Rangan,et al.  Plug in estimation in high dimensional linear inverse problems a rigorous analysis , 2018, NeurIPS.

[20]  Richard G. Baraniuk,et al.  BM3D-AMP: A new image recovery algorithm based on BM3D denoising , 2015, 2015 IEEE International Conference on Image Processing (ICIP).