Two-Layer Residual Sparsifying Transform Learning for Image Reconstruction

Signal models based on sparsity, low-rank and other properties have been exploited for image reconstruction from limited and corrupted data in medical imaging and other computational imaging applications. In particular, sparsifying transform models have shown promise in various applications, and offer numerous advantages such as efficiencies in sparse coding and learning. This work investigates pre-learning a two-layer extension of the transform model for image reconstruction, wherein the transform domain or filtering residuals of the image are further sparsified in the second layer. The proposed block coordinate descent optimization algorithms involve highly efficient updates. Preliminary numerical experiments demonstrate the usefulness of a two-layer model over the previous related schemes for CT image reconstruction from low-dose measurements.

[1]  Xuanqin Mou,et al.  Tensor-Based Dictionary Learning for Spectral CT Reconstruction , 2017, IEEE Transactions on Medical Imaging.

[2]  Yoram Bresler,et al.  Learning Filter Bank Sparsifying Transforms , 2018, IEEE Transactions on Signal Processing.

[3]  Lei Zhang,et al.  Low-Dose X-ray CT Reconstruction via Dictionary Learning , 2012, IEEE Transactions on Medical Imaging.

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

[5]  Jeffrey A. Fessler,et al.  Sparse-View X-Ray CT Reconstruction Using 𝓵1 Prior with Learned Transform , 2017, ArXiv.

[6]  Graham W. Taylor,et al.  Deconvolutional networks , 2010, 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[7]  Hakan Erdogan,et al.  Ordered subsets algorithms for transmission tomography. , 1999, Physics in medicine and biology.

[8]  C. Bouman,et al.  A recursive filter for noise reduction in statistical iterative tomographic imaging , 2006, Electronic Imaging.

[9]  Jeffrey A. Fessler,et al.  SPULTRA: Low-Dose CT Image Reconstruction With Joint Statistical and Learned Image Models , 2018, IEEE Transactions on Medical Imaging.

[10]  Jeffrey A. Fessler,et al.  Regularization Designs for Uniform Spatial Resolution and Noise Properties in Statistical Image Reconstruction for 3-D X-ray CT , 2015, IEEE Transactions on Medical Imaging.

[11]  A. Bruckstein,et al.  K-SVD : An Algorithm for Designing of Overcomplete Dictionaries for Sparse Representation , 2005 .

[12]  Yoram Bresler,et al.  Learning Sparsifying Transforms , 2013, IEEE Transactions on Signal Processing.

[13]  Yoram Bresler,et al.  $\ell_{0}$ Sparsifying Transform Learning With Efficient Optimal Updates and Convergence Guarantees , 2015, IEEE Transactions on Signal Processing.

[14]  W P Segars,et al.  Realistic CT simulation using the 4D XCAT phantom. , 2008, Medical physics.

[15]  Jeffrey A. Fessler,et al.  Low dose CT image reconstruction with learned sparsifying transform , 2016, 2016 IEEE 12th Image, Video, and Multidimensional Signal Processing Workshop (IVMSP).

[16]  Yoram Bresler,et al.  Data-Driven Learning of a Union of Sparsifying Transforms Model for Blind Compressed Sensing , 2015, IEEE Transactions on Computational Imaging.

[17]  L. Feldkamp,et al.  Practical cone-beam algorithm , 1984 .

[18]  Brendt Wohlberg,et al.  Convolutional Dictionary Learning: A Comparative Review and New Algorithms , 2017, IEEE Transactions on Computational Imaging.

[19]  Jeffrey A. Fessler,et al.  PWLS-ULTRA: An Efficient Clustering and Learning-Based Approach for Low-Dose 3D CT Image Reconstruction , 2017, IEEE Transactions on Medical Imaging.

[20]  Brendt Wohlberg,et al.  Learning Multi-Layer Transform Models , 2018, 2018 56th Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[21]  Michael Elad,et al.  Convolutional Neural Networks Analyzed via Convolutional Sparse Coding , 2016, J. Mach. Learn. Res..

[22]  Michael Elad,et al.  Multilayer Convolutional Sparse Modeling: Pursuit and Dictionary Learning , 2018, IEEE Transactions on Signal Processing.

[23]  Yoram Bresler,et al.  Efficient Blind Compressed Sensing Using Sparsifying Transforms with Convergence Guarantees and Application to Magnetic Resonance Imaging , 2015, SIAM J. Imaging Sci..

[24]  J. Fessler.  Statistical Image Reconstruction Methods for Transmission Tomography , 2000 .

[25]  Jeffrey A. Fessler,et al.  Relaxed Linearized Algorithms for Faster X-Ray CT Image Reconstruction , 2015, IEEE Transactions on Medical Imaging.

[26]  M. Elad,et al.  $rm K$-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation , 2006, IEEE Transactions on Signal Processing.