Hybrid-Weighted Total Variation and Nonlocal Low-Rank-Based Image Compressed Sensing Reconstruction

To reconstruct natural images from compressed sensing (CS) measurements accurately and effectively, a CS image reconstruction algorithm based on hybrid-weighted total variation (HWTV) and nonlocal low-rank (NLR) is proposed. It considers the local smoothness and nonlocal self-similarity (NSS) in image, improves traditional hybrid total variation (TV) model, and constructs a new edge detection operator with mean curvature to adaptively select the TV. The HWTV combines the advantages of first-order TV and second-order TV to preserve the edges of the image and avoid the staircase effect in the smooth areas. And NLR can effectively reduce the redundant information and retain the structural information of the image. In addition, the proposed algorithm constructs prior regularization terms with improved HWTV model and NLR model, and utilizes soft threshold function and smooth but non-convex function to solve the TV and low-rank optimization problems, respectively. Finally, the alternative direction multiplier method (ADMM) iterative strategy is used to separate the target model into several sub-problems, and the most efficient methods are adopted to solve each sub-problem. Experimental results show that, compared with the state-of-the-art CS reconstruction algorithms, the proposed algorithm can achieve higher reconstruction quality, especially in the case of low sampling rates.

[1]  Carola-Bibiane Schönlieb,et al.  A Combined First and Second Order Variational Approach for Image Reconstruction , 2012, Journal of Mathematical Imaging and Vision.

[2]  Chuan Chen,et al.  Alternating Direction Method of Multipliers for Nonlinear Image Restoration Problems , 2015, IEEE Transactions on Image Processing.

[3]  M. Unser Sampling-50 years after Shannon , 2000, Proceedings of the IEEE.

[4]  Tony F. Chan,et al.  High-Order Total Variation-Based Image Restoration , 2000, SIAM J. Sci. Comput..

[5]  Guangming Shi,et al.  Compressive Sensing via Nonlocal Low-Rank Regularization , 2014, IEEE Transactions on Image Processing.

[6]  Lan Tang,et al.  Group-based sparse representation for image compressive sensing reconstruction with non-convex regularization , 2017, Neurocomputing.

[7]  Ting-Zhu Huang,et al.  Total variation and high-order total variation adaptive model for restoring blurred images with Cauchy noise , 2019, Comput. Math. Appl..

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

[9]  Wen Gao,et al.  Image Denoising via Bandwise Adaptive Modeling and Regularization Exploiting Nonlocal Similarity , 2016, IEEE Transactions on Image Processing.

[10]  Arvid Lundervold,et al.  Noise removal using fourth-order partial differential equation with applications to medical magnetic resonance images in space and time , 2003, IEEE Trans. Image Process..

[11]  Baoxin Li,et al.  Single image super-resolution using collaborative representation and non-local self-similarity , 2018, Signal Process..

[12]  Gabriele Steidl,et al.  A Second Order Nonsmooth Variational Model for Restoring Manifold-Valued Images , 2015, SIAM J. Sci. Comput..

[13]  Pheng-Ann Heng,et al.  Adaptive total variation denoising based on difference curvature , 2010, Image Vis. Comput..

[14]  L. Rudin,et al.  Nonlinear total variation based noise removal algorithms , 1992 .

[15]  Emmanuel J. Candès,et al.  Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information , 2004, IEEE Transactions on Information Theory.

[16]  Heye Zhang,et al.  Reweighted Anisotropic Total Variation Minimization for Limited-Angle CT Reconstruction , 2017, IEEE Transactions on Nuclear Science.

[17]  Jian Zhang,et al.  Improved total variation based image compressive sensing recovery by nonlocal regularization , 2012, 2013 IEEE International Symposium on Circuits and Systems (ISCAS2013).

[18]  Gang Liu,et al.  High-order TVL1-based images restoration and spatially adapted regularization parameter selection , 2014, Comput. Math. Appl..