Joint modeling and reconstruction of a compressively-sensed set of correlated images

We model a set of images by jointly considering different types of correlations.The joint modeling-based minimization problem is solved efficiently.The proposed algorithm is extended for reconstruction of color image sets.We explain how and why the parameters are selected in our experiments.Our algorithms outperform many state-of-the-arts CS reconstruction methods. Employing correlation among images for improved reconstruction in compressive sensing is a conceptually attractive idea, although developing efficient modeling strategies and reconstruction algorithms are often the key to achieve any potential benefit. This paper presents a novel modeling strategy and an efficient reconstruction algorithm for processing a set of correlated images, jointly taking into consideration inter-image correlation, intra-image correlation and inter-channel correlation. The approach starts with joint modeling of the entire image set in the gradient domain, which supports simultaneous representation of local smoothness, nonlocal self-similarity of every single image, and inter-image correlation. Then an efficient algorithm is proposed to solve the joint formulation, using a Split-Bregman-based technique. Furthermore, to support color image reconstruction, the proposed algorithm is extended by using the concept of group sparsity to explore inter-channel correlation. The effectiveness of the proposed approach is demonstrated with extensive experiments on both grayscale and color image sets. Results are also compared with recently proposed compressive sensing recovery algorithms.

[1]  Ce Liu,et al.  Exploring new representations and applications for motion analysis , 2009 .

[2]  Zhenhua Tang,et al.  Reconstruction of multi-view compressed imaging using weighted total variation , 2014, Multimedia Systems.

[3]  Trac D. Tran,et al.  Fast and Efficient Compressive Sensing Using Structurally Random Matrices , 2011, IEEE Transactions on Signal Processing.

[4]  David L Donoho,et al.  Compressed sensing , 2006, IEEE Transactions on Information Theory.

[5]  Pierre Vandergheynst,et al.  Robust Image Reconstruction from Multiview Measurements , 2012, SIAM J. Imaging Sci..

[6]  Dacheng Tao,et al.  Large-Margin Multi-ViewInformation Bottleneck , 2014, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[7]  Wotao Yin,et al.  Group sparse optimization by alternating direction method , 2013, Optics & Photonics - Optical Engineering + Applications.

[8]  Rabab Kreidieh Ward,et al.  Algorithms to Approximately Solve NP Hard Row-Sparse MMV Recovery Problem: Application to Compressive Color Imaging , 2012, IEEE Journal on Emerging and Selected Topics in Circuits and Systems.

[9]  Yuan Yan Tang,et al.  Multiview Hessian discriminative sparse coding for image annotation , 2013, Comput. Vis. Image Underst..

[10]  James E. Fowler,et al.  Residual Reconstruction for Block-Based Compressed Sensing of Video , 2011, 2011 Data Compression Conference.

[11]  Tom Goldstein,et al.  The Split Bregman Method for L1-Regularized Problems , 2009, SIAM J. Imaging Sci..

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

[13]  W. Dong,et al.  Compressive sensing via reweighted TV and nonlocal sparsity regularisation , 2013 .

[14]  Pascal Frossard,et al.  Correlation estimation from compressed images , 2013, J. Vis. Commun. Image Represent..

[15]  Ianwei,et al.  Compressive Video Sampling with Approximate Message Passing Decoding , 2011 .

[16]  P. Sonneveld.  CGS, A Fast Lanczos-Type Solver for Nonsymmetric Linear systems , 1989 .

[17]  Ashwin A. Wagadarikar,et al.  Single disperser design for coded aperture snapshot spectral imaging. , 2008, Applied optics.

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

[19]  Michael B. Wakin,et al.  A geometric approach to multi-view compressive imaging , 2012, EURASIP J. Adv. Signal Process..

[20]  James E. Fowler,et al.  Video Compressed Sensing with Multihypothesis , 2011, 2011 Data Compression Conference.

[21]  Andy M. Yip,et al.  Recent Developments in Total Variation Image Restoration , 2004 .

[22]  Baoxin Li,et al.  Compressive imaging of color images , 2009, 2009 IEEE International Conference on Acoustics, Speech and Signal Processing.

[23]  Alan C. Bovik,et al.  Image information and visual quality , 2006, IEEE Trans. Image Process..

[24]  Lei Zhang,et al.  Image reconstruction with locally adaptive sparsity and nonlocal robust regularization , 2012, Signal Process. Image Commun..

[25]  Konstantinos N. Plataniotis,et al.  High-Accuracy Total Variation With Application to Compressed Video Sensing , 2013, IEEE Transactions on Image Processing.

[26]  Rabab K. Ward,et al.  Compressed sensing of color images , 2010, Signal Process..

[27]  Yin Zhang,et al.  An efficient augmented Lagrangian method with applications to total variation minimization , 2013, Computational Optimization and Applications.

[28]  S. Osher,et al.  Image restoration: Total variation, wavelet frames, and beyond , 2012 .

[29]  Maria Trocan,et al.  Compressed-sensing recovery of multiview image and video sequences using signal prediction , 2012, Multimedia Tools and Applications.

[30]  David Zhang,et al.  FSIM: A Feature Similarity Index for Image Quality Assessment , 2011, IEEE Transactions on Image Processing.

[31]  Marc Moonen,et al.  Joint DOA and multi-pitch estimation based on subspace techniques , 2012, EURASIP J. Adv. Signal Process..

[32]  Weifeng Liu,et al.  Multiview Hessian Regularization for Image Annotation , 2013, IEEE Transactions on Image Processing.

[33]  Yin Zhang,et al.  A New Compressive Video Sensing Framework for Mobile Broadcast , 2013, IEEE Transactions on Broadcasting.

[34]  J. Romberg,et al.  Imaging via Compressive Sampling , 2008, IEEE Signal Processing Magazine.

[35]  Alan C. Bovik,et al.  No-Reference Image Quality Assessment in the Spatial Domain , 2012, IEEE Transactions on Image Processing.

[36]  Ming Li,et al.  Motion-Aware Decoding of Compressed-Sensed Video , 2013, IEEE Transactions on Circuits and Systems for Video Technology.

[37]  Yin Zhang,et al.  Fixed-Point Continuation for l1-Minimization: Methodology and Convergence , 2008, SIAM J. Optim..

[38]  Guangming Shi,et al.  Model-Assisted Adaptive Recovery of Compressed Sensing with Imaging Applications , 2012, IEEE Transactions on Image Processing.

[39]  M. Salman Asif,et al.  Motion‐adaptive spatio‐temporal regularization for accelerated dynamic MRI , 2013, Magnetic resonance in medicine.

[40]  Richard Barrett,et al.  Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods , 1994, Other Titles in Applied Mathematics.

[41]  Ting Sun,et al.  Single-pixel imaging via compressive sampling , 2008, IEEE Signal Process. Mag..

[42]  Shree K. Nayar,et al.  Video from a single coded exposure photograph using a learned over-complete dictionary , 2011, 2011 International Conference on Computer Vision.

[43]  Chun-Shien Lu,et al.  Dictionary learning-based distributed compressive video sensing , 2010, 28th Picture Coding Symposium.

[44]  Gustavo de Veciana,et al.  An information fidelity criterion for image quality assessment using natural scene statistics , 2005, IEEE Transactions on Image Processing.

[45]  David Zhang,et al.  A comprehensive evaluation of full reference image quality assessment algorithms , 2012, 2012 19th IEEE International Conference on Image Processing.

[46]  Jian-Feng Cai,et al.  Split Bregman Methods and Frame Based Image Restoration , 2009, Multiscale Model. Simul..

[47]  Jean-Michel Morel,et al.  A Review of Image Denoising Algorithms, with a New One , 2005, Multiscale Model. Simul..

[48]  Dacheng Tao,et al.  Multi-View Intact Space Learning , 2015, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[49]  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).