Multi-Images Restoration Method with a Mixed-Regularization Approach for Cognitive Informatics

Cognitive image processing is an important part of cognitive informatics. High quality images are crucial for cognitive image processing, especially in small object recognition and image segmentation. Multi-images restoration provides an alternative approach for these problems. For example, with image denoising and image deblurring, the raw images can be better provided to improve the result of cognitive image processing. The improvement of imaging device's sampling rate provides a clue to design a common approach for multi-images restoration. This paper concerns with a mixed-regularization approach for solving multi-images (MRMI) restoration problems. The MRMI algorithm generalizes the original total variation (TV) based algorithm by fusing multiple noisy images to maximize the useful information restored from the degraded images. The proposed approach combines $\ell_{1}$ regularizer and $\mathbf{TV}_{p}$ regularizer to restore a latent image, which operates on two different domains, i.e., pixel and gradient. This mixed-regularization method can simultaneously exploit the sparsity of natural signal. The resulting problem is solved by the adaptation of generalized accelerated proximal gradient (GAPG) method. The effectiveness of our approach is validated in the context of multi-images denoising, deblurring and inpainting. Compared with some iterative shrinkage-thresholding algorithms, the experimental results indicates that our approach can restore a better image.

[1]  David Zhang,et al.  A Generalized Iterated Shrinkage Algorithm for Non-convex Sparse Coding , 2013, 2013 IEEE International Conference on Computer Vision.

[2]  E. Candès,et al.  Astronomical image representation by the curvelet transform , 2003, Astronomy & Astrophysics.

[3]  Robert D. Nowak,et al.  An EM algorithm for wavelet-based image restoration , 2003, IEEE Trans. Image Process..

[4]  Junbin Gao,et al.  Selective Multi-Source Total Variation Image Restoration , 2015, 2015 International Conference on Digital Image Computing: Techniques and Applications (DICTA).

[5]  Michael A. Saunders,et al.  Atomic Decomposition by Basis Pursuit , 1998, SIAM J. Sci. Comput..

[6]  Mario Bertero,et al.  Introduction to Inverse Problems in Imaging , 1998 .

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

[8]  Junfeng Yang,et al.  A Fast Algorithm for Edge-Preserving Variational Multichannel Image Restoration , 2009, SIAM J. Imaging Sci..

[9]  Ming-Jun Lai,et al.  An Unconstrained ℓq Minimization with 0 , 2011, SIAM J. Optim..

[10]  Marc Teboulle,et al.  Fast Gradient-Based Algorithms for Constrained Total Variation Image Denoising and Deblurring Problems , 2009, IEEE Transactions on Image Processing.

[11]  I. Johnstone,et al.  Adapting to Unknown Smoothness via Wavelet Shrinkage , 1995 .

[12]  ANTONIN CHAMBOLLE,et al.  An Algorithm for Total Variation Minimization and Applications , 2004, Journal of Mathematical Imaging and Vision.

[13]  Wangmeng Zuo,et al.  A Generalized Accelerated Proximal Gradient Approach for Total-Variation-Based Image Restoration , 2011, IEEE Transactions on Image Processing.

[14]  Michael Elad,et al.  Coordinate and subspace optimization methods for linear least squares with non-quadratic regularization , 2007 .

[15]  José M. Bioucas-Dias,et al.  Bayesian wavelet-based image deconvolution: a GEM algorithm exploiting a class of heavy-tailed priors , 2006, IEEE Transactions on Image Processing.

[16]  Luc Van Gool,et al.  One-Shot Video Object Segmentation , 2016, 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[17]  Y. She,et al.  Thresholding-based iterative selection procedures for model selection and shrinkage , 2008, 0812.5061.

[18]  Frédo Durand,et al.  Image and depth from a conventional camera with a coded aperture , 2007, SIGGRAPH 2007.

[19]  I. Daubechies,et al.  An iterative thresholding algorithm for linear inverse problems with a sparsity constraint , 2003, math/0307152.

[20]  Arvind Ganesh,et al.  Fast algorithms for recovering a corrupted low-rank matrix , 2009, 2009 3rd IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP).

[21]  José M. Bioucas-Dias,et al.  Fast Image Recovery Using Variable Splitting and Constrained Optimization , 2009, IEEE Transactions on Image Processing.

[22]  José M. Bioucas-Dias,et al.  A New TwIST: Two-Step Iterative Shrinkage/Thresholding Algorithms for Image Restoration , 2007, IEEE Transactions on Image Processing.

[23]  Junfeng Yang,et al.  A New Alternating Minimization Algorithm for Total Variation Image Reconstruction , 2008, SIAM J. Imaging Sci..

[24]  Rob Fergus,et al.  Fast Image Deconvolution using Hyper-Laplacian Priors , 2009, NIPS.

[25]  Michael Elad,et al.  Why Simple Shrinkage Is Still Relevant for Redundant Representations? , 2006, IEEE Transactions on Information Theory.

[26]  M. Lai,et al.  An Unconstrained $\ell_q$ Minimization with $0q\leq1$ for Sparse Solution of Underdetermined Linear Systems , 2011 .

[27]  Y. Nesterov.  Gradient methods for minimizing composite objective function , 2007 .

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