A new approach in decomposition over multiple-overcomplete dictionaries with application to image inpainting

Recently, great attention was intended toward overcomplete dictionaries and the sparse representations they can provide. In a wide variety of signal processing problems, sparsity serves a crucial property leading to high performance. Decomposition of a given signal over two or more dictionaries with sparse coefficients is investigated in this paper. This kind of decomposition is useful in many applications such as inpainting, denoising, demosaicing, speech source separation, high-quality zooming and so on. This paper addresses a novel technique of such a decomposition and investigates this idea through inpainting of images which is the process of reconstructing lost or deteriorated parts of images or videos.When samples are missed in an image, the the original sparsity level in representing coefficients is changed, so with an iterative method we can estimate the original level. Simulations are presented to demonstrate the validation of our approach.

[1]  Paul Tseng,et al.  Block coordinate relaxation methods for nonparamatric signal denoising , 1998, Defense, Security, and Sensing.

[2]  Michael Elad,et al.  Submitted to Ieee Transactions on Image Processing Image Decomposition via the Combination of Sparse Representations and a Variational Approach , 2022 .

[3]  Jeremy S. De Bonet,et al.  Multiresolution sampling procedure for analysis and synthesis of texture images , 1997, SIGGRAPH.

[4]  Guillermo Sapiro,et al.  Simultaneous structure and texture image inpainting , 2003, IEEE Trans. Image Process..

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

[6]  Alexei A. Efros,et al.  Texture synthesis by non-parametric sampling , 1999, Proceedings of the Seventh IEEE International Conference on Computer Vision.

[7]  Stanley Osher,et al.  Modeling Textures with Total Variation Minimization and Oscillating Patterns in Image Processing , 2003, J. Sci. Comput..

[8]  Christian Jutten,et al.  Image Denoising Using Sparse Representations , 2009, ICA.

[9]  D. Donoho,et al.  Simultaneous cartoon and texture image inpainting using morphological component analysis (MCA) , 2005 .

[10]  G. Aubert,et al.  Image decomposition: application to textured images and SAR images , 2003 .

[11]  Guillermo Sapiro,et al.  Image inpainting , 2000, SIGGRAPH.

[12]  Christian Jutten,et al.  A Fast Approach for Overcomplete Sparse Decomposition Based on Smoothed $\ell ^{0}$ Norm , 2008, IEEE Transactions on Signal Processing.

[13]  D. Donoho,et al.  Atomic Decomposition by Basis Pursuit , 2001 .