Image decomposition using optimally sparse representations and a variational approach

In this paper, a new method which combines the basis pursuit denoising algorithm (BPDN) and the total variation (TV) regularization scheme is presented for separating images into texture and cartoon parts. It is a modification of the model [1]. In this process, two appropriate dictionaries are used, one for the representation of texture parts-the dual tree complex wavelet transform (DT CWT) and the other for the cartoon parts-the second generation of curvelet transform. To direct the separation process and reduce the pseudo-Gibbs phenomenon, the curvelet transform is followed by a projected regularization method for cartoon parts. Experimental results show that new method cannot only decompose better for a given image but also reduce the runtime, in comparison to the MCA approach.

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

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

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

[4]  N. Kingsbury.  Image processing with complex wavelets , 1999, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[5]  E. Candès,et al.  Curvelets: A Surprisingly Effective Nonadaptive Representation for Objects with Edges , 2000 .

[6]  Yves Meyer,et al.  Oscillating Patterns in Image Processing and Nonlinear Evolution Equations: The Fifteenth Dean Jacqueline B. Lewis Memorial Lectures , 2001 .

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

[8]  Stanley Osher,et al.  Image Decomposition and Restoration Using Total Variation Minimization and the H1 , 2003, Multiscale Model. Simul..

[9]  Yongjian Hu,et al.  Image Fusion Based Visible Watermarking Using Dual-Tree Complex Wavelet Transform , 2003, IWDW.

[10]  Jacques Froment,et al.  Reconstruction of Wavelet Coefficients Using Total Variation Minimization , 2002, SIAM J. Sci. Comput..

[11]  E. Candès,et al.  New tight frames of curvelets and optimal representations of objects with piecewise C2 singularities , 2004 .

[12]  Luminita A. Vese,et al.  Image Decomposition Using Total Variation and div(BMO) , 2005, Multiscale Model. Simul..

[13]  Emily B. Fox,et al.  Detection and Localization of Aerosol Releases from Sparse Sensor Measurements , 2005 .

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

[15]  L. Lieu,et al.  Image Restoration and Decomposition via Bounded Total Variation and Negative Hilbert-Sobolev Spaces , 2008 .