Solving Optimization Problems That Employ Structural Similarity As The Fidelity Measure

Many tasks in image processing are carried out by solving appropriate optimization problems. As is well known, the square of the Euclidian distance is widely used as a fitting term, even though it has been shown not to be the best choice in terms of quantifying visual quality. To overcome this problem, a number of papers have examined the use of the Structural Similarity Index Measure (SSIM) as a fidelity term. In this paper, we propose a general framework for solving optimization problems in which the SSIM is employed as a fidelity measure. Within the context of quasi-convex optimization, an algorithm is also introduced in order to solve such optimization problems.

[1]  Michael Elad,et al.  Image Denoising Via Sparse and Redundant Representations Over Learned Dictionaries , 2006, IEEE Transactions on Image Processing.

[2]  Mohamed-Jalal Fadili,et al.  Total Variation Projection With First Order Schemes , 2011, IEEE Transactions on Image Processing.

[3]  Marcus A. Magnor,et al.  Perception-based visual quality measures , 2011, 2011 IEEE Conference on Visual Analytics Science and Technology (VAST).

[4]  Ying Liu,et al.  Structural Similarity-Optimal Total Variation Algorithm for Image Denoising , 2014 .

[5]  Pascal Getreuer,et al.  Total Variation Deconvolution using Split Bregman , 2012, Image Process. Line.

[6]  Wen Gao,et al.  SSIM-Motivated Rate-Distortion Optimization for Video Coding , 2012, IEEE Transactions on Circuits and Systems for Video Technology.

[7]  Eero P. Simoncelli,et al.  Image quality assessment: from error visibility to structural similarity , 2004, IEEE Transactions on Image Processing.

[8]  Robert W. Heath,et al.  Design of Linear Equalizers Optimized for the Structural Similarity Index , 2008, IEEE Transactions on Image Processing.

[9]  M. Nikolova.  An Algorithm for Total Variation Minimization and Applications , 2004 .

[10]  Julien Mairal,et al.  Convex optimization with sparsity-inducing norms , 2011 .

[11]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[12]  Zhou Wang,et al.  Structural Similarity-Based Approximation of Signals and Images Using Orthogonal Bases , 2010, ICIAR.

[13]  Dominique Brunet,et al.  A Study of the Structural Similarity Image Quality Measure with Applications to Image Processing , 2012 .

[14]  Patrick L. Combettes,et al.  Image restoration subject to a total variation constraint , 2004, IEEE Transactions on Image Processing.

[15]  A. Bovik,et al.  A universal image quality index , 2002, IEEE Signal Processing Letters.

[16]  Zhou Wang,et al.  Image classification based on complex wavelet structural similarity , 2013, Signal Process. Image Commun..

[17]  Daniel Cremers,et al.  The Natural Vectorial Total Variation Which Arises from Geometric Measure Theory , 2012, SIAM J. Imaging Sci..

[18]  Edward R. Vrscay,et al.  SSIM-inspired image restoration using sparse representation , 2012, EURASIP Journal on Advances in Signal Processing.

[19]  Wen Gao,et al.  Perceptual Video Coding Based on SSIM-Inspired Divisive Normalization , 2013, IEEE Transactions on Image Processing.