Simultaneous cartoon and texture reconstruction for image restoration by bivariate function

Abstract

We study the simultaneous cartoon and texture reconstruction problem. We propose a new model to approximate the cartoon and texture part by a sparse linear combination of some bases. A bivariate function is employed as the cost function. One of the variables is the decomposition image and the other is the sparse representation of the decomposition image. An alternating minimization algorithm is used to solve the minimization problem. We prove that the algorithm converges for both the l ₁-norm and the l ₀-norm. Numerical simulations are given to illustrate the efficiency of our method.

Keywords:

• image
• sparse
• total variation
• cartoon
• texture

AMS Subject Classifications::

• 68010
• 94A08

Acknowledgements

Research supported in part by NSFC Grant No. 60702030, NSF of Guangdong Grant No. 9251064201000009, CUHK400508 and the Wavelets and Information Processing Programme of the Centre for Wavelets, Approximation and Information Processing and Temasek Laboratories, National University of Singapore, Singapore.