TWO CURVELETS VARIATIONAL MODELS DEPEND ON DECOMPOSITION SPACES

Abstract

Wavelet has become an appealing image processing technique, due to the fact that the sparseness of wavelet expansion is equivalent to smoothness measure in Besov spaces so that the regularization of image can be performed by manipulating its wavelet coefficients. Unfortunately, wavelets have good performance especially at representing point singularities, but they fail to efficiently represent object edges. As one of computational harmonic analysis tools, curvelets have an essentially optimal representation of objects which is C2 away from a C2 edge. In this paper, we first apply constraint of curvelet-type decomposition spaces as a regularizing term to variational model for image denoising. Based on the equivalent relationship between semi-norm of curvelet-type decomposition spaces and the weighted curvelet coefficients, solution to the proposed model approximately equals to different curvelet shrinkages. As a second contribution, we also propose another image restoration model from image decomposition point of view. Furthermore, an equivalent theorem of two proposed models is given. Finally, the experiment results show the superiority of proposed models over traditional wavelet-based ones.