Total variation-wavelet-curvelet regularized optimization for image restoration

Solving image restoration problems requires the use of efficient regularization terms that represent certain features of the original image. Natural images generally have three features: smooth regions, textures, and edges. However, conventional optimization techniques typically adopt only one or two reg-ularization terms, and there is no regularized optimization problem that represents such features exactly and completely. By applying three regularization terms corresponding to these three features, we can restore images more efficiently in ill-posed conditions. We propose here total variation (TV), wavelet, and curvelet regularized optimization for image restoration. These regularization terms correspond exactly to the smooth region, textures, and edges. We also present an algorithm to solve the proposed optimization problem, and ensure its convergence. Experimental results revealed that our optimization technique was more effective for image restoration than conventional methods.