cam11-32 Minimization for Wavelet Frame Based Image Restoration.pdf

0 Minimization for Wavelet Frame Based Image Restoration Yong Zhang ∗ Bin Dong † Zhaosong Lu‡ May 12, 2011 Abstract The theory of (tight) wavelet frames has been extensively studied in the past twenty years and they are currently widely used for image restoration and other image processing and analysis problems. The success of wavelet frame based models, including balanced approach [20, 8] and analysis based approach [13, 32, 49], is due to their capability of sparsely approximating piecewise smooth functions like images. Motivated by the balanced approach and analysis based approach, we shall propose a wavelet frame based 0 minimization model, where the 0 of the frame coefficients are penalized. We adapt the penalty decomposition (PD) method of [40] to solve the proposed optimization problem. Numerical results showed that the proposed model solved by the PD method can generate images with better quality than those obtained by either analysis based approach or balanced approach in terms of restoring sharp features as well as maintaining smoothness of the recovered images. Some convergence analysis of the PD method will also be provided. Key words: 0 minimization, wavelet frame, image restoration. 1 Introduction Mathematics has been playing an important role in the modern developments of image processing and analysis. Image restoration, including image denoising, deblurring, inpainting, tomography, etc., is one of the most important areas in image processing and analysis. Its major purpose is to enhance the quality of a given image that is corrupted in various ways during the process of imaging, acquisition and communication, and enab