Research On Image Restoration Based On Coordinate Descent Method

As a fundamental problem of computer vision, a vast amount of researchers havedevoted to the research on image restoration and proposed a variety of models andcorresponding algorithms to solve them. Image restoration is the most basic problemof high level vision application, e.g. object recognition, and thus it is necessary to beof high effectiveness and efficience for the restoration models and methods. Totalvariation (TV) image restoration (TVIR), along with its simplicity and effectvieness,is most widely applied into various image restoration prblems. Because of itsnon-smoothness of TV regularizer, TVIR can not be solved by conventionaloptimization algorithms,.requiring more novel algorithms to solve it.In this paper, we propose a novel strategy to solve TVIR based on CoordinateDescent method (CoD). The basic idea of CoD is to decompose the original probleminto scalar optimization subproblems with respect to single coordinate, which can besolved efficiently, and the original problem can be solved within a reasonablesweeping pattern. We first solve the anisotropic TV image denoising problem withfidelity term being of1-norm via CoD, resulting in a algorithm named CoDMedian,which is actually a iterative weighted median filter. In the experiments of denoisingsalt and pepper noise, CoDMedian performed much better than normal medianfilters. Then, we applied CoD to solve the normal anisotropic TV image denoisingproblem with fidelity term being of2-norm, along with a cyclic sweeping pattern,resulting in a CoD based denoising algorithm, i.e., CoDenoise. By introducing anapproximation of isotropic TV regularizer, CoDenoise is also extended to isotropicTV image denoising problem. CoDenoise is comparable or superior to thewell-known algorithm, i.e., Chambolle, assessed by CPU running time,Peak-signal-to-noise-ratio (PSNR) and Complex Wevelet Sructural Similarity(SSIM).Meanwhile, by using alternating direction method of multipliers (ADMM), theTVIR, e.g., image deblurring, can be solved, splitting it into several subproblems,including a denoisng subproblem, which is solved by CoDenoise in our algorithm,named CoDALM. The experimental results of restoration from blurred and noisyimages inform that, CoDALM is comparable or superior to existing algorithms, e.g.,TwIST, FISTA and SALSA, in terms of restoration resualts amd is of higherefficiency in terms of computation time..We also extended the CoDenoise algorithm to directly solve delblurringproblem, rather than splitting it into subproblems. Similarly, it can be decomposed into sacalr optimization subproblems with respcet to single coordinate with the sameform of TV image denoising problem. Different from cyclic sweeping patternadopted in CoDMedian and CoDenoise, we proposed a novel random countersweeping pattern, resulting in CoDescent algorithm for TVIR. And in the deblurringexperiments, we demonstrated the restoraion results of CoDescent compared withTwIST, FISTA, SALSA and CoDALM, perfoming better or comparable, in terms ofrestoration effectiveness.