A HYBRID ALTERNATING MINIMIZATION ALGORITHM FOR STRUCTURED CONVEX OPTIMIZATION PROBLEMS WITH APPLICATION IN POISSONIAN IMAGE PROCESSING

Motivated by applications in image processing, we consider a class of structured convex optimization problems in which the objective function is the sum of two component functions with favorable structures, and, furthermore, both of which are composed with linear operators. In particular, to recover images degraded by Poisson noise, the famous Kullback-Leibler divergence can be adopted in data fitting, in which case one component function is separable, strongly convex and easy to minimize. The other component function usually allows an easily computable proximal operator. We then propose, analyze and test a hybrid algorithm particularly tailored for the underlying model structures, which can be viewed as a combination of the famous alternating minimization algorithm of Tseng and the alternating direction method of multipliers. Under mild conditions, global iterate convergence as well as ergodic O(1/N) sublinear convergence rate results measured by the function value residual and constraint violation of a reformulated constrained optimization problem are established, where N denotes the iteration counter. The proposed algorithm is applied to fractional-order total variation regularized image denoising and deblurring problems, where the noise obeys Poisson distribution. Our experimental results demonstrate the effectiveness of the proposed algorithm.

Automated summary

This paper considers a class of structured convex optimization problems in image processing, proposes a hybrid algorithm tailored for these problems, and tests its effectiveness under Poisson noise.