A combined first and fractional order regularization method for mixed Poisson-white spike noisy image restoration

In this paper we study the problem of restoring images affected by mixed Poisson-Square Cauchy noise. A multi-convex variational model is derived by integrating infimal convolution likelihood into a process of joint maximum a posteriori estimation, where a modified four-directional fractional-order total variation is united with the first order total variation to characterize the image prior. To solve the proposed model numerically, a block coefficient descent based algorithm is derived, in which variable splitting and alternating direction minimization of multipliers are utilized along with anisotropic diffusion and additive operator splitting to gain efficiency and quality. The obtained numerical results are compared with results obtained from two other total variation regularized models with different fidelities. The numerical discuss confirms the flexibility and validity of the proposed model.