A Total Variation Model for Multiplicative Noise Removal and Blind Inpainting

Multiplicative noise and artifacts removal are two important tasks in the field of image processing. In some applications, multiplicative noise and intensity missing always exist at the same time. In this paper, we introduce a new variational model based on total variation and l
₀
norm for simultaneously removing the multiplicative noise, estimating the location of missing pixels, and filling in them. To be specific, we use the total variation to regularize the estimated image, and use the l
₀
norm to make the missing pixels to be sparse. Moreover, based on the Gamma noise assumption, the data fidelity term is given by a new forward description of the degraded process. Then, for solving the proposed model, we develop an algorithm by exploiting the alternating direction method of multipliers (ADMM). The experiments validate that the proposed method can effectively restore the synthetic and real images damaged by the multiplicative Gamma noise and artifacts, and meanwhile estimate the location of missing pixels.