Poisson noise removal based on non-convex hybrid regularizers

The presence of TV regularizer always induces an unsatisfactory staircase effect. To overcome the staircase while better sustaining edge information, this work proposes a novel model for Poisson noise removal. The model is based on non-convex mixed regularizers, which involves introducing a non-convex penalty into a composition of the total variation and the higher-order total variation. The iterative reweighted $l_1$ algorithm was used to convert the non-convex model into a convex one. The classic alternating direction method of multipliers was then employed to obtain approximate solutions of the model. When applying this model to degraded images contaminated by Poisson noise of medium to high intensity, its performance in noise suppression was tested. The regularizer was compared with others in the terms of the visual effect of the picture, time cost, and several commonly accepted quantitative indicators for evaluation, such as peak signal-to-noise ratio, feature similarity index and structural similarity index. Numerical experiments showed that the present model not only eliminates block artifacts but also retains sharp edges.