A non-monotone proximal point method for image reconstruction using non-convex total variation models

Reconstructing images contaminated by noise is of fundamental importance in the data preprocessing stages, especially in digital image processing applications. In most practical applications involving image acquisition, the noises introduced in this process are of a known nature, with the most common being additive white Gaussian noise. In this context, continuous optimization algorithms have gained importance, such as the proximal point method (PPM) when applied to image denoising and filtering tasks. In this work, we propose a boosted version of the PPM for image denoising, called nmPPMDC, using a non-convex Total Variation model. The results obtained show that, with black and white images, nmPPMDC recovers images with less CPU time than PPM and that the convex model and, regarding SSIM and PSNR, have similar performance to known techniques such as DCA, BDCA and nmBDCA. nmPPMDC has the best CPU time, outperforming DCA and PPM in 83.33% of the experiments and the FISTA and BDCA techniques in all tests. The tests with medical images show that nmPPMDC with a non-convex model is more likely to obtain good results than the convex model, in addition to showing the superiority of nmPPMDC in relation to PPM, both in quality and CPU time.