Neural network have seen an explosion of interest over the last years and have been successfully applied across an extraordinary range of problem domains such as medicine, engineering, geology, physique, biology and especially image processing field. In image processing domain, the noise reduction is a very important task. Indeed, many approaches and methods have been developed and proposed in the literature. In this paper, we present a new restoration method for noisy images by minimizing the Total Variation (TV) under constraints using a multilayer neural network (MLP). The proposed method can restore degraded images and preserves the discontinuities. Effectiveness of our proposed approach is showed through the obtained results on different noisy images.