Loss functions for denoising compressed images: a comparative study

This paper faces the problem of denoising compressed images, obtained through a quantization in a known basis. The denoising is formulated as a variational inverse problem regularized by total variation, the emphasis being placed on the data-fidelity term which measures the distance between the noisy observation and the reconstruction. The paper introduces two new loss functions to jointly denoise and dequantize the corrupted image, which fully exploit the knowledge about the compression process, i.e., the transform and the quantization steps. Several numerical experiments demonstrate the effectiveness of the proposed loss functions and compare their performance with two more classical ones.