A variational approach to denoising problem

A digital image can be created by different digital devices, such as digital cameras, X-ray scanners, etc. In practice, such devices can give unexpected defects, for example, noise. The Gaussian noise and Poisson noise are very important, but their combination is important too. This mixed noise usually appears in electronic microscopic images, in aerospace images, etc. Our goal is to combine ROF model (for Gaussian noise removal) and modified ROF model (for Poisson noise removal) to create new model that can treat this combination effectively. Our model will treat this combination with considering proportion of noise between them.

Sparsity Based Poisson Denoising with Dictionary Learning

The problem of Poisson denoising appears in various imaging applications, such as low-light photography, medical imaging and microscopy. In cases of high SNR, several transformations exist so as to convert the Poisson noise into an additive i.i.d. Gaussian noise, for which many effective algorithms are available. However, in a low SNR regime, these transformations are significantly less accurate, and a strategy that relies directly on the true noise statistics is required. A recent work by Salmon et al. took this route, proposing a patch-based exponential image representation model based on GMM (Gaussian mixture model), leading to state-of-the-art results. In this paper, we propose to harness sparse-representation modeling to the image patches, adopting the same exponential idea. Our scheme uses a greedy pursuit with boot-strapping based stopping condition and dictionary learning within the denoising process. The reconstruction performance of the proposed scheme is competitive with leading methods in high SNR, and achieving state-of-the-art results in cases of low SNR.Comment: 13 pages, 9 figure