Multiscale Noise Estimation and Removal for Digital Images

Any image, digital or analog, contains not only information from the scene being photographed but also external interferences known as noise. The resulting image is the combination of the ideal image without noise with noise itself. The "ideal image without noise" is a mathematical abstraction and it is not available in reality. Thus, it is needed methods that given only the degraded image are capable to properly characterize noise. This characterization using the noisy image is known as blind noise estimation since it does not use any additional information out the the noisy image. Once noise has been properly characterized, the next step is to obtain a version of the image which is as close as possible to the ideal image. This process is known as blind denoising, since the ideal image is not available. Denoising methods exploit the property of auto-similarity of the small blocks that form the image to infer the geometry of the blocks of the ideal image. Denoising is a process guided by previous noise estimation. Given that both noise estimation and denoising are performed blindly, it is important that noise characterization is as complete as possible. In this thesis several techniques for noise estimation are discussed, from the simplest which just consider homoscedastic noise, through those which consider the Poissonian model, to finally the new technique that we propose to obtain a complex noise model that depends on both intensity and frequency. Regarding denoising, this thesis is mainly focuses on Bayesian techniques. The thesis finally reaches with the presentation of the Noise Clinic, the tool which we propose for automatic noise estimation and denoising. The Noise Clinic combines the automatic estimation of a complex noise model with its elimination at each of the scales of the image. This allows to restore a large typology of images, including those compressed with JPEG