This thesis explores the last evolutions on image denoising, and attempts to set a new and more coherent background regarding the different techniques involved. In consequence, it also presents a new image denoising algorithm with minimal artifacts and the best PSNR performance known so far.

A first result that is presented is DA3D, a frequency-based guided denoising algorithm inspired form DDID [Knaus-Zwicker 2013]. This algorithm achieves good results not only in terms of PSNR, but also (and especially) with respect to visual quality. DA3D works particularly well on enhancing the textures of the images and removing staircasing effects. DA3D works on top of another denoising algorithm, that is used as a guide, and almost always improve its results. In this way, frequency-based denoising can be applied on top of patch-based denoising algorithms, resulting on a hybrid method that keeps the strengths of both. The experiments demonstrate that, contarily to what was thought, frequency-based denoising can beat state-of-the-art algorithms without presenting artifacts.

In this work DA3D is presented, and ad-hoc shrinkage curves are computed depending on the algorithm used as guide.

The second result presented is Multi-Scale Denoising, a multiscale framework applicable to any denoising algorithm. A qualitative analysis shows that current denoising algorithms behave better on high-frequency noise. This is due to the relatively small size of patches and search windows used in these single scale algorithms. Instead of enlarging those windows, that can cause other sorts of problems, the work proposes to decompose the image on a pyramid, with the aid of the Discrete Cosine Transformation.

We introduce a new reconstruction scheme in the pyramid avoiding the appearance of ringing artifacts. This method removes most of the low-frequency noise, and improves both PSNR and visual results for smooth and textured areas.

A third main issue addressed in this thesis is the evaluation of denoising algorithms. Experiences indicate that the PSNR is not always a good indicator of visual quality for denoising algorithms, since, for example, an artifact on a smooth area can be more noticeable than a subtle alteration in a texture. A new metric is proposed to improve on this matter. Instead of a single value, a "Smooth PNSR'' and a "Texture PSNR'' are presented, to  measure the result of an algorithm for those two types of image regions. We claim that a denoising algorithm, in order to be considered acceptable, must at least perform well with respect to both metrics. Following this claim, an analysis of current algorithms is performed, and it is compared with the combined results of the Multi-Scale Framework and DA3D.

We found that the optimal solution for image denoising is the application of a frequency shrinkage, applied to regular regions only, while a multiscale patch based method serves as guide.This seems to resolve a long standing question for which DDID gave the first clue: what is the respective role of frequency shrinkage and self-similarity based methods for image denoising? We describe an image denoising algorithm that seems to perform better in quality and PSNR than any other based on the right combination of both denoising principles.

In our last contribution, a study on the feasibility of external denoising is carried out, where images are denoised by means of a big database of external noiseless patches. This follows a work of Levin and Nadler, in 2011, that claims that optimal Bayesian patch denoising is reachable by a simple integral formula provided it is applied to a gigantic and representative patch database.

We prove by a mathematical argument combined with empirical observations on the space of patches that this space can be factorized, thereby reducing considerably the number of patches needed in order to compute the integral on the space of patches.