Patch based methods give some of the best denoising results. Their theoretical performances are still unexplained
mathematically. We propose a novel insight of NL-Means based on an aggregation point of view. More precisely,
we describe the framework of PAC-Bayesian aggregation, show how it allows to derive some new patch based
methods and to characterize their theoretical performances, and present some numerical experiments.
This article presents the first adaptive quasi minimax estimator for geometrically regular images in the white noise
model. This estimator is computed using a thresholding in an adapted orthogonal bandlet basis optimized for the noisy
observed image. In order to analyze the quadratic risk of this best basis denoising, the thresholding in an orthogonal
bandlets basis is recasted as a model selection process. The resulting estimator is computed with a fast algorithm whose
theoretical performance can be derived. This efficiency is confirmed through numerical experiments on natural images.
This paper introduces a new class of bases, called bandelet bases,
which decompose the image along vectors that are elongated in the
direction of a geometric flow. This geometric flow indicates the
direction in which the image grey levels have regular variations.
The image decomposition in a bandelet basis is implemented with
a fast subband filtering algorithm. Bandelet bases lead to optimal approximation rates for geometrically regular images. For image compression, the bandelet basis geometry is optimized with a fast best basis algorithm. Comparisons are made for image compression with wavelet basis.