Manifold Learning via the Principle Bundle Approach

In this paper, we propose a novel principal bundle model and apply it to the image denoising problem. This model is based on the fact that the patch manifold admits canonical groups actions such as rotation. We introduce an image denoising algorithm, called the diffusive vector non-local Euclidean median (dvNLEM), by combining the traditional nonlocal Euclidean median (NLEM), the rotational structure in the patch space, and the diffusion distance. A theoretical analysis of dvNLEM, as well as the traditional nonlocal Euclidean median (NLEM), is provided to explain why these algorithms work. In particular, we show how accurate we could obtain the true neighbors associated with the rotationally invariant distance (RID) and Euclidean distance in the patch space when noise exists, and how we could apply the diffusion geometry to stabilize the selected metric. The dvNLEM is applied to an image database of 1,361 images and a comparison with the NLEM is provided. Different image quality assessments based on the error-sensitivity or the human visual system are applied to evaluate the performance

MRI noise estimation and denoising using non-local PCA

NOTICE: this is the author’s version of a work that was accepted for publication in Medical Image AnalysisChanges resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Medical Image Analysis, [Volume 22, Issue 1, May 2015, Pages 35–47] DOI 10.1016/j.media.2015.01.004This paper proposes a novel method for MRI denoising that exploits both the sparseness and self-similarity properties of the MR images. The proposed method is a two-stage approach that first filters the noisy image using a non local PCA thresholding strategy by automatically estimating the local noise level present in the image and second uses this filtered image as a guide image within a rotationally invariant non-local means filter. The proposed method internally estimates the amount of local noise presents in the images that enables applying it automatically to images with spatially varying noise levels and also corrects the Rician noise induced bias locally. The proposed approach has been compared with related state-of-the-art methods showing competitive results in all the studied cases.We are grateful to Dr. Matteo Mangioni and Dr. Alessandro Foi for their help on running their BM4D method in our comparisons. We want also to thank Dr. Luis Marti-Bonmati and Dr. Angel Alberich-Bayarri from Quiron Hospital of Valencia for providing the real clinical data used in this paper. This study has been carried out with financial support from the French State, managed by the French National Research Agency (ANR) in the frame of the Investments for the future Programme IdEx Bordeaux (ANR-10-IDEX-03-02), Cluster of excellence CPU and TRAIL (HR-DTI ANR-10-LABX-57).Manjón Herrera, JV.; Coupé, P.; Buades, A. (2015). MRI noise estimation and denoising using non-local PCA. Medical Image Analysis. 22(1):35-47. doi:10.1016/j.media.2015.01.004S354722

Adaptive Representations for Image Restoration

In the �eld of image processing, building good representation models for natural images is crucial for various applications, such as image restora- tion, sampling, segmentation, etc. Adaptive image representation models are designed for describing the intrinsic structures of natural images. In the classical Bayesian inference, this representation is often known as the prior of the intensity distribution of the input image. Early image priors have forms such as total variation norm, Markov Random Fields (MRF), and wavelets. Recently, image priors obtained from machine learning tech- niques tend to be more adaptive, which aims at capturing the natural image models via learning from larger databases. In this thesis, we study adaptive representations of natural images for image restoration. The purpose of image restoration is to remove the artifacts which degrade an image. The degradation comes in many forms such as image blurs, noises, and artifacts from the codec. Take image denoising for an example. There are several classic representation methods which can generate state- of-the-art results. The �rst one is the assumption of image self-similarity. However, this representation has the issue that sometimes the self-similarity assumption would fail because of high noise levels or unique image contents. The second one is the wavelet based nonlocal representation, which also has a problem in that the �xed basis function is not adaptive enough for any arbitrary type of input images. The third is the sparse coding using over- complete dictionaries, which does not have the hierarchical structure that is similar to the one in human visual system and is therefore prone to denoising artifacts. My research started from image denoising. Through the thorough review and evaluation of state-of-the-art denoising methods, it was found that the representation of images is substantially important for the denoising tech- nique. At the same time, an improvement on one of the nonlocal denoising method was proposed, which improves the representation of images by the integration of Gaussian blur, clustering and Rotationally Invariant Block Matching. Enlightened by the successful application of sparse coding in compressive sensing, we exploited the image self-similarity by using a sparse representation based on wavelet coe�cients in a nonlocal and hierarchical way, which generates competitive results compared to the state-of-the-art denoising algorithms. Meanwhile, another adaptive local �lter learned by Genetic Programming (GP) was proposed for e�cient image denoising. In this work, we employed GP to �nd the optimal representations for local im- age patches through training on massive datasets, which yields competitive results compared to state-of-the-art local denoising �lters. After success- fully dealt with the denoising part, we moved to the parameter estimation for image degradation models. For instance, image blur identi�cation uses deep learning, which has recently been proposed as a popular image repre- sentation approach. This work has also been extended to blur estimation based on the fact that the second step of the framework has been replaced with general regression neural network. In a word, in this thesis, spatial cor- relations, sparse coding, genetic programming, deep learning are explored as adaptive image representation models for both image restoration and parameter estimation. We conclude this thesis by considering methods based on machine learning to be the best adaptive representations for natural images. We have shown that they can generate better results than conventional representation mod- els for the tasks of image denoising and deblurring