2,114 research outputs found
Wavelets and sparse methods for image reconstruction and classification in neuroimaging
This dissertation contributes to neuroimaging literature in the fields of compressed sensing magnetic resonance imaging (CS-MRI) and image-based detection of Alzheimer’s disease (AD). It consists of three main contributions, based on wavelets and sparse methods.
The first contribution is a method for wavelet packet basis optimisation for sparse approximation and compressed sensing reconstruction of magnetic resonance (MR) images of the brain. The proposed method is based on the basis search algorithm developed by Coifman and Wickerhauser, with a cost function designed specifically for compressed sensing. It is tested on MR images available from the Alzheimer’s Disease Neuroimaging Initiative (ADNI).
The second contribution consists of evaluating and comparing several sparse classification methods in an application to detection of AD based on positron emission tomography (PET) images of the brain. This comparison includes univariate feature selection, feature clustering and classifiers that automatically select a small subset of features due to their mathematical or algorithmic construction. The evaluation is based on PET images available from ADNI.
The third contribution is proposing an extension of wavelet-based scattering networks (originally proposed by Mallat and Bruna) to three-dimensional tomographic images. The proposed extension is evaluated as a feature representation in an application to detection of AD based on MR images available from ADNI.
There are several possible extensions of the work presented in this dissertation. The wavelet packet basis search method proposed in the first contribution can be improved to take into account the coherence between the sparse approximation basis and the sensing basis. The evaluation presented in the second contribution can be extended with additional algorithms to make it more comprehensive. The three-dimensional scattering networks that are the core part of the third contribution can be combined with other machine learning methods, such as manifold learning or deep convolutional neural networks.
As a whole, the methods proposed in this dissertation contribute to the work towards efficient screening for Alzheimer’s disease, by making MRI scans of the brain faster and helping to automate image analysis for AD detection.
The first contribution is a method for wavelet packet basis optimisation for sparse approximation and compressed sensing reconstruction of magnetic resonance (MR) images of the brain. The proposed method is based on the basis search algorithm developed by Coifman and Wickerhauser, with a cost function designed specifically for compressed sensing. It is tested on MR images available from the Alzheimer’s Disease Neuroimaging Initiative (ADNI).
The second contribution consists of evaluating and comparing several sparse classification methods in an application to detection of AD based on positron emission tomography (PET) images of the brain. This comparison includes univariate feature selection, feature clustering and classifiers that automatically select a small subset of features due to their mathematical or algorithmic construction. The evaluation is based on PET images available from ADNI.
The third contribution is proposing an extension of wavelet-based scattering networks (originally proposed by Mallat and Bruna) to three-dimensional tomographic images. The proposed extension is evaluated as a feature representation in an application to detection of AD based on MR images available from ADNI.
There are several possible extensions of the work presented in this dissertation. The wavelet packet basis search method proposed in the first contribution can be improved to take into account the coherence between the sparse approximation basis and the sensing basis. The evaluation presented in the second contribution can be extended with additional algorithms to make it more comprehensive. The three-dimensional scattering networks that are the core part of the third contribution can be combined with other machine learning methods, such as manifold learning or deep convolutional neural networks.
This dissertation contributes to neuroimaging literature in the fields of compressed sensing magnetic resonance imaging (CS-MRI) and image-based detection of Alzheimer’s disease (AD). It consists of three main contributions, based on wavelets and sparse methods.
The first contribution is a method for wavelet packet basis optimisation for sparse approximation and compressed sensing reconstruction of magnetic resonance (MR) images of the brain. The proposed method is based on the basis search algorithm developed by Coifman and Wickerhauser, with a cost function designed specifically for compressed sensing. It is tested on MR images available from the Alzheimer’s Disease Neuroimaging Initiative (ADNI).
The second contribution consists of evaluating and comparing several sparse classification methods in an application to detection of AD based on positron emission tomography (PET) images of the brain. This comparison includes univariate feature selection, feature clustering and classifiers that automatically select a small subset of features due to their mathematical or algorithmic construction. The evaluation is based on PET images available from ADNI.
The third contribution is proposing an extension of wavelet-based scattering networks (originally proposed by Mallat and Bruna) to three-dimensional tomographic images. The proposed extension is evaluated as a feature representation in an application to detection of AD based on MR images available from ADNI.
There are several possible extensions of the work presented in this dissertation. The wavelet packet basis search method proposed in the first contribution can be improved to take into account the coherence between the sparse approximation basis and the sensing basis. The evaluation presented in the second contribution can be extended with additional algorithms to make it more comprehensive. The three-dimensional scattering networks that are the core part of the third contribution can be combined with other machine learning methods, such as manifold learning or deep convolutional neural networks.
As a whole, the methods proposed in this dissertation contribute to the work towards efficient screening for Alzheimer’s disease, by making MRI scans of the brain faster and helping to automate image analysis for AD detection.Open Acces
Sharp Oracle Inequalities for Aggregation of Affine Estimators
We consider the problem of combining a (possibly uncountably infinite) set of
affine estimators in non-parametric regression model with heteroscedastic
Gaussian noise. Focusing on the exponentially weighted aggregate, we prove a
PAC-Bayesian type inequality that leads to sharp oracle inequalities in
discrete but also in continuous settings. The framework is general enough to
cover the combinations of various procedures such as least square regression,
kernel ridge regression, shrinking estimators and many other estimators used in
the literature on statistical inverse problems. As a consequence, we show that
the proposed aggregate provides an adaptive estimator in the exact minimax
sense without neither discretizing the range of tuning parameters nor splitting
the set of observations. We also illustrate numerically the good performance
achieved by the exponentially weighted aggregate
A Panorama on Multiscale Geometric Representations, Intertwining Spatial, Directional and Frequency Selectivity
The richness of natural images makes the quest for optimal representations in
image processing and computer vision challenging. The latter observation has
not prevented the design of image representations, which trade off between
efficiency and complexity, while achieving accurate rendering of smooth regions
as well as reproducing faithful contours and textures. The most recent ones,
proposed in the past decade, share an hybrid heritage highlighting the
multiscale and oriented nature of edges and patterns in images. This paper
presents a panorama of the aforementioned literature on decompositions in
multiscale, multi-orientation bases or dictionaries. They typically exhibit
redundancy to improve sparsity in the transformed domain and sometimes its
invariance with respect to simple geometric deformations (translation,
rotation). Oriented multiscale dictionaries extend traditional wavelet
processing and may offer rotation invariance. Highly redundant dictionaries
require specific algorithms to simplify the search for an efficient (sparse)
representation. We also discuss the extension of multiscale geometric
decompositions to non-Euclidean domains such as the sphere or arbitrary meshed
surfaces. The etymology of panorama suggests an overview, based on a choice of
partially overlapping "pictures". We hope that this paper will contribute to
the appreciation and apprehension of a stream of current research directions in
image understanding.Comment: 65 pages, 33 figures, 303 reference
Low Complexity Regularization of Linear Inverse Problems
Inverse problems and regularization theory is a central theme in contemporary
signal processing, where the goal is to reconstruct an unknown signal from
partial indirect, and possibly noisy, measurements of it. A now standard method
for recovering the unknown signal is to solve a convex optimization problem
that enforces some prior knowledge about its structure. This has proved
efficient in many problems routinely encountered in imaging sciences,
statistics and machine learning. This chapter delivers a review of recent
advances in the field where the regularization prior promotes solutions
conforming to some notion of simplicity/low-complexity. These priors encompass
as popular examples sparsity and group sparsity (to capture the compressibility
of natural signals and images), total variation and analysis sparsity (to
promote piecewise regularity), and low-rank (as natural extension of sparsity
to matrix-valued data). Our aim is to provide a unified treatment of all these
regularizations under a single umbrella, namely the theory of partial
smoothness. This framework is very general and accommodates all low-complexity
regularizers just mentioned, as well as many others. Partial smoothness turns
out to be the canonical way to encode low-dimensional models that can be linear
spaces or more general smooth manifolds. This review is intended to serve as a
one stop shop toward the understanding of the theoretical properties of the
so-regularized solutions. It covers a large spectrum including: (i) recovery
guarantees and stability to noise, both in terms of -stability and
model (manifold) identification; (ii) sensitivity analysis to perturbations of
the parameters involved (in particular the observations), with applications to
unbiased risk estimation ; (iii) convergence properties of the forward-backward
proximal splitting scheme, that is particularly well suited to solve the
corresponding large-scale regularized optimization problem
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