Hyperspectral (HS) imaging, which consists of acquiring a same scene in several hundreds of contiguous spectral bands (a three dimensional data cube), has opened a new range of relevant applications, such as target detection [MS02], classification [C.-03] and spectral unmixing [BDPD+12]. However, while HS sensors provide abundant spectral information, their spatial resolution is generally more limited. Thus, fusing the HS image with other highly resolved images of the same scene, such as multispectral (MS) or panchromatic (PAN) images is an interesting problem. The problem of fusing a high spectral and low spatial resolution image with an auxiliary image of higher spatial but lower spectral resolution, also known as multi-resolution image fusion, has been explored for many years [AMV+11]. From an application point of view, this problem is also important as motivated by recent national programs, e.g., the Japanese next-generation space-borne ...

In this doctoral thesis several scale-free texture segmentation procedures based on two fractal attributes, the Hölder exponent, measuring the local regularity of a texture, and local variance, are proposed.A piecewise homogeneous fractal texture model is built, along with a synthesis procedure, providing images composed of the aggregation of fractal texture patches with known attributes and segmentation. This synthesis procedure is used to evaluate the proposed methods performance.A first method, based on the Total Variation regularization of a noisy estimate of local regularity, is illustrated and refined thanks to a post-processing step consisting in an iterative thresholding and resulting in a segmentation.After evidencing the limitations of this first approach, deux segmentation methods, with either "free" or "co-located" contours, are built, taking in account jointly the local regularity and the local variance.These two procedures are formulated as convex nonsmooth functional minimization problems.We ...

The solution to many image restoration and reconstruction problems is often defined as the minimizer of a penalized criterion that accounts simultaneously for the data and the prior. This thesis deals more specifically with the minimization of edge-preserving penalized criteria. We focus on algorithms for large-scale problems. The minimization of penalized criteria can be addressed using a half-quadratic approach (HQ). Converging HQ algorithms have been proposed. However, their numerical cost is generally too high for large-scale problems. An alternative is to implement inexact HQ algorithms. Nonlinear conjugate gradient algorithms can also be considered using scalar HQ algorithms for the line search (NLCG+HQ1D). Some issues on the convergence of the aforementioned algorithms remained open until now. In this thesis we : - Prove the convergence of inexact HQ algorithms and NLCG+HQ1D. - Point out strong links between HQ algorithms and NLCG+HQ1D. ...

Multisensor data fusion technology combines data and information from multiple sensors to achieve improved accuracies and better inference about the environment than could be achieved by the use of a single sensor alone. In this dissertation, we propose parametric and nonparametric multisensor data fusion algorithms with a broad range of applications. Image registration is a vital first step in fusing sensor data. Among the wide range of registration techniques that have been developed for various applications, mutual information based registration algorithms have been accepted as one of the most accurate and robust methods. Inspired by the mutual information based approaches, we propose to use the joint R´enyi entropy as the dissimilarity metric between images. Since the R´enyi entropy of an image can be estimated with the length of the minimum spanning tree over the corresponding graph, the proposed information-theoretic registration ...

The abundance of large and heterogeneous systems is rendering contemporary data more pervasive, intricate, and with a non-regular structure. With classical techniques facing troubles to deal with the irregular (non-Euclidean) domain where the signals are defined, a popular approach at the heart of graph signal processing (GSP) is to: (i) represent the underlying support via a graph and (ii) exploit the topology of this graph to process the signals at hand. In addition to the irregular structure of the signals, another critical limitation is that the observed data is prone to the presence of perturbations, which, in the context of GSP, may affect not only the observed signals but also the topology of the supporting graph. Ignoring the presence of perturbations, along with the couplings between the errors in the signal and the errors in their support, can drastically hinder ...

System identification studies how to construct mathematical models for dynamical systems from the input and output data, which finds applications in many scenarios, such as predicting future output of the system or building model based controllers for regulating the output the system. Among many other methods, convex optimization is becoming an increasingly useful tool for solving system identification problems. The reason is that many identification problems can be formulated as, or transformed into convex optimization problems. This transformation is commonly referred to as the convexification technique. The first theme of the thesis is to understand the efficacy of the convexification idea by examining two specific examples. We first establish that a l1 norm based approach can indeed help in exploiting the sparsity information of the underlying parameter vector under certain persistent excitation assumptions. After that, we analyze how the nuclear ...

This work is focused on the processing of multichannel and multisource audio signals. From an audio mixture of several audio sources recorded in a reverberant room, we wish to es- timate the acoustic responses (a.k.a. mixing filters) between the sources and the microphones. To solve this inverse problem one need to take into account additional hypotheses on the nature of the acoustic responses. Our approach consists in first identifying mathematically the neces- sary hypotheses on the acoustic responses for their estimation and then building cost functions and algorithms to effectively estimate them. First, we considered the case where the source signals are known. We developed a method to estimate the acoustic responses based on a convex regularization which exploits both the temporal sparsity of the filters and the exponentially decaying envelope. Real-world experi- ments confirmed the effectiveness of this method ...

Reverberation consists of a complex acoustic phenomenon that occurs inside rooms. Many audio signal processing methods, addressing source localization, signal enhancement and other tasks, often assume absence of reverberation. Consequently, reverberant environments are considered challenging as state-ofthe-art methods can perform poorly. The acoustics of a room can be described using a variety of mathematical models, among which, physical models are the most complete and accurate. The use of physical models in audio signal processing methods is often non-trivial since it can lead to ill-posed inverse problems. These inverse problems require proper regularization to achieve meaningful results and involve the solution of computationally intensive large-scale optimization problems. Recently, however, sparse regularization has been applied successfully to inverse problems arising in different scientific areas. The increased computational power of modern computers and the development of new efficient optimization algorithms makes it possible ...

Ill-posed inverse problems appear in many signal and image processing applications, such as deblurring, super-resolution and compressed sensing. The common approach to address them is to design a specific algorithm, or recently, a specific deep neural network, for each problem. Both signal processing and machine learning tactics have drawbacks: traditional reconstruction strategies exhibit limited performance for complex signals, such as natural images, due to the hardness of their mathematical modeling; while modern works that circumvent signal modeling by training deep convolutional neural networks (CNNs) suffer from a huge performance drop when the observation model used in training is inexact. In this work, we develop and analyze reconstruction algorithms that are not restricted to a specific signal model and are able to handle different observation models. Our main contributions include: (a) We generalize the popular sparsity-based CoSaMP algorithm to any signal ...

In this thesis, signal and image processing algorithms based on sparsity and interval convex programming are developed for inverse problems. Inverse signal processing problems are solved by minimizing the ℓ1 norm or the Total Variation (TV) based cost functions in the literature. A modified entropy functional approximating the absolute value function is defined. This functional is also used to approximate the ℓ1 norm, which is the most widely used cost function in sparse signal processing problems. The modified entropy functional is continuously differentiable, and convex. As a result, it is possible to develop iterative, globally convergent algorithms for compressive sensing, denoising and restoration problems using the modified entropy functional. Iterative interval convex programming algorithms are constructed using Bregman’s D-Projection operator. In sparse signal processing, it is assumed that the signal can be represented using a sparse set of coefficients in ...

The field of Life Science Engineering (LSE) is rapidly expanding and predicted to grow strongly in the next decades. It covers areas of food and medical research, plant and pests’ research, and environmental research. In each research area, engineers try to find equations that model a certain life science problem. Once found, they research different numerical techniques to solve for the unknown variables of these equations. Afterwards, solution improvement is examined by adopting more accurate conventional techniques, or developing novel algorithms. In particular, signal and image processing techniques are widely used to solve those LSE problems require pattern recognition. However, due to the continuous evolution of the life science problems and their natures, these solution techniques can not cover all aspects, and therefore demanding further enhancement and improvement. The thesis presents numerical algorithms of digital signal and image processing to ...

The first part of this dissertation considers distributed learning problems over networked agents. The general objective of distributed adaptation and learning is the solution of global, stochastic optimization problems through localized interactions and without information about the statistical properties of the data. Regularization is a useful technique to encourage or enforce structural properties on the resulting solution, such as sparsity or constraints. A substantial number of regularizers are inherently non-smooth, while many cost functions are differentiable. We propose distributed and adaptive strategies that are able to minimize aggregate sums of objectives. In doing so, we exploit the structure of the individual objectives as sums of differentiable costs and non-differentiable regularizers. The resulting algorithms are adaptive in nature and able to continuously track drifts in the problem; their recursions, however, are subject to persistent perturbations arising from the stochastic nature of ...

To reduce scanning time or improve spatio-temporal resolution in some MRI applications, parallel MRI acquisition techniques with multiple coils have emerged since the early 90’s as powerful methods. In these techniques, MRI images have to be reconstructed from ac- quired undersampled “k-space” data. To this end, several reconstruction techniques have been proposed such as the widely-used SENSitivity Encoding (SENSE) method. However, the reconstructed images generally present artifacts due to the noise corrupting the ob- served data and coil sensitivity profile estimation errors. In this work, we present novel SENSE-based reconstruction methods which proceed with regularization in the complex wavelet domain so as to promote the sparsity of the solution. These methods achieve ac- curate image reconstruction under degraded experimental conditions, in which neither the SENSE method nor standard regularized methods (e.g. Tikhonov) give convincing results. The proposed approaches relies on ...

Inverse problems related to physical processes are of great importance in practically every field related to signal processing, such as tomography, acoustics, wireless communications, medical and radar imaging, to name only a few. At the same time, many of these problems are quite challenging due to their ill-posed nature. On the other hand, signals originating from physical phenomena are often governed by laws expressible through linear Partial Differential Equations (PDE), or equivalently, integral equations and the associated Green’s functions. In addition, these phenomena are usually induced by sparse singularities, appearing as sources or sinks of a vector field. In this thesis we primarily investigate the coupling of such physical laws with a prior assumption on the sparse origin of a physical process. This gives rise to a “dual” regularization concept, formulated either as sparse analysis (cosparse), yielded by a PDE ...

Image formation algorithms in a variety of applications have explicit or implicit dependence on a mathematical model of the observation process. Inaccuracies in the observation model may cause various degradations and artifacts in the reconstructed images. The application of interest in this thesis is synthetic aperture radar (SAR) imaging, which particularly suffers from motion-induced model errors. These types of errors result in phase errors in SAR data which cause defocusing of the reconstructed images. Particularly focusing on imaging of fields that admit a sparse representation, we propose a sparsity-driven method for joint SAR imaging and phase error correction. In this technique, phase error correction is performed during the image formation process. The problem is set up as an optimization problem in a nonquadratic regularization-based framework. The method involves an iterative algorithm each iteration of which consists of consecutive steps of ...