## General Approaches for Solving Inverse Problems with Arbitrary Signal Models (2020)

Sensing physical fields: Inverse problems for the diffusion equation and beyond

Due to significant advances made over the last few decades in the areas of (wireless) networking, communications and microprocessor fabrication, the use of sensor networks to observe physical phenomena is rapidly becoming commonplace. Over this period, many aspects of sensor networks have been explored, yet a thorough understanding of how to analyse and process the vast amounts of sensor data collected remains an open area of research. This work, therefore, aims to provide theoretical, as well as practical, advances this area. In particular, we consider the problem of inferring certain underlying properties of the monitored phenomena, from our sensor measurements. Within mathematics, this is commonly formulated as an inverse problem; whereas in signal processing, it appears as a (multidimensional) sampling and reconstruction problem. Indeed it is well known that inverse problems are notoriously ill-posed and very demanding to solve; meanwhile ...

Murray-Bruce, John — Imperial College London

Deep learning for semantic description of visual human traits

The recent progress in artificial neural networks (rebranded as “deep learning”) has significantly boosted the state-of-the-art in numerous domains of computer vision offering an opportunity to approach the problems which were hardly solvable with conventional machine learning. Thus, in the frame of this PhD study, we explore how deep learning techniques can help in the analysis of one the most basic and essential semantic traits revealed by a human face, namely, gender and age. In particular, two complementary problem settings are considered: (1) gender/age prediction from given face images, and (2) synthesis and editing of human faces with the required gender/age attributes. Convolutional Neural Network (CNN) has currently become a standard model for image-based object recognition in general, and therefore, is a natural choice for addressing the first of these two problems. However, our preliminary studies have shown that the ...

Antipov, Grigory — Télécom ParisTech (Eurecom)

Tradeoffs and limitations in statistically based image reconstruction problems

Advanced nuclear medical imaging systems collect multiple attributes of a large number of photon events, resulting in extremely large datasets which present challenges to image reconstruction and assessment. This dissertation addresses several of these challenges. The image formation process in nuclear medical imaging can be posed as a parametric estimation problem where the image pixels are the parameters of interest. Since nuclear medical imaging applications are often ill-posed inverse problems, unbiased estimators result in very noisy, high-variance images. Typically, smoothness constraints and a priori information are used to reduce variance in medical imaging applications at the cost of biasing the estimator. For such problems, there exists an inherent tradeoff between the recovered spatial resolution of an estimator, overall bias, and its statistical variance; lower variance can only be bought at the price of decreased spatial resolution and/or increased overall bias. ...

Kragh, Tom — University of Michigan

Cosparse regularization of physics-driven inverse problems

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 ...

Kitić, Srđan — Université de Rennes 1

Gaussian Process Modelling for Audio Signals

Audio signals are characterised and perceived based on how their spectral make-up changes with time. Uncovering the behaviour of latent spectral components is at the heart of many real-world applications involving sound, but is a highly ill-posed task given the infinite number of ways any signal can be decomposed. This motivates the use of prior knowledge and a probabilistic modelling paradigm that can characterise uncertainty. This thesis studies the application of Gaussian processes to audio, which offer a principled non-parametric way to specify probability distributions over functions whilst also encoding prior knowledge. Along the way we consider what prior knowledge we have about sound, the way it behaves, and the way it is perceived, and write down these assumptions in the form of probabilistic models. We show how Bayesian time-frequency analysis can be reformulated as a spectral mixture Gaussian process, ...

William Wilkinson — Queen Mary University of London

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 ...

Antonello, Niccolò — KU Leuven

Music Language Models for Automatic Music Transcription

Much like natural language, music is highly structured, with strong priors on the likelihood of note sequences. In automatic speech recognition (ASR), these priors are called language models, which are used in addition to acoustic models and participate greatly to the success of today's systems. However, in Automatic Music Transcription (AMT), ASR's musical equivalent, Music Language Models (MLMs) are rarely used. AMT can be defined as the process of extracting a symbolic representation from an audio signal, describing which notes were played at what time. In this thesis, we investigate the design of MLMs using recurrent neural networks (RNNs) and their use for AMT. We first look into MLM performance on a polyphonic prediction task. We observe that using musically-relevant timesteps results in desirable MLM behaviour, which is not reflected in usual evaluation metrics. We compare our model against benchmark ...

Ycart, Adrien — Queen Mary University of London

Multi-channel EMG pattern classification based on deep learning

In recent years, a huge body of data generated by various applications in domains like social networks and healthcare have paved the way for the development of high performance models. Deep learning has transformed the field of data analysis by dramatically improving the state of the art in various classification and prediction tasks. Combined with advancements in electromyography it has given rise to new hand gesture recognition applications, such as human computer interfaces, sign language recognition, robotics control and rehabilitation games. The purpose of this thesis is to develop novel methods for electromyography signal analysis based on deep learning for the problem of hand gesture recognition. Specifically, we focus on methods for data preparation and developing accurate models even when few data are available. Electromyography signals are in general one-dimensional time-series with a rich frequency content. Various feature sets have ...

Tsinganos, Panagiotis — University of Patras, Greece - Vrije Universiteit Brussel, Belgium

Resistivity distribution estimation, widely known as Electrical Impedance Tomography (EIT), is a non linear ill-posed inverse problem. However, the partial derivative equation ruling this experiment yields no analytical solution for arbitrary conductivity distribution. Thus, solving the forward problem requires an approximation. The Finite Element Method (FEM) provides us with a computationally cheap forward model which preserves the non linear image-data relation and also reveals sufficiently accurate for the inversion. Within the Bayesian approach, Markovian priors on the log-conductivity distribution are introduced for regularization. The neighborhood system is directly derived from the FEM triangular mesh structure. We first propose a maximum a posteriori (MAP) estimation with a Huber-Markov prior which favours smooth distributions while preserving locally discontinuous features. The resulting criterion is minimized with the pseudo-conjugate gradient method. Simulation results reveal significant improvements in terms of robustness to noise, computation rapidity ...

Martin, Thierry — Laboratoire des signaux et systèmes

Sparsity Models for Signals: Theory and Applications

Many signal and image processing applications have benefited remarkably from the theory of sparse representations. In its classical form this theory models signal as having a sparse representation under a given dictionary -- this is referred to as the "Synthesis Model". In this work we focus on greedy methods for the problem of recovering a signal from a set of deteriorated linear measurements. We consider four different sparsity frameworks that extend the aforementioned synthesis model: (i) The cosparse analysis model; (ii) the signal space paradigm; (iii) the transform domain strategy; and (iv) the sparse Poisson noise model. Our algorithms of interest in the first part of the work are the greedy-like schemes: CoSaMP, subspace pursuit (SP), iterative hard thresholding (IHT) and hard thresholding pursuit (HTP). It has been shown for the synthesis model that these can achieve a stable recovery ...

Giryes, Raja — Technion

Bayesian Fusion of Multi-band Images: A Powerful Tool for Super-resolution

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 ...

Wei, Qi — University of Toulouse

Bayesian Compressed Sensing using Alpha-Stable Distributions

During the last decades, information is being gathered and processed at an explosive rate. This fact gives rise to a very important issue, that is, how to effectively and precisely describe the information content of a given source signal or an ensemble of source signals, such that it can be stored, processed or transmitted by taking into consideration the limitations and capabilities of the several digital devices. One of the fundamental principles of signal processing for decades is the Nyquist-Shannon sampling theorem, which states that the minimum number of samples needed to reconstruct a signal without error is dictated by its bandwidth. However, there are many cases in our everyday life in which sampling at the Nyquist rate results in too many data and thus, demanding an increased processing power, as well as storage requirements. A mathematical theory that emerged ...

Tzagkarakis, George — University of Crete

Deep Learning Techniques for Visual Counting

The explosion of Deep Learning (DL) added a boost to the already rapidly developing field of Computer Vision to such a point that vision-based tasks are now parts of our everyday lives. Applications such as image classification, photo stylization, or face recognition are nowadays pervasive, as evidenced by the advent of modern systems trivially integrated into mobile applications. In this thesis, we investigated and enhanced the visual counting task, which automatically estimates the number of objects in still images or video frames. Recently, due to the growing interest in it, several Convolutional Neural Network (CNN)-based solutions have been suggested by the scientific community. These artificial neural networks, inspired by the organization of the animal visual cortex, provide a way to automatically learn effective representations from raw visual data and can be successfully employed to address typical challenges characterizing this task, ...

Ciampi Luca — University of Pisa

Robust Network Topology Inference and Processing of Graph Signals

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 ...

Rey, Samuel — King Juan Carlos University

Signal and Image Processing Algorithms Using Interval Convex Programming and Sparsity

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 ...

Kose, Kivanc — Bilkent University

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