Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)

The implicit objective of the biennial "international - Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST) is to foster collaboration between international scientific teams by disseminating ideas through both specific oral/poster presentations and free discussions. For its second edition, the iTWIST workshop took place in the medieval and picturesque town of Namur in Belgium, from Wednesday August 27th till Friday August 29th, 2014. The workshop was conveniently located in "The Arsenal" building within walking distance of both hotels and town center. iTWIST'14 has gathered about 70 international participants and has featured 9 invited talks, 10 oral presentations, and 14 posters on the following themes, all related to the theory, application and generalization of the "sparsity paradigm": Sparsity-driven data sensing and processing; Union of low dimensional subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph sensing/processing; Blind inverse problems and dictionary learning; Sparsity and computational neuroscience; Information theory, geometry and randomness; Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?; Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website: http://sites.google.com/site/itwist1

Recent Advances in Signal Processing

The signal processing task is a very critical issue in the majority of new technological inventions and challenges in a variety of applications in both science and engineering fields. Classical signal processing techniques have largely worked with mathematical models that are linear, local, stationary, and Gaussian. They have always favored closed-form tractability over real-world accuracy. These constraints were imposed by the lack of powerful computing tools. During the last few decades, signal processing theories, developments, and applications have matured rapidly and now include tools from many areas of mathematics, computer science, physics, and engineering. This book is targeted primarily toward both students and researchers who want to be exposed to a wide variety of signal processing techniques and algorithms. It includes 27 chapters that can be categorized into five different areas depending on the application at hand. These five categories are ordered to address image processing, speech processing, communication systems, time-series analysis, and educational packages respectively. The book has the advantage of providing a collection of applications that are completely independent and self-contained; thus, the interested reader can choose any chapter and skip to another without losing continuity

Information Theory and Its Application in Machine Condition Monitoring

Condition monitoring of machinery is one of the most important aspects of many modern industries. With the rapid advancement of science and technology, machines are becoming increasingly complex. Moreover, an exponential increase of demand is leading an increasing requirement of machine output. As a result, in most modern industries, machines have to work for 24 hours a day. All these factors are leading to the deterioration of machine health in a higher rate than before. Breakdown of the key components of a machine such as bearing, gearbox or rollers can cause a catastrophic effect both in terms of financial and human costs. In this perspective, it is important not only to detect the fault at its earliest point of inception but necessary to design the overall monitoring process, such as fault classification, fault severity assessment and remaining useful life (RUL) prediction for better planning of the maintenance schedule. Information theory is one of the pioneer contributions of modern science that has evolved into various forms and algorithms over time. Due to its ability to address the non-linearity and non-stationarity of machine health deterioration, it has become a popular choice among researchers. Information theory is an effective technique for extracting features of machines under different health conditions. In this context, this book discusses the potential applications, research results and latest developments of information theory-based condition monitoring of machineries

Autoregressive process parameters estimation from Compressed Sensing measurements and Bayesian dictionary learning

The main contribution of this thesis is the introduction of new techniques which allow to perform signal processing operations on signals represented by means of compressed sensing. Exploiting autoregressive modeling of the original signal, we obtain a compact yet representative description of the signal which can be estimated directly in the compressed domain. This is the key concept on which the applications we introduce rely on. In fact, thanks to proposed the framework it is possible to gain information about the original signal given compressed sensing measurements. This is done by means of autoregressive modeling which can be used to describe a signal through a small number of parameters. We develop a method to estimate these parameters given the compressed measurements by using an ad-hoc sensing matrix design and two different coupled estimators that can be used in different scenarios. This enables centralized and distributed estimation of the covariance matrix of a process given the compressed sensing measurements in a efficient way at low communication cost. Next, we use the characterization of the original signal done by means of few autoregressive parameters to improve compressive imaging. In particular, we use these parameters as a proxy to estimate the complexity of a block of a given image. This allows us to introduce a novel compressive imaging system in which the number of allocated measurements is adapted for each block depending on its complexity, i.e., spatial smoothness. The result is that a careful allocation of the measurements, improves the recovery process by reaching higher recovery quality at the same compression ratio in comparison to state-of-the-art compressive image recovery techniques. Interestingly, the parameters we are able to estimate directly in the compressed domain not only can improve the recovery but can also be used as feature vectors for classification. In fact, we also propose to use these parameters as more general feature vectors which allow to perform classification in the compressed domain. Remarkably, this method reaches high classification performance which is comparable with that obtained in the original domain, but with a lower cost in terms of dataset storage. In the second part of this work, we focus on sparse representations. In fact, a better sparsifying dictionary can improve the Compressed Sensing recovery performance. At first, we focus on the original domain and hence no dimensionality reduction by means of Compressed Sensing is considered. In particular, we develop a Bayesian technique which, in a fully automated fashion, performs dictionary learning. More in detail, using the uncertainties coming from atoms selection in the sparse representation step, this technique outperforms state-of-the-art dictionary learning techniques. Then, we also address image denoising and inpainting tasks using the aforementioned technique with excellent results. Next, we move to the compressed domain where a better dictionary is expected to provide improved recovery. We show how the Bayesian dictionary learning model can be adapted to the compressive case and the necessary assumptions that must be made when considering random projections. Lastly, numerical experiments confirm the superiority of this technique when compared to other compressive dictionary learning techniques

Compressive Acquisition and Processing of Sparse Analog Signals

Since the advent of the first digital processing units, the importance of digital signal processing has been steadily rising. Today, most signal processing happens in the digital domain, requiring that analog signals be first sampled and digitized before any relevant data can be extracted from them. The recent explosion of the demands for data acquisition, storage and processing, however, has pushed the capabilities of conventional acquisition systems to their limits in many application areas. By offering an alternative view on the signal acquisition process, ideas from sparse signal processing and one of its main beneficiaries compressed sensing (CS), aim at alleviating some of these problems. In this thesis, we look into the ways the application of a compressive measurement kernel impacts the signal recovery performance and investigate methods to infer the current signal complexity from the compressive observations. We then study a particular application, namely that of sub-Nyquist sampling and processing of sparse analog multiband signals in spectral, angular and spatial domains.Seit dem Aufkommen der ersten digitalen Verarbeitungseinheiten hat die Bedeutung der digitalen Signalverarbeitung stetig zugenommen. Heutzutage findet die meiste Signalverarbeitung im digitalen Bereich statt, was erfordert, dass analoge Signale zuerst abgetastet und digitalisiert werden, bevor relevante Daten daraus extrahiert werden können. Jahrzehntelang hat die herkömmliche äquidistante Abtastung, die durch das Nyquist-Abtasttheorem bestimmt wird, zu diesem Zweck ein nahezu universelles Mittel bereitgestellt. Der kürzliche explosive Anstieg der Anforderungen an die Datenerfassung, -speicherung und -verarbeitung hat jedoch die Fähigkeiten herkömmlicher Erfassungssysteme in vielen Anwendungsbereichen an ihre Grenzen gebracht. Durch eine alternative Sichtweise auf den Signalerfassungsprozess können Ideen aus der sparse Signalverarbeitung und einer ihrer Hauptanwendungsgebiete, Compressed Sensing (CS), dazu beitragen, einige dieser Probleme zu mindern. Basierend auf der Annahme, dass der Informationsgehalt eines Signals oft viel geringer ist als was von der nativen Repräsentation vorgegeben, stellt CS ein alternatives Konzept für die Erfassung und Verarbeitung bereit, das versucht, die Abtastrate unter Beibehaltung des Signalinformationsgehalts zu reduzieren. In dieser Arbeit untersuchen wir einige der Grundlagen des endlichdimensionalen CSFrameworks und seine Verbindung mit Sub-Nyquist Abtastung und Verarbeitung von sparsen analogen Signalen. Obwohl es seit mehr als einem Jahrzehnt ein Schwerpunkt aktiver Forschung ist, gibt es noch erhebliche Lücken beim Verständnis der Auswirkungen von komprimierenden Ansätzen auf die Signalwiedergewinnung und die Verarbeitungsleistung, insbesondere bei rauschbehafteten Umgebungen und in Bezug auf praktische Messaufgaben. In dieser Dissertation untersuchen wir, wie sich die Anwendung eines komprimierenden Messkerns auf die Signal- und Rauschcharakteristiken auf die Signalrückgewinnungsleistung auswirkt. Wir erforschen auch Methoden, um die aktuelle Signal-Sparsity-Order aus den komprimierten Messungen abzuleiten, ohne auf die Nyquist-Raten-Verarbeitung zurückzugreifen, und zeigen den Vorteil, den sie für den Wiederherstellungsprozess bietet. Nachdem gehen wir zu einer speziellen Anwendung, nämlich der Sub-Nyquist-Abtastung und Verarbeitung von sparsen analogen Multibandsignalen. Innerhalb des Sub-Nyquist-Abtastung untersuchen wir drei verschiedene Multiband-Szenarien, die Multiband-Sensing in der spektralen, Winkel und räumlichen-Domäne einbeziehen.Since the advent of the first digital processing units, the importance of digital signal processing has been steadily rising. Today, most signal processing happens in the digital domain, requiring that analog signals be first sampled and digitized before any relevant data can be extracted from them. For decades, conventional uniform sampling that is governed by the Nyquist sampling theorem has provided an almost universal means to this end. The recent explosion of the demands for data acquisition, storage and processing, however, has pushed the capabilities of conventional acquisition systems to their limits in many application areas. By offering an alternative view on the signal acquisition process, ideas from sparse signal processing and one of its main beneficiaries compressed sensing (CS), have the potential to assist alleviating some of these problems. Building on the premise that the signal information rate is often much lower than what is dictated by its native representation, CS provides an alternative acquisition and processing framework that attempts to reduce the sampling rate while preserving the information content of the signal. In this thesis, we explore some of the basic foundations of the finite-dimensional CS framework and its connection to sub-Nyquist sampling and processing of sparse continuous analog signals with application to multiband sensing. Despite being a focus of active research for over a decade, there still remain signi_cant gaps in understanding the implications that compressive approaches have on the signal recovery and processing performance, especially against noisy settings and in relation to practical sampling problems. This dissertation aims at filling some of these gaps. More specifically, we look into the ways the application of a compressive measurement kernel impacts signal and noise characteristics and the relation it has to the signal recovery performance. We also investigate methods to infer the current complexity of the signal scene from the reduced-rate compressive observations without resorting to Nyquist-rate processing and show the advantage this knowledge offers to the recovery process. Having considered some of the universal aspects of compressive systems, we then move to studying a particular application, namely that of sub-Nyquist sampling and processing of sparse analog multiband signals. Within the sub-Nyquist sampling framework, we examine three different multiband scenarios that involve multiband sensing in spectral, angular and spatial domains. For each of them, we provide a sub-Nyquist receiver architecture, develop recovery methods and numerically evaluate their performance

Remote Sensing

This dual conception of remote sensing brought us to the idea of preparing two different books; in addition to the first book which displays recent advances in remote sensing applications, this book is devoted to new techniques for data processing, sensors and platforms. We do not intend this book to cover all aspects of remote sensing techniques and platforms, since it would be an impossible task for a single volume. Instead, we have collected a number of high-quality, original and representative contributions in those areas

Tracing star formation and AGN activity at radio frequencies

My research has focused on locating and measuring star formation and AGN activity in different environments with interferometric and single-dish radio observations. As my first PhD project, I studied the complex interaction between an intermediate redshift (z 0.3) starburst galaxy and a nearby ( 7 kpc separation) QSO using sub-arcsecond VLA observations. I found new evidence for jet-induced star formation activity in the companion galaxy, making the system a strong candidate for this rare, and potentially important process in the early Universe. In my second paper, I investigated the infrared-radio correlation (IRRC) of spheroid- and disc-dominated galaxies in the COSMOS field out to z 1.5. With 1.4 GHz data and Herschel photometry I found that the redshift evolution reported in recent works is due to an increasing radio excess emission associated with spheroid-dominated galaxies, compared to disc-dominated ones, i.e. the ‘purest’ star-forming systems in our sample. I theorize that the extra radio power in spheroid-dominated systems is due to low-level AGN activity, even though these sources were not identified by most commonly-used diagnostics as AGN hosts. This finding will significantly increase the accuracy of future high-redshift radio surveys measuring star formation. In my third project I assembled and analysed the largest-to-date low-z IRRC sample of galaxies. I demonstrated the importance of selection effects influencing IRRC statistics, and carried out an improved IRRC analysis that yielded more accurate measures of the correlation’s properties. With rich ancillary data it will provide insight into the physical processes that give rise to the IRRC. Finally, I adopted an MCMC-based model optimization to fit a radiative transfer model to ammonia line spectra of a binary molecular cloud core. I determined the physical structures and the masses of the cores and found they are gravitationally unbound