Networked Slepian-Wolf: theory, algorithms, and scaling laws

Consider a set of correlated sources located at the nodes of a network, and a set of sinks that are the destinations for some of the sources. The minimization of cost functions which are the product of a function of the rate and a function of the path weight is considered, for both the data-gathering scenario, which is relevant in sensor networks, and general traffic matrices, relevant for general networks. The minimization is achieved by jointly optimizing a) the transmission structure, which is shown to consist in general of a superposition of trees, and b) the rate allocation across the source nodes, which is done by Slepian-Wolf coding. The overall minimization can be achieved in two concatenated steps. First, the optimal transmission structure is found, which in general amounts to finding a Steiner tree, and second, the optimal rate allocation is obtained by solving an optimization problem with cost weights determined by the given optimal transmission structure, and with linear constraints given by the Slepian-Wolf rate region. For the case of data gathering, the optimal transmission structure is fully characterized and a closed-form solution for the optimal rate allocation is provided. For the general case of an arbitrary traffic matrix, the problem of finding the optimal transmission structure is NP-complete. For large networks, in some simplified scenarios, the total costs associated with Slepian-Wolf coding and explicit communication (conditional encoding based on explicitly communicated side information) are compared. Finally, the design of decentralized algorithms for the optimal rate allocation is analyzed

Distributed field estimation in wireless sensor networks

This work takes into account the problem of distributed estimation of a physical field of interest through a wireless sesnor networks

Distributed field estimation in wireless sensor networks

This work takes into account the problem of distributed estimation of a physical field of interest through a wireless sesnor networks

Compressive Sensing Using Random Demodulation

The new theory of Compressive Sensing allows wideband signals to be sampled at a rate much closer to the information contained within. This rate is much lower than the Nyquist rate required by Shannon’s sampling theory. This “Analog to Information Conversion” has allowed an outlet for already overloaded Analog to Digital converters [15]. Although the locations of frequencies can’t be known a priori, the expected sparseness of a signal can be. This is the circumstance that allows this method to be possible. In order to accomplish this very low rate, there is some trade off in sampling rate reduction to computing load. In contrast to the uniform sampling in common acquisition processes, nonlinear methods must be used resulting in convex programming algorithms becoming a necessity to recover the signal. This thesis tests this new theory using a Random Demodulation data acquisition scheme set forth in [1]. The scheme involves a demodulation step that spreads the information content across the spectrum before an anti-aliasing filter prepares for an Analog to Digital converter to sample it at a very slow rate. The acquisition process is simulated using a computer, the data is run through an optimization algorithm and the recovery results are analyzed. Finally, the paper then compares the results to the Compressive Sensing theoretical and empirical results of others

Visible Light Communication (VLC)

Visible light communication (VLC) using light-emitting diodes (LEDs) or laser diodes (LDs) has been envisioned as one of the key enabling technologies for 6G and Internet of Things (IoT) systems, owing to its appealing advantages, including abundant and unregulated spectrum resources, no electromagnetic interference (EMI) radiation and high security. However, despite its many advantages, VLC faces several technical challenges, such as the limited bandwidth and severe nonlinearity of opto-electronic devices, link blockage and user mobility. Therefore, significant efforts are needed from the global VLC community to develop VLC technology further. This Special Issue, “Visible Light Communication (VLC)”, provides an opportunity for global researchers to share their new ideas and cutting-edge techniques to address the above-mentioned challenges. The 16 papers published in this Special Issue represent the fascinating progress of VLC in various contexts, including general indoor and underwater scenarios, and the emerging application of machine learning/artificial intelligence (ML/AI) techniques in VLC

Constrained Learning And Inference

Data and learning have become core components of the information processing and autonomous systems upon which we increasingly rely on to select job applicants, analyze medical data, and drive cars. As these systems become ubiquitous, so does the need to curtail their behavior. Left untethered, they are susceptible to tampering (adversarial examples) and prone to prejudiced and unsafe actions. Currently, the response of these systems is tailored by leveraging domain expert knowledge to either construct models that embed the desired properties or tune the training objective so as to promote them. While effective, these solutions are often targeted to specific behaviors, contexts, and sometimes even problem instances and are typically not transferable across models and applications. What is more, the growing scale and complexity of modern information processing and autonomous systems renders this manual behavior tuning infeasible. Already today, explainability, interpretability, and transparency combined with human judgment are no longer enough to design systems that perform according to specifications. The present thesis addresses these issues by leveraging constrained statistical optimization. More specifically, it develops the theoretical underpinnings of constrained learning and constrained inference to provide tools that enable solving statistical problems under requirements. Starting with the task of learning under requirements, it develops a generalization theory of constrained learning akin to the existing unconstrained one. By formalizing the concept of probability approximately correct constrained (PACC) learning, it shows that constrained learning is as hard as its unconstrained learning and establishes the constrained counterpart of empirical risk minimization (ERM) as a PACC learner. To overcome challenges involved in solving such non-convex constrained optimization problems, it derives a dual learning rule that enables constrained learning tasks to be tackled by through unconstrained learning problems only. It therefore concludes that if we can deal with classical, unconstrained learning tasks, then we can deal with learning tasks with requirements. The second part of this thesis addresses the issue of constrained inference. In particular, the issue of performing inference using sparse nonlinear function models, combinatorial constrained with quadratic objectives, and risk constraints. Such models arise in nonlinear line spectrum estimation, functional data analysis, sensor selection, actuator scheduling, experimental design, and risk-aware estimation. Although inference problems assume that models and distributions are known, each of these constraints pose serious challenges that hinder their use in practice. Sparse nonlinear functional models lead to infinite dimensional, non-convex optimization programs that cannot be discretized without leading to combinatorial, often NP-hard, problems. Rather than using surrogates and relaxations, this work relies on duality to show that despite their apparent complexity, these models can be fit efficiently, i.e., in polynomial time. While quadratic objectives are typically tractable (often even in closed form), they lead to non-submodular optimization problems when subject to cardinality or matroid constraints. While submodular functions are sometimes used as surrogates, this work instead shows that quadratic functions are close to submodular and can also be optimized near-optimally. The last chapter of this thesis is dedicated to problems involving risk constraints, in particular, bounded predictive mean square error variance estimation. Despite being non-convex, such problems are equivalent to a quadratically constrained quadratic program from which a closed-form estimator can be extracted. These results are used throughout this thesis to tackle problems in signal processing, machine learning, and control, such as fair learning, robust learning, nonlinear line spectrum estimation, actuator scheduling, experimental design, and risk-aware estimation. Yet, they are applicable much beyond these illustrations to perform safe reinforcement learning, sensor selection, multiresolution kernel estimation, and wireless resource allocation, to name a few

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

Digital Color Imaging

This paper surveys current technology and research in the area of digital color imaging. In order to establish the background and lay down terminology, fundamental concepts of color perception and measurement are first presented us-ing vector-space notation and terminology. Present-day color recording and reproduction systems are reviewed along with the common mathematical models used for representing these devices. Algorithms for processing color images for display and communication are surveyed, and a forecast of research trends is attempted. An extensive bibliography is provided