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

In pursuit of high resolution radar using pursuit algorithms

Radar receivers typically employ matched filters designed to maximize signal to noise ratio (SNR) in a single target environment. In a multi-target environment, however, matched filter estimates of target environment often consist of spurious targets because of radar signal sidelobes. As a result, matched filters are not suitable for use in high resolution radars operating in multi-target environments. Assuming a point target model, we show that the radar problem can be formulated as a linear under-determined system with a sparse solution. This suggests that radar can be considered as a sparse signal recovery problem. However, it is shown that the sensing matrix obtained using common radar signals does not usually satisfy the mutual coherence condition. This implies that using recovery techniques available in compressed sensing literature may not result in the optimal solution. In this thesis, we focus on the greedy algorithm approach to solve the problem and show that it naturally yields a quantitative measure for radar resolution. In addition, we show that the limitations of the greedy algorithms can be attributed to the close relation between greedy matching pursuit algorithms and the matched filter. This suggests that improvements to the resolution capability of the greedy pursuit algorithms can be made by using a mismatched signal dictionary. In some cases, unlike the mismatched filter, the proposed mismatched pursuit algorithm is shown to offer improved resolution and stability without any noticeable difference in detection performance. Further improvements in resolution are proposed by using greedy algorithms in a radar system using multiple transmit waveforms. It is shown that while using the greedy algorithms together with linear channel combining can yield significant resolution improvement, a greedy approach using nonlinear channel combining also shows some promise. Finally, a forward-backward greedy algorithm is proposed for target environments comprising of point targets as well as extended targets

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 $\ell^2$-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

Signal acquisition challenges in mobile systems

In recent decades, the advent of mobile computing has changed human lives by providing information that was not available in the past. The mobile computing platform opens a new door to the connected world in which various forms of hand-held and wearable systems are ubiquitous. A single mobile device plays multiple roles and shapes human lives towards a better future. In these systems, sensor-based data acquisition plays an essential role in generating and providing useful information. The increased number of sensors is embedded in a single device in order to process various signal modalities. In practice, more than 30 data converters are required in designing a mobile system in which the data-converting blocks become among the most power-hungry components in battery-operated systems. Due to the increased variety of sensors, mobile systems are meant to face several obstacles. For example, the increased number of sensors increase system power consumption during the system operation. The increased power consumption directly affects operation time because mobile systems are powered by a limited energy source. Moreover, an increased amount of information also gives rise to bandwidth problems in communication due to the increased volume of data transmission. Also, this system design requires a larger area in a silicon die so that multiple signal paths can be placed without cross-channel interference. Therefore, the system design has presented a challenge in terms of trying to resolve the design constraints such as power consumption, bandwidth usage, storage space, and design complexity issues. To overcome these obstacles, in this dissertation, efficient data acquisition and processing methods are investigated. Specifically, this thesis considers the problems of energy-efficient sampling and binary event detection. This dissertation begins by presenting a new signal sampling scheme that enables higher precision signal conversion in compressed-sensing-based signal acquisition. The proposed scheme is based on the popular successive approximation register and employs a modified compressive sensing technique to increase the resolution of successive-approximation-register (SAR) analog-to-digital converter (ADC) architecture. Circuit-level architecture is discussed to implement the proposed scheme using the SAR ADC architecture. A non-uniform quantization scheme is proposed and it improves data quality after data acquisition. The proposed scheme is expected to be used for medium- or high- frequency data conversion. Secondly, the possibility of using fewer ADCs than channels is studied by leveraging sparse-signal representation and blind-source-separation (BSS) techniques. In particular, this dissertation examines the problem of using a single ADC or quantizer system for digitizing multi-channel inputs. Mixing and de-mixing strategies are extensively studied for sampling frequency-sparse signals and the proposed multi-channel architecture can be easily implemented using today's analog/mixed-signal circuits. The third part of this dissertation investigates a binary hypothesis testing problem. In mobile devices such as smartphones and tablet PCs, a major portion of energy is consumed in user interfaces (LCD display and touch input processing). For accurate detection and better user interface, energy-efficient sensing and detection schemes are necessary to manage multiple sensor inputs. A highly efficient detection scheme is presented that can detect binary events reliably with a fraction of the energy consumption required in the conventional energy detection.Electrical and Computer Engineerin