Structured Compressed Sensing: From Theory to Applications

Compressed sensing (CS) is an emerging field that has attracted considerable research interest over the past few years. Previous review articles in CS limit their scope to standard discrete-to-discrete measurement architectures using matrices of randomized nature and signal models based on standard sparsity. In recent years, CS has worked its way into several new application areas. This, in turn, necessitates a fresh look on many of the basics of CS. The random matrix measurement operator must be replaced by more structured sensing architectures that correspond to the characteristics of feasible acquisition hardware. The standard sparsity prior has to be extended to include a much richer class of signals and to encode broader data models, including continuous-time signals. In our overview, the theme is exploiting signal and measurement structure in compressive sensing. The prime focus is bridging theory and practice; that is, to pinpoint the potential of structured CS strategies to emerge from the math to the hardware. Our summary highlights new directions as well as relations to more traditional CS, with the hope of serving both as a review to practitioners wanting to join this emerging field, and as a reference for researchers that attempts to put some of the existing ideas in perspective of practical applications.Comment: To appear as an overview paper in IEEE Transactions on Signal Processin

Support Recovery of Sparse Signals

We consider the problem of exact support recovery of sparse signals via noisy measurements. The main focus is the sufficient and necessary conditions on the number of measurements for support recovery to be reliable. By drawing an analogy between the problem of support recovery and the problem of channel coding over the Gaussian multiple access channel, and exploiting mathematical tools developed for the latter problem, we obtain an information theoretic framework for analyzing the performance limits of support recovery. Sharp sufficient and necessary conditions on the number of measurements in terms of the signal sparsity level and the measurement noise level are derived. Specifically, when the number of nonzero entries is held fixed, the exact asymptotics on the number of measurements for support recovery is developed. When the number of nonzero entries increases in certain manners, we obtain sufficient conditions tighter than existing results. In addition, we show that the proposed methodology can deal with a variety of models of sparse signal recovery, hence demonstrating its potential as an effective analytical tool.Comment: 33 page

Brain–Machine Interface and Visual Compressive Sensing-Based Teleoperation Control of an Exoskeleton Robot

This paper presents a teleoperation control for an exoskeleton robotic system based on the brain-machine interface and vision feedback. Vision compressive sensing, brain-machine reference commands, and adaptive fuzzy controllers in joint-space have been effectively integrated to enable the robot performing manipulation tasks guided by human operator's mind. First, a visual-feedback link is implemented by a video captured by a camera, allowing him/her to visualize the manipulator's workspace and movements being executed. Then, the compressed images are used as feedback errors in a nonvector space for producing steady-state visual evoked potentials electroencephalography (EEG) signals, and it requires no prior information on features in contrast to the traditional visual servoing. The proposed EEG decoding algorithm generates control signals for the exoskeleton robot using features extracted from neural activity. Considering coupled dynamics and actuator input constraints during the robot manipulation, a local adaptive fuzzy controller has been designed to drive the exoskeleton tracking the intended trajectories in human operator's mind and to provide a convenient way of dynamics compensation with minimal knowledge of the dynamics parameters of the exoskeleton robot. Extensive experiment studies employing three subjects have been performed to verify the validity of the proposed method

Compressive Sensing Applications in Measurement: Theoretical issues, algorithm characterization and implementation

At its core, signal acquisition is concerned with efficient algorithms and protocols capable to capture and encode the signal information content. For over five decades, the indisputable theoretical benchmark has been represented by the wellknown Shannon’s sampling theorem, and the corresponding notion of information has been indissolubly related to signal spectral bandwidth. The contemporary society is founded on almost instantaneous exchange of information, which is mainly conveyed in a digital format. Accordingly, modern communication devices are expected to cope with huge amounts of data, in a typical sequence of steps which comprise acquisition, processing and storage. Despite the continual technological progress, the conventional acquisition protocol has come under mounting pressure and requires a computational effort not related to the actual signal information content. In recent years, a novel sensing paradigm, also known as Compressive Sensing, briefly CS, is quickly spreading among several branches of Information Theory. It relies on two main principles: signal sparsity and incoherent sampling, and employs them to acquire the signal directly in a condensed form. The sampling rate is related to signal information rate, rather than to signal spectral bandwidth. Given a sparse signal, its information content can be recovered even fromwhat could appear to be an incomplete set of measurements, at the expense of a greater computational effort at reconstruction stage. My Ph.D. thesis builds on the field of Compressive Sensing and illustrates how sparsity and incoherence properties can be exploited to design efficient sensing strategies, or to intimately understand the sources of uncertainty that affect measurements. The research activity has dealtwith both theoretical and practical issues, inferred frommeasurement application contexts, ranging fromradio frequency communications to synchrophasor estimation and neurological activity investigation. The thesis is organised in four chapters whose key contributions include: • definition of a general mathematical model for sparse signal acquisition systems, with particular focus on sparsity and incoherence implications; • characterization of the main algorithmic families for recovering sparse signals from reduced set of measurements, with particular focus on the impact of additive noise; • implementation and experimental validation of a CS-based algorithmfor providing accurate preliminary information and suitably preprocessed data for a vector signal analyser or a cognitive radio application; • design and characterization of a CS-based super-resolution technique for spectral analysis in the discrete Fourier transform(DFT) domain; • definition of an overcomplete dictionary which explicitly account for spectral leakage effect; • insight into the so-called off-the-grid estimation approach, by properly combining CS-based super-resolution and DFT coefficients polar interpolation; • exploration and analysis of sparsity implications in quasi-stationary operative conditions, emphasizing the importance of time-varying sparse signal models; • definition of an enhanced spectral content model for spectral analysis applications in dynamic conditions by means of Taylor-Fourier transform (TFT) approaches

Compressed sensing reconstruction of convolved sparse signals

Abstract—This paper addresses the problem of efficient sam-pling and reconstruction of sparse spike signals, which have been convolved with low-pass filters. A modified compressed sensing (CS) framework is proposed, termed dictionary-based deconvolution CS (DDCS) to achieve this goal. DDCS builds on the assumption that a low-pass filter can be represented sparsely in a dictionary of blurring atoms. Identification of both the sparse spike signal and the sparsely parameterized blurring function is performed by an alternating scheme that minimizes each variable independently, while keeping the other constant. Simulation results reveal that the proposed DDSS scheme achieves an improved reconstruction performance when compared to traditional CS recovery. I

Multipolar Acoustic Source Reconstruction from Sparse Far-Field Data using ALOHA

The reconstruction of multipolar acoustic or electromagnetic sources from their far-field signature plays a crucial role in numerous applications. Most of the existing techniques require dense multi-frequency data at the Nyquist sampling rate. The availability of a sub-sampled grid contributes to the null space of the inverse source-to-data operator, which causes significant imaging artifacts. For this purpose, additional knowledge about the source or regularization is required. In this letter, we propose a novel two-stage strategy for multipolar source reconstruction from sub-sampled sparse data that takes advantage of the sparsity of the sources in the physical domain. The data at the Nyquist sampling rate is recovered from sub-sampled data and then a conventional inversion algorithm is used to reconstruct sources. The data recovery problem is linked to a spectrum recovery problem for the signal with the \textit{finite rate of innovations} (FIR) that is solved using an annihilating filter-based structured Hankel matrix completion approach (ALOHA). For an accurate reconstruction, a Fourier inversion algorithm is used. The suitability of the approach is supported by experiments.Comment: 11 pages, 2 figure