We introduce a new approach to radar imaging based on the concept of compressive sensing (CS). In CS, a low-dimensional, nonadaptive, linear projection is used to acquire an efficient representation of a compressible signal directly using just a few measurements. The signal is then reconstructed by solving an inverse problem either through a linear program or a greedy pursuit. We demonstrate that CS has the potential to make two significant improvements to radar systems: (i) eliminating the need for the pulse compression matched filter at the receiver, and (ii) reducing the required receiver analog-to-digital conversion bandwidth so that it need operate only at the radar reflectivity's potentially low "information rate" rather than at its potentially high Nyquist rate. These ideas could enable the design of new, simplified radar systems, shifting the emphasis from expensive receiver hardware to smart signal recovery algorithms.

/pdf/compressive-radar-imaging-47z5fx3bs3.pdf

Compressive Radar Imaging

Low-complexity video encoding has been applicable to several emerging applications. Recently, distributed video coding (DVC) has been proposed to reduce encoding complexity to the order of that for still image encoding. In addition, compressive sensing (CS) has been applicable to directly capture compressed image data efficiently. In this paper, by integrating the respective characteristics of DVC and CS, a distributed compressive video sensing (DCVS) framework is proposed to simultaneously capture and compress video data, where almost all computation burdens can be shifted to the decoder, resulting in a very low-complexity encoder. At the decoder, compressed video can be efficiently reconstructed using the modified GPSR (gradient projection for sparse reconstruction) algorithm. With the assistance of the proposed initialization and stopping criteria for GRSR, derived from statistical dependencies among successive video frames, our modified GPSR algorithm can terminate faster and reconstruct better video quality. The performance of our DCVS method is demonstrated via simulations to outperform three known CS reconstruction algorithms.

Distributed compressive video sensing

Power and bandwidth are scarce resources in dense wireless sensor networks and it is widely recognized that joint optimization of the operations of sensing, processing and communication can result in significant savings in the use of network resources. In this paper, a distributed joint source-channel communication architecture is proposed for energy-efficient estimation of sensor field data at a distant destination and the corresponding relationships between power, distortion, and latency are analyzed as a function of number of sensor nodes. The approach is applicable to a broad class of sensed signal fields and is based on distributed computation of appropriately chosen projections of sensor data at the destination - phase-coherent transmissions from the sensor nodes enable exploitation of the distributed beamforming gain for energy efficiency. Random projections are used when little or no prior knowledge is available about the signal field. Distinct features of the proposed scheme include: (1) processing and communication are combined into one distributed projection operation; (2) it virtually eliminates the need for in-network processing and communication; (3) given sufficient prior knowledge about the sensed data, consistent estimation is possible with increasing sensor density even with vanishing total network power; and (4) consistent signal estimation is possible with power and latency requirements growing at most sublinearly with the number of sensor nodes even when little or no prior knowledge about the sensed data is assumed at the sensor nodes.

/pdf/joint-source-channel-communication-for-distributed-553jzdd0bf.pdf

Joint Source–Channel Communication for Distributed Estimation in Sensor Networks

Compressive Sensing (CS) shows high promise for fully distributed compression in wireless sensor networks (WSNs). In theory, CS allows the approximation of the readings from a sensor field with excellent accuracy, while collecting only a small fraction of them at a data gathering point. However, the conditions under which CS performs well are not necessarily met in practice. CS requires a suitable transformation that makes the signal sparse in its domain. Also, the transformation of the data given by the routing protocol and network topology and the sparse representation of the signal have to be incoherent, which is not straightforward to achieve in real networks. In this work we address the data gathering problem in WSNs, where routing is used in conjunction with CS to transport random projections of the data.We analyze synthetic and real data sets and compare the results against those of random sampling. In doing so, we consider a number of popular transformations and we find that, with real data sets, none of them are able to sparsify the data while being at the same time incoherent with respect to the routing matrix. The obtained performance is thus not as good as expected and finding a suitable transformation with good sparsification and incoherence properties remains an open problem for data gathering in static WSNs.

/pdf/on-the-interplay-between-routing-and-signal-representation-1xf25f3gy6.pdf

On the interplay between routing and signal representation for Compressive Sensing in wireless sensor networks

The performance of estimating the common support for jointly sparse signals based on their projections onto lower-dimensional space is analyzed. Support recovery is formulated as a multiple-hypothesis testing problem. Both upper and lower bounds on the probability of error are derived for general measurement matrices, by using the Chernoff bound and Fano's inequality, respectively. The upper bound shows that the performance is determined by a quantity measuring the measurement matrix incoherence, while the lower bound reveals the importance of the total measurement gain. The lower bound is applied to derive the minimal number of samples needed for accurate direction-of-arrival (DOA) estimation for a sparse representation based algorithm. When applied to Gaussian measurement ensembles, these bounds give necessary and sufficient conditions for a vanishing probability of error for majority realizations of the measurement matrix. Our results offer surprising insights into sparse signal recovery. For example, as far as support recovery is concerned, the well-known bound in Compressive Sensing with the Gaussian measurement matrix is generally not sufficient unless the noise level is low. Our study provides an alternative performance measure, one that is natural and important in practice, for signal recovery in Compressive Sensing and other application areas exploiting signal sparsity.

https://www.ese.wustl.edu/~nehorai/research/sparse/Sparse_Support_Recovery_Slides_2009.pdf

Performance Analysis for Sparse Support Recovery

/pdf/universal-distributed-sensing-via-random-projections-3dv4ffl1p4.pdf

Baron

Papers

Universal distributed sensing via random projections