Measurement Matrix Design for Compressive Sensing Based MIMO Radar

In colocated multiple-input multiple-output (MIMO) radar using compressive sensing (CS), a receive node compresses its received signal via a linear transformation, referred to as measurement matrix. The samples are subsequently forwarded to a fusion center, where an L1-optimization problem is formulated and solved for target information. CS-based MIMO radar exploits the target sparsity in the angle-Doppler-range space and thus achieves the high localization performance of traditional MIMO radar but with many fewer measurements. The measurement matrix is vital for CS recovery performance. This paper considers the design of measurement matrices that achieve an optimality criterion that depends on the coherence of the sensing matrix (CSM) and/or signal-to-interference ratio (SIR). The first approach minimizes a performance penalty that is a linear combination of CSM and the inverse SIR. The second one imposes a structure on the measurement matrix and determines the parameters involved so that the SIR is enhanced. Depending on the transmit waveforms, the second approach can significantly improve SIR, while maintaining CSM comparable to that of the Gaussian random measurement matrix (GRMM). Simulations indicate that the proposed measurement matrices can improve detection accuracy as compared to a GRMM

Adaptive Measurement Network for CS Image Reconstruction

Conventional compressive sensing (CS) reconstruction is very slow for its characteristic of solving an optimization problem. Convolu- tional neural network can realize fast processing while achieving compa- rable results. While CS image recovery with high quality not only de- pends on good reconstruction algorithms, but also good measurements. In this paper, we propose an adaptive measurement network in which measurement is obtained by learning. The new network consists of a fully-connected layer and ReconNet. The fully-connected layer which has low-dimension output acts as measurement. We train the fully-connected layer and ReconNet simultaneously and obtain adaptive measurement. Because the adaptive measurement fits dataset better, in contrast with random Gaussian measurement matrix, under the same measuremen- t rate, it can extract the information of scene more efficiently and get better reconstruction results. Experiments show that the new network outperforms the original one.Comment: 11pages,8figure

Signal Recovery and System Calibration from Multiple Compressive Poisson Measurements

The measurement matrix employed in compressive sensing typically cannot be known precisely a priori, and must be estimated via calibration. One may take multiple compressive measurements, from which the measurement matrix and underlying signals may be estimated jointly. This is of interest as well when the measurement matrix may change as a function of the details of what is measured. This problem has been considered recently for Gaussian measurement noise, and here we develop this idea with application to Poisson systems. An optimization-based algorithm is proposed, and associated theoretical performance guarantees are established based on newly derived concentration-of-measure results. A Bayesian model is then introduced, to improve exibility and generality. Connections between the optimization-based methods and the Bayesian model are developed, and example results are presented for a real compressive x-ray imaging system

Global optimization methods for localization in compressive sensing

The dissertation discusses compressive sensing and its applications to localization in multiple-input multiple-output (MIMO) radars. Compressive sensing is a paradigm at the intersection between signal processing and optimization. It advocates the sensing of “sparse” signals (i.e., represented using just a few terms from a basis expansion) by using a sampling rate much lower than that required by the Nyquist-Shannon sampling theorem (i.e., twice the highest frequency present in the signal of interest). Low-rate sampling reduces implementation’s constraints and translates into cost savings due to fewer measurements required. This is particularly true in localization applications when the number of measurements is commensurate to antenna elements. The theory of compressive sensing provides precise guidance on how the measurements should be acquired, and which optimization algorithm should be used for signal recovery. The first part of the dissertation addresses the application of compressive sensing for localization in the spatial domain, specifically direction of arrival (DOA), using MIMO radar. A sparse localization framework is proposed for a MIMO array in which transmit and receive elements are placed at random. This allows for a dramatic reduction in the number of elements needed, while still attaining performance comparable to that of a filled (Nyquist) array. By leveraging properties of structured random matrices, a bound on the coherence of the resulting measurement matrix is obtained, and conditions under which the measurement matrix satisfies the so-called isotropy property are detailed. The coherence and isotropy concepts are used to establish uniform and non-uniform recovery guarantees within the proposed spatial compressive sensing framework. In particular, it is shown that non-uniform recovery is guaranteed if the product of the number of transmit and receive elements, MN (which is also the number of degrees of freedom), scales with K (log G)2, where K is the number of targets and G is proportional to the array aperture and determines the angle resolution. In contrast with a filled virtual MIMO array where the product MN scales linearly with G, the logarithmic dependence on G in the proposed framework supports the high-resolution provided by the virtual array aperture while using a small number of MIMO radar elements. The second part of the dissertation focuses on the sparse recovery problem at the heart of compressive sensing. An algorithm, dubbed Multi-Branch Matching Pursuit (MBMP), is presented which combines three different paradigms: being a greedy method, it performs iterative signal support estimation; as a rank-aware method, it is able to exploit signal subspace information when multiple snapshots are available; and, as its name foretells, it possesses a multi-branch structure which allows it to trade-off performance (e.g., measurements) for computational complexity. A sufficient condition under which MBMP can recover a sparse signal is obtained. This condition, named MB-coherence, is met when the columns of the measurement matrix are sufficiently “incoherent” and when the signal-to-noise ratio is sufficiently high. The condition shows that successful recovery with MBMP is guaranteed for dictionaries which do not satisfy previously known conditions (e.g., coherence, cumulative coherence, or the Hanman relaxed coherence). Finally, by leveraging the MBMP algorithm, a framework for target detection from a set of compressive sensing radar measurements is established. The proposed framework does not require any prior information about the targets’ scene, and it is competitive with respect to state-of-the-art detection compressive sensing algorithms

Video Compressive Sensing for Dynamic MRI

We present a video compressive sensing framework, termed kt-CSLDS, to accelerate the image acquisition process of dynamic magnetic resonance imaging (MRI). We are inspired by a state-of-the-art model for video compressive sensing that utilizes a linear dynamical system (LDS) to model the motion manifold. Given compressive measurements, the state sequence of an LDS can be first estimated using system identification techniques. We then reconstruct the observation matrix using a joint structured sparsity assumption. In particular, we minimize an objective function with a mixture of wavelet sparsity and joint sparsity within the observation matrix. We derive an efficient convex optimization algorithm through alternating direction method of multipliers (ADMM), and provide a theoretical guarantee for global convergence. We demonstrate the performance of our approach for video compressive sensing, in terms of reconstruction accuracy. We also investigate the impact of various sampling strategies. We apply this framework to accelerate the acquisition process of dynamic MRI and show it achieves the best reconstruction accuracy with the least computational time compared with existing algorithms in the literature.Comment: 30 pages, 9 figure