A multiple-input multiple-output (MIMO) radar system, unlike a standard phased-array radar, can choose freely the probing signals transmitted via its antennas to maximize the power around the locations of the targets of interest, or more generally to approximate a given transmit beampattern, and also to minimize the cross-correlation of the signals reflected back to the radar by the targets of interest. In this paper, we show how the above desirable features can be achieved by designing the covariance matrix of the probing signal vector transmitted by the radar. Moreover, in a numerical study, we show that the proper choice of the probing signals can significantly improve the performance of adaptive MIMO radar techniques. Additionally, we demonstrate the advantages of several MIMO transmit beampattern designs, including a beampattern matching design and a minimum sidelobe beampattern design, over their phased-array counterparts.

Online detection of changes in stochastic systems, referred to as sequential change detection or quickest change detection, is an important research topic in statistics, signal processing, and information theory, and has a wide range of applications. This survey starts with the basics of sequential change detection, and then moves on to generalizations and extensions of sequential change detection theory and methods. We also discuss some new dimensions that emerge at the intersection of sequential change detection with other areas, along with a selection of modern applications and remarks on open questions.

We propose a new multistatic adaptive microwave imaging (MAMI) method for early breast cancer detection. MAMI is a two-stage robust Capon beamforming (RCB) based image formation algorithm. MAMI exhibits higher resolution, lower sidelobes, and better noise and interference rejection capabilities than the existing approaches. The effectiveness of using MAMI for breast cancer detection is demonstrated via a simulated 3-D breast model and several numerical examples

This paper describes a novel approach to change-point detection when the observed high-dimensional data may have missing elements. The performance of classical methods for change-point detection typically scales poorly with the dimensionality of the data, so that a large number of observations are collected after the true change-point before it can be reliably detected. Furthermore, missing components in the observed data handicap conventional approaches. The proposed method addresses these challenges by modeling the dynamic distribution underlying the data as lying close to a time-varying low-dimensional submanifold embedded within the ambient observation space. Specifically, streaming data is used to track a submanifold approximation, measure deviations from this approximation, and calculate a series of statistics of the deviations for detecting when the underlying manifold has changed in a sharp or unexpected manner. The approach described in this paper leverages several recent results in the field of high-dimensional data analysis, including subspace tracking with missing data, multiscale analysis techniques for point clouds, online optimization, and change-point detection performance analysis. Simulations and experiments highlight the robustness and efficacy of the proposed approach in detecting an abrupt change in an otherwise slowly varying low-dimensional manifold.

We develop a mixture procedure to monitor parallel streams of data for a change-point that affects only a subset of them, without assuming a spatial structure relating the data streams to one another. Observations are assumed initially to be independent standard normal random variables. After a change-point the observations in a subset of the streams of data have nonzero mean values. The subset and the post-change means are unknown. The procedure we study uses stream specific generalized likelihood ratio statistics, which are combined to form an overall detection statistic in a mixture model that hypothesizes an assumed fraction $p_{0}$ of affected data streams. An analytic expression is obtained for the average run length (ARL) when there is no change and is shown by simulations to be very accurate. Similarly, an approximation for the expected detection delay (EDD) after a change-point is also obtained. Numerical examples are given to compare the suggested procedure to other procedures for unstructured problems and in one case where the problem is assumed to have a well-defined geometric structure. Finally we discuss sensitivity of the procedure to the assumed value of $p_{0}$ and suggest a generalization.

We extend the theory of low-rank matrix recovery and completion to the case when Poisson observations for a linear combination or a subset of the entries of a matrix are available, which arises in various applications with count data. We consider the usual matrix recovery formulation through maximum likelihood with proper constraints on the matrix M of size d ₁ -by-d ₂ , and establish theoretical upper and lower bounds on the recovery error. Our bounds for matrix completion are nearly optimal up to a factor on the order of O(log(d ₁ d ₂ )). These bounds are obtained by combining techniques for recovering sparse vectors with compressed measurements in Poisson noise, those for analyzing low-rank matrices, as well as those for one-bit matrix completion [Davenport , “1-bit Matrix Completion, Information and Inference,” Information and Inference, vol. 3, no. 3, pp. 189-223, Sep. 2014] (although these two problems are different in nature). The adaptation requires new techniques exploiting properties of the Poisson likelihood function and tackling the difficulties posed by the locally sub-Gaussian characteristic of the Poisson distribution. Our results highlight a few important distinctions of the Poisson case compared to the prior work including having to impose a minimum signal-to-noise requirement on each observed entry and a gap in the upper and lower bounds. We also develop a set of efficient iterative algorithms and demonstrate their good performance on synthetic examples and real data.