Source localization by matched-field processing (MFP) generally involves solving a number of computationally intensive partial differential equations. This paper introduces a technique that mitigates this computational workload by “compressing” these computations. Drawing on key concepts from the recently developed field of compressed sensing, it shows how a low-dimensional proxy for the Green’s function can be constructed by backpropagating a small set of random receiver vectors. Then the source can be located by performing a number of “short” correlations between this proxy and the projection of the recorded acoustic data in the compressed space. Numerical experiments in a Pekeris ocean waveguide are presented that demonstrate that this compressed version of MFP is as effective as traditional MFP even when the compression is significant. The results are particularly promising in the broadband regime where using as few as two random backpropagations per frequency performs almost as well as the traditiona...
In this paper, we effectively demonstrate how classical localization procedures under a least-squares framework such as matched-field processing (MFP) may be solved in a reduced-dimensional space even without a-priori knowledge of the best'' dimension-reducing transform. This property has been shown in similar forms in the mainstream canon of Compressed Sensing (CS) literature. have described a number of useful variations on the theme of CS @cite_8 including a matched filtering detector. They have also described the smashed filter'' that is designed primarily for classification between a finite number of sets, but could easily be extended to parametric estimation. Wakin has also established some rigorous results on parameter estimation that relate the recovery properties of a general compressive estimation problem to the properties of the manifold that these parameters induce. This work could be used to analyze this problem via its manifold parameters @cite_14 .
@cite_14 @cite_8
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A field known as Compressive Sensing (CS) has recently emerged to help address the growing challenges of capturing and processing high-dimensional signals and data sets. CS exploits the surprising fact that the information contained in a sparse signal can be preserved in a small number of compressive (or random) linear measurements of that signal. Strong theoretical guarantees have been established on the accuracy to which sparse or near-sparse signals can be recovered from noisy compressive measurements. In this paper, we address similar questions in the context of a different modeling framework. Instead of sparse models, we focus on the broad class of manifold models, which can arise in both parametric and non-parametric signal families. Building upon recent results concerning the stable embeddings of manifolds within the measurement space, we establish both deterministic and probabilistic instance-optimal bounds in @math for manifold-based signal recovery and parameter estimation from noisy compressive measurements. In line with analogous results for sparsity-based CS, we conclude that much stronger bounds are possible in the probabilistic setting. Our work supports the growing empirical evidence that manifold-based models can be used with high accuracy in compressive signal processing. The recently introduced theory of compressive sensing enables the recovery of sparse or compressible signals from a small set of nonadaptive, linear measurements. If properly chosen, the number of measurements can be much smaller than the number of Nyquist-rate samples. Interestingly, it has been shown that random projections are a near-optimal measurement scheme. This has inspired the design of hardware systems that directly implement random measurement protocols. However, despite the intense focus of the community on signal recovery, many (if not most) signal processing problems do not require full signal recovery. In this paper, we take some first steps in the direction of solving inference problems-such as detection, classification, or estimation-and filtering problems using only compressive measurements and without ever reconstructing the signals involved. We provide theoretical bounds along with experimental results.