Adaptive compressive sampling using partially observable markov decision processes

Zahedi, Ramin; Krakow, Lucas W.; Chong, Edwin K. P.; Pezeshki, Ali

doi:10.1109/icassp.2012.6289109

Cited by 3 publications

(2 citation statements)

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“…We verify this claim throughout several simulations. In fact, we have previously verified this claim for static and time-varying 1-sparse signals in noisy environments in [32] and [33].…”

Section: Introductionsupporting

confidence: 57%

Adaptive Estimation of Time-Varying Sparse Signals

et al. 2013

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We consider the problem of adaptively designing compressive measurement matrices for estimating time-varying sparse signals. We formulate this problem as a partially observable Markov decision process. This formulation allows us to use Bellman's principle of optimality in the implementation of multistep lookahead designs of compressive measurements. We compare the performance of adaptive versus traditional non-adaptive designs and study the value of multi-step (non-myopic) versus one-step (myopic) lookahead adaptive schemes by introducing two variations of the compressive measurement design problem. In the first variation, we consider the problem of sequentially selecting measurement matrices with fixed dimensions from a prespecified library of measurement matrices. In the second variation, the number of compressive measurements, i.e., the number of rows of the measurement matrix, is adaptively chosen. Once the number of measurements is determined, the matrix entries are chosen according to a prespecified adaptive scheme. Each of these two problems is judged by a separate performance criterion. The gauge of efficiency in the first problem is the conditional mutual information between the sparse signal support and measurements. The second problem applies a linear combination of the number of measurements and conditional mutual information as the performance measure. Through several simulations, we study the effectiveness of different designs in various settings. The primary focus in these simulations is the application of a method known as rollout. However, the computational load required for using the rollout method has also inspired us to adapt two data association heuristics to the compressive sensing paradigm. These heuristics show promising decreases in the amount of computation for propagating distributions and searching for optimal solutions.

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“…We verify this claim throughout several simulations. In fact, we have previously verified this claim for static and time-varying 1-sparse signals in noisy environments in [32] and [33].…”

Section: Introductionsupporting

confidence: 57%

Adaptive Estimation of Time-Varying Sparse Signals

et al. 2013

Self Cite

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“…The notion of adaptively optimizing linear compressive measurements in a closed-loop setting for reconstructing sparse signals has been investigated in a number of recent papers in the compressive sensing literature; for example, [1], [2], [3], [4]. The basic idea is to sequentially design the measurement vectors by exploiting information derived from past measurements with a goal of either improving the resulting estimation performance or reducing the total number of measurements (for achieving a desired performance) as compared with batch designs.…”

Section: Introductionmentioning

confidence: 99%

Exploiting adaptive beamforming for compressive measurements

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Wang

et al. 2012

2012 IEEE 7th Sensor Array and Multichannel Signal Processing Workshop (SAM)

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Beamformers are spatial filters that focus energy in a particular direction while attempting to eliminate interference from other directions. This paper compares several adaptive approaches that seek to provide detection performance equivalent to classical techniques while using fewer beams, a form of measurement compression. Using an apriori distribution on the source locations together with an initial set of beams as a starting point, these algorithms adaptively form a sequence of beams based on posterior distributions of the source locations. Two methods are considered: one attempts to maximize the trace of the Fisher information and the other maximizes mutual information based on a Gaussian posterior approximation.

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