Adaptive Estimation of Time-Varying Sparse Signals


We take a look at the challenge of designing adaptively compressive measurement matrices for the purpose of estimating time-varying sparse signals. We approach this challenge by modeling it as a Markov decision process with some degree of observability. Because of this formulation, we are able to use Bellman's principle of optimality in the implementation of multi-step lookahead designs of compressive measurement procedures. We investigate the value of multi-step (non-myopic) lookahead adaptive schemes as opposed to one-step (myopic) lookahead adaptive schemes by introducing two different iterations of the compressive measurement design problem. We then compare the performance of adaptive designs to that of traditional non-adaptive designs. In the first iteration of this problem, we consider the problem of selecting measurement matrices with fixed dimensions sequentially from a library of measurement matrices that has been specified in advance. In the second iteration, an adaptive selection process is used to determine the number of compressive measurements, also known as the number of rows of the measurement matrix. When the total number of measurements has been established, the entries of the matrix are then selected in accordance with a previously outlined adaptive scheme. One of these two issues will be evaluated based on its own distinct set of performance standards. In the first problem, the conditional mutual information between the sparse signal support and measurements serves as a measurement of how effectively the solution was implemented. The performance metric for the second problem is a linear combination of the total number of measurements and the conditional mutual information. We investigate the usefulness of a variety of different designs in a range of contexts by running a number of simulations. The implementation of a strategy known as rollout serves as the primary focal point of these simulations. The amount of computation that must be done in order to use the rollout method, on the other hand, is what motivated us to modify two data association heuristics so that they can be applied to the compressive sensing paradigm. These heuristics show potential for reducing the amount of computation required to search for optimal solutions and to propagate distributions.

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