Projection Design for Statistical Compressive Sensing: A Tight Frame Based Approach

In this paper, we develop a framework to design sensing matrices for compressive sensing applications that lead to good mean squared error (MSE) performance subject to sensing cost constraints. By capitalizing on the MSE of the oracle estimator, whose performance has been shown to act as a benchmark...

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Vydáno v:IEEE transactions on signal processing Ročník 61; číslo 8; s. 2016 - 2029
Hlavní autoři: Wei Chen, Rodrigues, M. R. D., Wassell, I. J.
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York, NY IEEE 01.04.2013
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:
Algorithm design and analysis
Algorithms
Applied sciences
Compressed sensing
Compressive sensing
Detection
Detection, estimation, filtering, equalization, prediction
Dictionaries
Exact sciences and technology
Exact solutions
Frames
Image reconstruction
Information, signal and communications theory
Mathematical analysis
Matrices
Optimization
overcomplete dictionary
Recovery
Sampling, quantization
sensing projection design
Sensors
Signal and communications theory
Signal, noise
Sparse matrices
sparse representation
Studies
Telecommunications and information theory
tight frames
Vectors
Performance evaluation
Overcomplete dictionary
Iterative method
Performance standard
Algorithm
Optimization
Mean square error
tight frames
Relaxation
Compressive sensing
Estimator efficiency
Matching pursuit
Signal processing
Sparse representation
Oracle
Compressed sensing
sensing projection design
ISSN:1053-587X, 1941-0476
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Popis
Shrnutí:In this paper, we develop a framework to design sensing matrices for compressive sensing applications that lead to good mean squared error (MSE) performance subject to sensing cost constraints. By capitalizing on the MSE of the oracle estimator, whose performance has been shown to act as a benchmark to the performance of standard sparse recovery algorithms, we use the fact that a Parseval tight frame is the closest design - in the Frobenius norm sense - to the solution of a convex relaxation of the optimization problem that relates to the minimization of the MSE of the oracleestimator with respect to the equivalent sensing matrix, subject to sensing energy constraints. Based on this result, we then propose two sensing matrix designs that exhibit two key properties: the designs are closed form rather than iterative; the designs exhibit superior performance in relation to other designs in the literature, which is revealed by our numerical investigation in various scenarios with different sparse recovery algorithms including basis pursuit de-noise (BPDN), the Dantzig selector and orthogonal matching pursuit (OMP).
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ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2013.2245661