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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| Published in | IEEE transactions on signal processing Vol. 61; no. 8; pp. 2016 - 2029 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
New York, NY
IEEE
01.04.2013
Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1053-587X 1941-0476 |
| DOI | 10.1109/TSP.2013.2245661 |
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| Abstract | 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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| AbstractList | 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). 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: i) the designs are closed form rather than iterative; ii) 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). |
| Author | Rodrigues, M. R. D. Wei Chen Wassell, I. J. |
| Author_xml | – sequence: 1 surname: Wei Chen fullname: Wei Chen email: wc253@cam.ac.uk organization: Comput. Lab., Univ. of Cambridge, Cambridge, UK – sequence: 2 givenname: M. R. D. surname: Rodrigues fullname: Rodrigues, M. R. D. email: m.rodrigues@ucl.ac.uk organization: Dept. of Electron. & Electr. Eng., Univ. Coll. London, London, UK – sequence: 3 givenname: I. J. surname: Wassell fullname: Wassell, I. J. email: ijw24@cam.ac.uk organization: Comput. Lab., Univ. of Cambridge, Cambridge, UK |
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| Keywords | 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 |
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| SubjectTerms | 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 |
| Title | Projection Design for Statistical Compressive Sensing: A Tight Frame Based Approach |
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