Adaptive matching pursuit with constrained total least squares
Open Access
- 4 April 2012
- journal article
- Published by Springer Science and Business Media LLC in EURASIP Journal on Advances in Signal Processing
- Vol. 2012 (1), 76
- https://doi.org/10.1186/1687-6180-2012-76
Abstract
Compressive sensing (CS) can effectively recover a signal when it is sparse in some discrete atoms. However, in some applications, signals are sparse in a continuous parameter space, e.g., frequency space, rather than discrete atoms. Usually, we divide the continuous parameter into finite discrete grid points and build a dictionary from these grid points. However, the actual targets may not exactly lie on the grid points no matter how densely the parameter is grided, which introduces mismatch between the predefined dictionary and the actual one. In this article, a novel method, namely adaptive matching pursuit with constrained total least squares (AMP-CTLS), is proposed to find actual atoms even if they are not included in the initial dictionary. In AMP-CTLS, the grid and the dictionary are adaptively updated to better agree with measurements. The convergence of the algorithm is discussed, and numerical experiments demonstrate the advantages of AMP-CTLS.Keywords
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This publication has 22 references indexed in Scilit:
- Sensitivity to Basis Mismatch in Compressed SensingIEEE Transactions on Signal Processing, 2011
- Sparsity-Cognizant Total Least-Squares for Perturbed Compressive SamplingIEEE Transactions on Signal Processing, 2011
- An approach of regularization parameter estimation for sparse signal recoveryPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2010
- Analysis of Orthogonal Matching Pursuit Using the Restricted Isometry PropertyIEEE Transactions on Information Theory, 2010
- Direction-of-Arrival Estimation Using a Mixed $\ell _{2,0}$ Norm ApproximationIEEE Transactions on Signal Processing, 2010
- CoSaMP: Iterative signal recovery from incomplete and inaccurate samplesApplied and Computational Harmonic Analysis, 2009
- Subspace Pursuit for Compressive Sensing Signal ReconstructionIEEE Transactions on Information Theory, 2009
- Uniform Uncertainty Principle and Signal Recovery via Regularized Orthogonal Matching PursuitFoundations of Computational Mathematics, 2008
- Compressive Sensing [Lecture Notes]IEEE Signal Processing Magazine, 2007
- Matching pursuits with time-frequency dictionariesIEEE Transactions on Signal Processing, 1993