Title :
Joint recovery of sparse signals and parameter perturbations with parameterized measurement models
Author :
Johnson, Erik C. ; Jones, Douglas L.
Author_Institution :
Dept. of Electr. & Comput. Eng., Univ. of Illinois at Urbana-Champaign, Urbana, IL, USA
Abstract :
Many applications involve sparse signals with unknown, continuous parameters; a common example is a signal consisting of several sinusoids of unknown frequency. Applying compressed sensing techniques to these signals requires a highly oversampled dictionary for good approximation, but these dictionaries violate the RIP conditions and produce inconsistent results. We consider recovering both a sparse vector and parameter perturbations from an initial set of parameters. Joint recovery allows for accurate reconstructions without highly oversampled dictionaries. Our algorithm for sparse recovery solves a series of linearized subproblems. Recovery error for noiseless simulated measurements is near zero for coarse dictionaries, but increases with the oversampling. This technique is also used to reconstruct Radio Frequency data. The algorithm estimates sharp peaks and transmitter frequencies, demonstrating the potential practical use of the algorithm on real data.
Keywords :
compressed sensing; frequency estimation; linear programming; perturbation techniques; signal reconstruction; RIP conditions; compressed sensing techniques; joint recovery; noiseless simulated measurements; oversampled dictionary; parameter perturbations; parameterized measurement; radio frequency data; recovery error; sparse signals; sparse vector; transmitter frequencies; Dictionaries; Frequency estimation; Linear programming; Noise measurement; Programming; Vectors; Frequency Estimation; Parameter Perturbations; Parameterized Model; Sparse Reconstruction; Sparse Signal;
Conference_Titel :
Acoustics, Speech and Signal Processing (ICASSP), 2013 IEEE International Conference on
Conference_Location :
Vancouver, BC
DOI :
10.1109/ICASSP.2013.6638796