Spectral Super-resolution With Prior Knowledge

Abstract

We address the problem of super-resolution frequency recovery using prior knowledge of the structure of a spectrally sparse, undersampled signal. In many applications of interest, some structure information about the signal spectrum is often known. The prior information might be simply knowing precisely some signal frequencies or the likelihood of a particular frequency component in the signal. We devise a general semidefinite program to recover these frequencies using theories of positive trigonometric polynomials. Our theoretical analysis shows that, given sufficient prior information, perfect signal reconstruction is possible using signal samples no more than thrice the number of signal frequencies. Numerical experiments demonstrate great performance enhancements using our method. We show that the nominal resolution necessary for the grid-free results can be improved if prior information is suitably employed.

arXiv comment13 pages, 8 figures. arXiv admin note: text overlap with arXiv:1404.7041, arXiv:1311.0950

References in corpus (7)

• From Theory to Practice: Sub-Nyquist Sampling of Sparse Wideband Analog Signals
• Structured Compressed Sensing: From Theory to Applications
• Modified-CS: Modifying Compressive Sensing for Problems with Partially Known Support
• The MUSIC Algorithm for Sparse Objects: A Compressed Sensing Analysis
• Line Spectrum Estimation with Probabilistic Priors
• MUSIC for Single-Snapshot Spectral Estimation: Stability and Super-resolution
• Spike detection from inaccurate samplings