The MUSIC Algorithm for Sparse Objects: A Compressed Sensing Analysis

The MUSIC algorithm, and its extension for imaging sparse extended objects, with noisy data is analyzed by compressed sensing (CS) techniques. A thresholding rule is developed to augment the standard MUSIC algorithm. The notion of restricted isometry property (RIP) and an upper bound on the restricted isometry constant (RIC) are employed to establish sufficient conditions for the exact localization by MUSIC with or without noise. In the noiseless case, the sufficient condition gives an upper bound on the numbers of random sampling and incident directions necessary for exact localization. In the noisy case, the sufficient condition assumes additionally an upper bound for the noise-to-object ratio in terms of the RIC and the dynamic range of objects. This bound points to the superresolution capability of the MUSIC algorithm. Rigorous comparison of performance between MUSIC and the CS minimization principle, Basis Pursuit Denoising (BPDN), is given. In general, the MUSIC algorithm guarant...

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Albert Fannjiang
• Keywords: CORR 2010, Education, MUSIC Algorithm, Sufficient Condition, Upper Bound