Jointly Sparse Signal Recovery with Prior Info

Natalie Durgin, Rachel Grotheer, Chenxi Huang, Shuang Li, Anna Ma, Deanna Needell, Jing Qin

Abstract: The multiple measurement vector (MMV) problem with jointly sparse signals has been of recent interest across many fields and can be solved via ℓ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2,1</inf> minimization. In such applications, prior information is typically available and utilizing weights to incorporate the prior information has only been empirically shown to be advantageous. In this work, we prove theoretical guarantees for a weighted ℓ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2,1</inf> minimization approach to solving the MMV problem where the underlying signals admit a jointly sparse structure. Our theoretical findings are complemented with empirical results on simulated and real world video data.