Performance limits of matching pursuit algorithms

In this paper, we examine the performance limits of the Orthogonal Matching Pursuit (OMP) algorithm, which has proven to be effective in solving for sparse solutions to inverse problem arising in overcomplete representations. To identify these limits, we exploit the connection between sparse solution problem and multiple access channel (MAC) in wireless communication domain. The forward selective nature of OMP helps it to be recognized as a successive interference cancellation (SIC) scheme that decodes non-zero entries one at a time in a specific order. We leverage this SIC decoding order and utilize the criterion for successful decoding to develop the information-theoretic performance limitation for OMP, which involves factors such as dictionary dimension, signal-to-noise-ratio, and importantly, the relative behavior of the non-zeros entries. Supported by computer simulations, our proposed criterion is demonstrated to be asymptotically effective in explaining the behavior of OMP.