Adaptive matching pursuit for sparse signal recovery
This work addresses the computational challenge of sparse recovery in signal processing, offering a faster and more effective solution for applications like regression and classification, though it is incremental as it builds on prior matching pursuit methods.
The authors tackled the hard non-convex and mixed integer problem of maximizing Spike and Slab priors for sparse signal recovery by proposing a new greedy and adaptive matching pursuit (AMP) algorithm, which provides a superior cost-quality trade-off over existing alternatives, as confirmed on simulated and real-world image recovery data.
Spike and Slab priors have been of much recent interest in signal processing as a means of inducing sparsity in Bayesian inference. Applications domains that benefit from the use of these priors include sparse recovery, regression and classification. It is well-known that solving for the sparse coefficient vector to maximize these priors results in a hard non-convex and mixed integer programming problem. Most existing solutions to this optimization problem either involve simplifying assumptions/relaxations or are computationally expensive. We propose a new greedy and adaptive matching pursuit (AMP) algorithm to directly solve this hard problem. Essentially, in each step of the algorithm, the set of active elements would be updated by either adding or removing one index, whichever results in better improvement. In addition, the intermediate steps of the algorithm are calculated via an inexpensive Cholesky decomposition which makes the algorithm much faster. Results on simulated data sets as well as real-world image recovery challenges confirm the benefits of the proposed AMP, particularly in providing a superior cost-quality trade-off over existing alternatives.