Compressive sensing meets game theory

We introduce the Multiplicative Update Selector and Estimator (MUSE) algorithm for sparse approximation in underdetermined linear regression problems. Given f = Φα∗ + µ, the MUSE provably and efficiently finds a k-sparse vector ˆα such that Φˆα − f ∞ ≤ µ ∞ + O 1√ k , for any k-sparse vector α∗ , any measurement matrix Φ, and any noise vector µ. We cast the sparse approximation problem as a zerosum game over a properly chosen new space; this reformulation provides salient computational advantages in recovery. When the measurement matrix Φ provides stable embedding to sparse vectors (the so-called restricted isometry property in compressive sensing), the MUSE also features guarantees on α∗ − ˆα 2. Simulation results demonstrate the scalability and performance of the MUSE in solving sparse approximation problems based on the Dantzig Selector.

• Type: Journal
• Year: 2011
• Where: ICASSP
• Authors: Sina Jafarpour, Robert E. Schapire, Volkan Cevher
• Keywords: ICASSP 2011, MUSE, Signal Processing, Sparse Approximation, Sparse Approximation Problems