Compressed Sensing Meets Game Theory

We introduce the MUSE Algorithm and prove that for any ksparse vector α∗, any measurement matrix Φ, and any noise vector ε, given f = Φα∗ + ε, the proposed algorithm finds a k-sparse vector α̂ such that ∥Φα̂−f∥∞ ≤ ∥ε∥∞+O ( 1 √ k ) . The proposed algorithm is based on reformulating the sparse approximation problem as a zero-sum game over a properly chosen new space. If the projection matrix satisfies the restricted isometry property, then the measurement domain l∞guarantee can be translated to a data domain l2-guarantee. Simulation results support the fidelity of the proposed algorithm.