Robust method for finding sparse solutions to linear inverse problems using an L2 regularization

Abstract: We analyzed the performance of a biologically inspired algorithm called the Corrected Projections Algorithm (CPA) when a sparseness constraint is required to unambiguously reconstruct an observed signal using atoms from an overcomplete dictionary. By changing the geometry of the estimation problem, CPA gives an analytical expression for a binary variable that indicates the presence or absence of a dictionary atom using an L2 regularizer. The regularized solution can be implemented using an efficient real-time Kalman-filter type of algorithm. The smoother L2 regularization of CPA makes it very robust to noise, and CPA outperforms other methods in identifying known atoms in the presence of strong novel atoms in the signal.