Title: 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.