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We analyzed the performance of a biologically inspired algorithm called theCorrected Projections Algorithm (CPA) when a sparseness constraint is requiredto unambiguously reconstruct an observed signal using atoms from anovercomplete dictionary. By changing the geometry of the estimation problem,CPA gives an analytical expression for a binary variable that indicates thepresence or absence of a dictionary atom using an L2 regularizer. Theregularized solution can be implemented using an efficient real-timeKalman-filter type of algorithm. The smoother L2 regularization of CPA makes itvery robust to noise, and CPA outperforms other methods in identifying knownatoms in the presence of strong novel atoms in the signal.

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