Recovery of localised structure from signals with non-sparse components

R. Broughton, I. Coope, P. Renaud, Rachael Tappenden


We consider the recovery of localised structure from signals consisting of a piecewise constant structure and sparse components. A new algorithm is presented which aims to reconstruct signals of this type from a limited set of observed data. The algorithm is broken down into two subproblems which both involve minimisation of an $l_1$-regularised least squares problem. Numerical results are presented which demonstrate the effectiveness and efficiency of the proposed method.

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