Abstract:This paper studies the continuous-domain inverse problem of recovering Radon measures on the one-dimensional torus from low-frequency Fourier coefficients, where Kc is the cutoff frequency. Our approach consists in minimizing the total-variation norm among all Radon measures that are consistent with the observations. We call this problem the basis pursuit in the continuum (BPC). We characterize the solution set of (BPC) in terms of uniqueness and describe its sparse solutions which are sums of few signed Dirac ma… Show more
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