An “algebraic” reconstruction of piecewise-smooth functions from integral measurements

Abstract : This paper presents some results on a well-known problem in Algebraic Signal Sampling and in other areas of applied mathematics: reconstruction of piecewise-smooth functions from their integral measurements (like moments, Fourier coefficients, Radon transform, etc.). Our results concern reconstruction (from the moments) of signals in two specific classes: linear combinations of shifts of a given function, and “piecewise D-finite functions” which satisfy on each continuity interval a linear differential equation with polynomial coefficients.
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Dima Batenkov, Niv Sarig, Yosef Yomdin. An “algebraic” reconstruction of piecewise-smooth functions from integral measurements. SAMPTA'09, May 2009, Marseille, France. Special Session on sampling using finite rate of innovation principles. ⟨hal-00452200⟩

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