A NOTE ON A FIXED POINT METHOD FOR DECONVOLUTION

Abstract : In this paper we study a particular multidimensional deconvolution problem. The distribution of the noise is assumed to be of the form $G(dx) = (1 − \alpha)\delta(dx) + \alpha g(x)dx$, where $\delta$ is the Dirac mass at $0\in R^d$ , $g : R^d → [0, \infty)$ is a density and $\alpha \in [0, 1 2 [$. We propose a new estimation procedure, which is not based on a Fourier approach, but on a fixed point method. The performances of the procedure are studied over isotropic Besov balls for Lp loss functions, $1\leq p<\infty$. A numerical study illustrates the method.
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Céline Duval. A NOTE ON A FIXED POINT METHOD FOR DECONVOLUTION. Statistics, Taylor & Francis: STM, Behavioural Science and Public Health Titles, 2017, 51 (2), pp.347-362. ⟨10.1080/02331888.2016.1265967⟩. ⟨hal-01199599v2⟩

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