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arXiv · 1703.01665

Anisotropic functional Laplace deconvolution

Rida Benhaddou·Marianna Pensky·Rasika Rajapakshage
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Abstract

In the present paper we consider the problem of estimating a three-dimensional function $f$ based on observations from its noisy Laplace convolution. Our study is motivated by the analysis of Dynamic Contrast Enhanced (DCE) imaging data. We construct an adaptive wavelet-Laguerre estimator of $f$, derive minimax lower bounds for the $L^2$-risk when $f$ belongs to a three-dimensional Laguerre-Sobolev ball and demonstrate that the wavelet-Laguerre estimator is adaptive and asymptotically near-optimal in a wide range of Laguerre-Sobolev spaces. We carry out a limited simulations study and show that the estimator performs well in a finite sample setting. Finally, we use the technique for the solution of the Laplace deconvolution problem on the basis of DCE Computerized Tomography data.

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Rida Benhaddou, Marianna Pensky, Rasika Rajapakshage. 2017-03-05. Anisotropic functional Laplace deconvolution. https://arxiv.org/abs/1703.01665

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