Optimal Spherical Deconvolution

Optimal Spherical Deconvolution

This paper addresses the issue of optimal deconvolution density estimation on the 2-sphere. Indeed, by using the transitive group action of the rotation matrices on the 2-dimensional unit sphere, rotational errors can be introduced analogous to the Euclidean case. The resulting density turns out to be convolution in the Lie group sense and so the statistical problem is to recover the true under...

Spherical Deconvolution

This paper proposes nonparametric deconvolution density estimation over S 2. Here we would think of the S 2 elements of interest being corrupted by random SO(3) elements (rotations). The resulting density on the observations would be a convolution of the SO(3) density with the true S 2 density. Consequently, the methodology, as in the Euclidean case, would be to use Fourier analysis on SO(3) an...

Localized spherical deconvolution

The dictionary approach for spherical deconvolution

We consider the problem of estimating a density of probability from indirect data in the spherical convolution model. We aim at building an estimate of the unknown density as a linear combination of functions of an overcomplete dictionary. The procedure is devised through a well-calibrated `1-penalized criterion. The spherical deconvolution setting has been barely studied so far, and the two ma...

On Optimal Uniform Deconvolution

This paper concerns the nonstandard problem of uniform deconvolution for nonperiodic functions over the real line. New algorithms are developed for this nonstandard statistical problem and integrated mean squared error bounds are established. We show that the upper bound of the integrated mean squared error for our new procedure is the same as for the standard case; hence these new estimators a...