Application of second generation wavelets to blind spherical deconvolution

We adress the problem of spherical deconvolution in a non parametric statistical framework, where both the signal and the operator kernel are subject to error measurements. After a preliminary treatment of the kernel, we apply a thresholding procedure to the signal in a second generation wavelet basis. Under standard assumptions on the kernel, we study the theoritical performance of the resulting algorithm in terms of L losses (p ≥ 1) on Besov spaces on the sphere. We hereby extend the application of second generation spherical wavelets to the blind deconvolution framework [16]. The procedure is furthermore adaptive with regard both to the target function sparsity and smoothness, and the kernel blurring effect. We end with the study of a concrete example, putting into evidence the improvement of our procedure on the recent blockwise-SVD algorithm [6].