  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 $L^p$ losses ($p\geq 1$) on
Besov spaces on the sphere. We hereby extend the application of second
generation spherical wavelets to the blind deconvolution framework. 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.
