In this paper, we propose a unified theoretical and practical spherical approximation
framework for functional inverse problems on the hypersphere S d− 1. More specifically, we …

Many scientific inquiries in natural sciences involve approximating a spherical field-namely
a scalar quantity defined over a continuum of directions-from generalised samples of the …

Inverse problems defined naturally on the sphere are becoming increasingly of interest. In
this article we provide a general framework for evaluation of inverse problems on the …

We propose a discretization method for continuous-domain linear inverse problems with
multiple-order total-variation (TV) regularization. It is based on a recent result that proves …

We propose and study a class of novel algorithms that aim at solving bilinear and quadratic
inverse problems. Using a convex relaxation based on tensorial lifting, and applying first …

Trying to identify the state of a physical system from the knowledge of a few indirect
measurements is an ubiquitous problem in applied sciences known as inverse problem …

We propose a novel algorithm to solve a general class of linear ill-posed inverse problems.
For our numerical tests, we consider ill-posed problems on the sphere as they appear in the …

In the present paper we consider minimization based formulations of inverse problems
$(x,\Phi)\in\mbox {argmin}\{\mathcal {J}(x,\Phi; y)\colon (x,\Phi)\in M_ {ad}(y)\} $ for the …

We focus on nonconvex and nonsmooth minimization problems with a composite objective,
where the differentiable part of the objective is freed from the usual and restrictive global …

We show that inverse problems with a truncated quadratic regularization are NP-hard in
general to solve or even approximate up to an additive error. This stands in contrast to the …