Nonlinear approximation spaces for inverse problems

This paper is concerned with the ubiquitous inverse problem of recovering an unknown function u from finitely many measurements, possibly affected by noise. In recent years, inversion methods based on linear approximation spaces were introduced in [1, 2] certified recovery bounds. It however known that become ineffective for approximating simple and relevant families functions, such as piecewise smooth typically occur hyperbolic PDEs (shocks) or images (edges). For families, nonlinear [3] are to significantly improve performance. The first contribution this provide bounds procedures spaces. second application framework general bidimensional shapes cell-average data. We also discuss how our results n-term relates classical compressed sensing.