Nearly optimal nested sensors location for polynomial regression on complex geometries

We compute nearly optimal nested sensors configurations for global polynomial regression on domains with a complex shape, by resorting to the recent CATCH (Caratheodory-Tchakaloff) subsampling technique (sparse discrete moment matching via NonNegative Least Squares). For example, this allows to compress thousands of low-discrepancy sampling points on a many-sided nonconvex polygon into a small subset of weighted points, keeping the size of the uniform regression error estimates with compression ratios of 1-2 orders of magnitude. Since the l1-norm of the weights remains constant by construction, this technique differs substan- tially from the most popular compressed sensing methods based on l1- minimization (such as Basis Pursuit).