2017/10/25 by Hernán García, Camilo Hernández, García, Hernán +5
Engineering · Mathematics · #FOS: Mathematics #Mathematical Approximation and Integration #Microwave Imaging and Scattering Analysis #Optimization and Control (math.OC) #Sparse and Compressive Sensing Techniques #math.OC
paper · pdf · doi:10.48550/arxiv.1710.09496
arxiv created 2017/10/25 · openalex publication_date 2017/10/25 · arxiv updated 2017/10/27 · openalex created_date 2017/11/10 · openalex updated_date 2026/08/04
We propose convex optimization algorithms to recover a good approximation of a point measure μ on the unit sphere S⊆ ℝn from its moments with respect to a set of real-valued functions f1,…, fm. Given a finite subset C⊆ S the algorithm produces a measure μ^* supported on C and we prove that μ^* is a good approximation to μ whenever the functions f1,…, fm are a sufficiently large random sample of independent Kostlan-Shub-Smale polynomials. More specifically, we give sufficient conditions for the validity of the equality μ=μ^* when μ is supported on C and prove that μ^* is close to the best approximation to μ supported on C provided that all points in the support of μ are close to C.