2014/12/10 by Tamir Bendory, Shai Dekel, Bendory, Tamir +3 · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Computer and information sciences #Information Theory (cs.IT) #Mathematical Analysis and Transform Methods #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1412.3284
openalex publication_date 2014/12/10 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28
In this work we consider the problem of recovering an ensemble of Diracs on\nthe sphere from its projection onto spaces of spherical harmonics. We show that\nunder an appropriate separation condition on the unknown locations of the\nDiracs, the ensemble can be recovered through Total Variation norm\nminimization. The proof of the uniqueness of the solution uses the method of\n`dual' interpolating polynomials and is based on [8], where the theory was\ndeveloped for trigonometric polynomials. We also show that in the special case\nof non-negative ensembles, a sparsity condition is sufficient for exact\nrecovery.\n