2016/10/31 by Christina Frederick, Frederick, Christina
Engineering · Mathematics · #15A09 #15A12 #94A12 #94A20 #94A24 #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Numerical Analysis (math.NA) #Numerical methods in inverse problems #Sparse and Compressive Sensing Techniques
paper · pdf · doi:10.48550/arxiv.1611.00600
openalex publication_date 2016/10/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider sampling strategies for a class of multivariate bandlimited\nfunctions f that have a spectrum consisting of disjoint frequency bands.\nTaking advantage of the special spectral structure, we provide formulas\nrelating f to the samples f(y), y\∈ X, where X is a periodic nonuniform\nsampling set. In this case, we show that the reconstruction can be viewed as an\niterative process involving certain Vandermonde matrices, resulting in a link\nbetween the invertibility of these matrices to the existence of certain\nsampling sets that guarantee a unique recovery. Furthermore, estimates of\ninverse Vandermonde matrices are used to provide explicit L2-stability\nestimates for the reconstruction of this class of functions.\n