Recovering Piecewise Smooth Functions from Nonuniform Fourier Measurements [chapter]

Ben Adcock, Milana Gataric, Anders C. Hansen
2015 Lecture Notes in Computational Science and Engineering  
In this paper, we consider the problem of reconstructing piecewise smooth functions to high accuracy from nonuniform samples of their Fourier transform. We use the framework of nonuniform generalized sampling (NUGS) to do this, and to ensure high accuracy we employ reconstruction spaces consisting of splines or (piecewise) polynomials. We analyze the relation between the dimension of the reconstruction space and the bandwidth of the nonuniform samples, and show that it is linear for splines and
more » ... ear for splines and piecewise polynomials of fixed degree, and quadratic for piecewise polynomials of varying degree.
doi:10.1007/978-3-319-19800-2_8 fatcat:2tbfqvbvtfgp3bl3u7544wsqjq