Milana Gataric

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In this paper, we consider the fundamental problem of recovering a univariate function f from a finite collection of pointwise samples of its Fourier transform taking nonuniformly. In the first part of the paper, we show that, under suitable conditions on the sampling frequencies – specifically, its density and its bandwidth – it is possible to recover f in(More)
In this paper, we consider the problem of recovering a compactly-supported multivariate function from a collection of pointwise samples of its Fourier transform taken nonuniformly. We do this by using the concept of weighted Fourier frames. A seminal result of Beurling shows that sample points give rise to a classical Fourier frame provided they are(More)
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(More)
We present recently devised approach for recovery of compactly supported multivariate functions from nonuniform samples of their Fourier transforms. This is the so-called nonuniform generalized sampling (NUGS), based on a generalized sampling framework which permits an arbitrary choice of the reconstruction space and where nonuniform sampling is modeled via(More)
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