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We consider the problem of reconstruction of a non-linear finite-parametric model M = Mp(x), with p = (p1, . . . , pr) a set of parameters, from a set of measurements μj(M). In this paper μj(M) are always the moments mj(M) = ∫ xMp(x)dx. This problem is a central one in Signal Processing, Statistics, and in many other applications. We concentrate on a direct… (More)

- Boris Ettinger, Niv Sarig, Yosef Yomdin
- ArXiv
- 2007

We address in this paper the following two closely related problems: 1. How to represent functions with singularities (up to a prescribed accuracy) in a compact way? 2. How to reconstruct such functions from a small number of measurements? The stress is on a comparison of linear and nonlinear approaches. As a model case we use piecewise-constant functions… (More)

- Dima Batenkov, Niv Sarig, Yosef Yomdin
- 2009

This paper presents some results on a well-known problem in Algebraic Signal Sampling and in other areas of applied mathematics: reconstruction of piecewise-smooth functions from their integral measurements (like moments, Fourier coefficients, Radon transform, etc.). Our results concern reconstruction (from the moments) of signals in two specific classes:… (More)

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