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• W1715895200 abstract "We consider the problem of reconstruction of a non-linear finite-parametric model $M=M_p(x),$ with $p=(p_1,...,p_r)$ a set of parameters, from a set of measurements $mu_j(M)$. In this paper $mu_j(M)$ are always the moments $m_j(M)=int x^jM_p(x)dx$. This problem is a central one in Signal Processing, Statistics, and in many other applications. We concentrate on a direct (and somewhat naive) approach to the above problem: we simply substitute the model function $M_p(x)$ into the measurements $mu_j$ and compute explicitly the resulting symbolic expressions of $mu_j(M_p)$ in terms of the parameters $p$. Equating these symbolic expressions to the actual measurement results, we produce a system of nonlinear equations on the parameters $p$, which we consequently try to solve. The aim of this paper is to review some recent results (mostly of cite{Vet5,Mil1,Mil2,Put1,Vet4,Vet3,Mil3,Mil4,Vet2}) in this direction, stressing the algebraic structure of the arising systems and mathematical tools required for their solutions. In particular, we discuss the relation of the reconstruction problem above with the recent results of cite{bfy,bry,chr,pak1,pak2,pak3,pry,ry} on the vanishing problem of generalized polynomial moments and on the Cauchy-type integrals of algebraic functions. The accompanying paper cite{Kis1} (this volume) provides a solution method for a wide class of reconstruction problems as above, based on the study of linear differential equations with rational coefficient, which are satisfied by the moment generating function of the problem." @default.
• W1715895200 created "2016-06-24" @default.
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• W1715895200 date "2008-10-29" @default.
• W1715895200 modified "2023-09-27" @default.
• W1715895200 title "Signal Acquisition from Measurements via Non-Linear Models" @default.
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