NDLI: Nonideal sampling and interpolation from noisy observations in shift-invariant spaces

Content Provider	IEEE Xplore Digital Library
Author	Eldar, Y.C. Unser, M.
Copyright Year	1991
Abstract	Digital analysis and processing of signals inherently relies on the existence of methods for reconstructing a continuous-time signal from a sequence of corrupted discrete-time samples. In this paper, a general formulation of this problem is developed that treats the interpolation problem from ideal, noisy samples, and the deconvolution problem in which the signal is filtered prior to sampling, in a unified way. The signal reconstruction is performed in a shift-invariant subspace spanned by the integer shifts of a generating function, where the expansion coefficients are obtained by processing the noisy samples with a digital correction filter. Several alternative approaches to designing the correction filter are suggested, which differ in their assumptions on the signal and noise. The classical deconvolution solutions (least-squares, Tikhonov, and Wiener) are adapted to our particular situation, and new methods that are optimal in a minimax sense are also proposed. The solutions often have a similar structure and can be computed simply and efficiently by digital filtering. Some concrete examples of reconstruction filters are presented, as well as simple guidelines for selecting the free parameters (e.g., regularization) of the various algorithms
Sponsorship	IEEE Signal Processing Society
Starting Page	2636
Ending Page	2651
Page Count	16
File Size	669359
File Format	PDF
ISSN	1053587X
Volume Number	54
Issue Number	7
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2006-07-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Sampling methods Interpolation Signal sampling Signal processing Deconvolution Digital filters Signal analysis Signal reconstruction Signal generators Noise generators sampling interpolation minimax reconstruction
Content Type	Text
Resource Type	Article
Subject	Signal Processing Electrical and Electronic Engineering

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