Approximation of frame based missing data recovery

Recovering missing data from its partial samples is a fundamental problem in mathematics and it has wide range of applications in image and signal processing. While many such algorithms have been developed recently, there are very few papers available on their error estimations. This paper is to ana...

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Bibliographic Details
Published in:Applied and computational harmonic analysis Vol. 31; no. 2; pp. 185 - 204
Main Authors: Cai, Jian-Feng, Shen, Zuowei, Ye, Gui-Bo
Format: Journal Article
Language:English
Published: Elsevier Inc 01.09.2011
Subjects:
[formula omitted] minimization
Algorithms
Approximation
Covering number
Error estimation
Errors
Framelet
Frames
Mathematical analysis
Mathematical models
Missing data
Missing data recovery
Uniform law of large numbers
Framelet
ℓ 1 minimization
Error estimation
Covering number
Missing data recovery
Uniform law of large numbers
ISSN:1063-5203, 1096-603X
Online Access:Get full text
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Summary:Recovering missing data from its partial samples is a fundamental problem in mathematics and it has wide range of applications in image and signal processing. While many such algorithms have been developed recently, there are very few papers available on their error estimations. This paper is to analyze the error of a frame based data recovery approach from random samples. In particular, we estimate the error between the underlying original data and the approximate solution that interpolates (or approximates with an error bound depending on the noise level) the given data that has the minimal ℓ 1 norm of the canonical frame coefficients among all the possible solutions.
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ISSN:1063-5203
1096-603X
DOI:10.1016/j.acha.2010.11.007