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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| Published in: | Applied and computational harmonic analysis Vol. 31; no. 2; pp. 185 - 204 |
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| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
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01.09.2011
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| ISSN: | 1063-5203, 1096-603X |
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| Abstract | 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. |
|---|---|
| AbstractList | 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 sub(1) norm of the canonical frame coefficients among all the possible solutions. 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. |
| Author | Cai, Jian-Feng Ye, Gui-Bo Shen, Zuowei |
| Author_xml | – sequence: 1 givenname: Jian-Feng surname: Cai fullname: Cai, Jian-Feng email: cai@math.ucla.edu organization: Department of Mathematics, University of California, Los Angeles, United States – sequence: 2 givenname: Zuowei surname: Shen fullname: Shen, Zuowei email: matzuows@nus.edu.sg organization: Department of Mathematics, National University of Singapore, Singapore – sequence: 3 givenname: Gui-Bo surname: Ye fullname: Ye, Gui-Bo email: yeg@uci.edu organization: Department of Computer Science, University of California, Irvine, United States |
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| Keywords | Framelet ℓ 1 minimization Error estimation Covering number Missing data recovery Uniform law of large numbers |
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