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Compressed Sensing With Cross Validation.
- Source :
-
IEEE Transactions on Information Theory . Dec2009, Vol. 55 Issue 12, p5773-5782. 10p. 2 Graphs. - Publication Year :
- 2009
-
Abstract
- Compressed sensing (CS) decoding algorithms can efficiently recover an N-dimensional real-valued vector x to within a factor of its best k-term approximation by taking m = O(k log N/k) measurements y = Φx. If the sparsity or approximate sparsity level of x were known, then this theoretical guarantee would imply quality assurance of the resulting estimate. However, because the underlying sparsity of the signal x is unknown, the quality of a CS estimate ... using m measurements is not assured. It is nevertheless shown in this paper that sharp bounds on the error ||x - ...||𝓁N2 can be achieved with no effort. More precisely, suppose that a maximum number measurements m is preimposed. One can reserve 10 log p of these m measurements and compute a sequence of possible estimates (...j)pj=1 to x from the m - 10 log p remaining measurements; errors ||x - ...j||𝓁N2 for j = 1,..., p can then be bounded high probability. As a consequence, numerical upper and lower bounds on the error between x and the best k-term approximation to x can be estimated for p values of k with almost no cost. observation has applications outside CS as well. [ABSTRACT FROM AUTHOR]
- Subjects :
- *ALGORITHMS
*MATHEMATICS
*DATA transmission systems
*PIXELS
*PROBABILITY theory
Subjects
Details
- Language :
- English
- ISSN :
- 00189448
- Volume :
- 55
- Issue :
- 12
- Database :
- Academic Search Index
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- 47101225
- Full Text :
- https://doi.org/10.1109/TIT.2009.2032712