Compressed sensing with a jackknife and a bootstrap
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2018
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| _version_ | 1866913302717661184 |
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| author | Tygert, Mark Ward, Rachel Zbontar, Jure |
| author_facet | Tygert, Mark Ward, Rachel Zbontar, Jure |
| contents | Compressed sensing proposes to reconstruct more degrees of freedom in a signal than the number of values actually measured. Compressed sensing therefore risks introducing errors -- inserting spurious artifacts or masking the abnormalities that medical imaging seeks to discover. The present case study of estimating errors using the standard statistical tools of a jackknife and a bootstrap yields error "bars" in the form of full images that are remarkably representative of the actual errors (at least when evaluated and validated on data sets for which the ground truth and hence the actual error is available). These images show the structure of possible errors -- without recourse to measuring the entire ground truth directly -- and build confidence in regions of the images where the estimated errors are small. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1809_06959 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Compressed sensing with a jackknife and a bootstrap Tygert, Mark Ward, Rachel Zbontar, Jure Image and Video Processing Signal Processing Methodology Compressed sensing proposes to reconstruct more degrees of freedom in a signal than the number of values actually measured. Compressed sensing therefore risks introducing errors -- inserting spurious artifacts or masking the abnormalities that medical imaging seeks to discover. The present case study of estimating errors using the standard statistical tools of a jackknife and a bootstrap yields error "bars" in the form of full images that are remarkably representative of the actual errors (at least when evaluated and validated on data sets for which the ground truth and hence the actual error is available). These images show the structure of possible errors -- without recourse to measuring the entire ground truth directly -- and build confidence in regions of the images where the estimated errors are small. |
| title | Compressed sensing with a jackknife and a bootstrap |
| topic | Image and Video Processing Signal Processing Methodology |
| url | https://arxiv.org/abs/1809.06959 |