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A Sampling Theorem for Deconvolution in Two Dimensions
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| 자료유형 | 학위논문 |
|---|---|
| 서명/저자사항 | A Sampling Theorem for Deconvolution in Two Dimensions. |
| 개인저자 | McDonald, Joseph. |
| 단체저자명 | New York University. Mathematics. |
| 발행사항 | [S.l.]: New York University., 2019. |
| 발행사항 | Ann Arbor: ProQuest Dissertations & Theses, 2019. |
| 형태사항 | 121 p. |
| 기본자료 저록 | Dissertations Abstracts International 81-06B. Dissertation Abstract International |
| ISBN | 9781392742068 |
| 학위논문주기 | Thesis (Ph.D.)--New York University, 2019. |
| 일반주기 |
Source: Dissertations Abstracts International, Volume: 81-06, Section: B.
Advisor: Fernandez-Granda, Carlos. |
| 이용제한사항 | This item must not be sold to any third party vendors.This item must not be sold to any third party vendors. |
| 요약 | We show that in two dimensions, in the case of regular sampling, the signal can be recovered exactly under certain sampling distance and minimum separation conditions on the signal support. By proving the existence of a dual certificate in these conditions the minimum of the total variation (TV) norm is guaranteed as the solution to the deconvolution problem. In the discrete setting this is the l1-norm minimum and is solvable by standard optimization methods. We introduce a method of interpolation with Gaussian kernels and provide a novel geometric argument to prove the two-dimensional result with an intuitive extension to higher dimensions.Empirical work is also presented including simulations against which we compare our analytical results as well as numerical results that characterize conditions when this problem is ill-posed. Additionally we include simulations with other kernels relevant to applications in microscopy and optics, showing that successful recovery of sparse signals through l1-norm minimization can be achieved for a diverse set of problems. |
| 일반주제명 | Applied mathematics. Mathematics. |
| 언어 | 영어 |
| 바로가기 | 
: 이 자료의 원문은 한국교육학술정보원에서 제공합니다. |
