Detection of Edges in Spectral Data II. Nonlinear Enhancement
| dc.contributor.author | GELB, ANNE | |
| dc.contributor.author | TADMOR, EITAN | |
| dc.date.accessioned | 2008-10-20T17:59:29Z | |
| dc.date.available | 2008-10-20T17:59:29Z | |
| dc.date.issued | 2000 | |
| dc.description.abstract | We discuss a general framework for recovering edges in piecewise smooth functions with finitely many jump discontinuities, where [f](x) := f(x+)โf(xโ) โ 0. Our approach is based on two main aspectsโlocalization using appropriate concentration kernels and separation of scales by nonlinear enhancement. To detect such edges, one employs concentration kernels, K_๐(ยท), depending on the small scale ๐. Itis shown that odd kernels, properly scaled, and admissible (in the sense of having small Wโ1,โ- moments of order O(๐)) satisfy K_๐ โ f(x) = [f](x) + O(๐), thus recovering both the location and amplitudes of all edges. As an example we consider general concentration kernels of the form KฯN (t) = ๐จฯ(k/N) sin kt to detect edges from the first 1/๐ = N spectral modes of piecewise smooth fโs. Here we improve in generality and simplicity over our previous study in [A. Gelb and E. Tadmor, Appl. Comput. Harmon. Anal., 7 (1999), pp. 101โ135]. Both periodic and nonperiodic spectral projections are considered. We identify, in particular, a new family of exponential factors, ฯexp(ยท), with superior localization properties. The other aspect of our edge detection involves a nonlinear enhancement procedure which is based on separation of scales between the edges, where K_๐ โ f(x) โผ [f](x) โ 0, and the smooth regions where K_๐ โ f = O(๐) โผ 0. Numerical examples demonstrate that by coupling concentration kernels with nonlinear enhancement one arrives at effective edge detectors. | en |
| dc.format.extent | 245473 bytes | |
| dc.format.mimetype | application/pdf | |
| dc.identifier.citation | A. Gelb & E. Tadmor (2000). Detection of Edges in Spectral Data II. Nonlinear Enhancement. SIAM Journal on Numerical Analysis 38 (2000) 1389-1408. | en |
| dc.identifier.uri | http://hdl.handle.net/1903/8646 | |
| dc.language.iso | en_US | en |
| dc.publisher | Copyright: Society for Industrial and Applied Mathematics | en |
| dc.relation.isAvailableAt | College of Computer, Mathematical & Physical Sciences | en_us |
| dc.relation.isAvailableAt | Mathematics | en_us |
| dc.relation.isAvailableAt | Digital Repository at the University of Maryland | en_us |
| dc.relation.isAvailableAt | University of Maryland (College Park, MD) | en_us |
| dc.subject | piecewise smoothness | en |
| dc.subject | concentration kernels | en |
| dc.subject | spectral expansions | en |
| dc.title | Detection of Edges in Spectral Data II. Nonlinear Enhancement | en |
| dc.type | Article | en |