کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4607564 1337869 2011 26 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Compactly supported shearlets are optimally sparse
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
Compactly supported shearlets are optimally sparse
چکیده انگلیسی

Cartoon-like images, i.e., C2C2 functions which are smooth apart from a C2C2 discontinuity curve, have by now become a standard model for measuring sparse (nonlinear) approximation properties of directional representation systems. It was already shown that curvelets, contourlets, as well as shearlets do exhibit sparse approximations within this model, which are optimal up to a log-factor. However, all those results are only applicable to band-limited generators, whereas, in particular, spatially compactly supported generators are of uttermost importance for applications.In this paper, we present the first complete proof of optimally sparse approximations of cartoon-like images by using a particular class of directional representation systems, which indeed consists of compactly supported elements. This class will be chosen as a subset of (non-tight) shearlet frames with shearlet generators having compact support and satisfying some weak directional vanishing moment conditions.


► Approximation rates for bivariate functions exhibiting curvilinear singularities.
► Cartoon-like images are C2C2 functions, which are smooth apart from a C2C2 discontinuity curve.
► Compactly supported shearlet frames achieve the optimal approximation rate for cartoon-like images.
► First complete proof of optimally sparse approximations by a compactly supported system.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Approximation Theory - Volume 163, Issue 11, November 2011, Pages 1564–1589
نویسندگان
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