期刊
MULTISCALE MODELING & SIMULATION
卷 4, 期 3, 页码 992-1039出版社
SIAM PUBLICATIONS
DOI: 10.1137/040619454
关键词
wavelets; bandelets; geometric representation; nonlinear approximation
Finding efficient geometric representations of images is a central issue to improving image compression and noise removal algorithms. We introduce bandelet orthogonal bases and frames that are adapted to the geometric regularity of an image. Images are approximated by finding a best bandelet basis or frame that produces a sparse representation. For functions that are uniformly regular outside a set of edge curves that are geometrically regular, the main theorem proves that bandelet approximations satisfy an optimal asymptotic error decay rate. A bandelet image compression scheme is derived. For computational applications, a fast discrete bandelet transform algorithm is introduced, with a fast best basis search which preserves asymptotic approximation and coding error decay rates.
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