Bandelet Image Approximation and Compression
- 1 January 2005
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in Multiscale Modeling & Simulation
- Vol. 4 (3), 992-1039
- https://doi.org/10.1137/040619454
Abstract
Finding ecien t geometric representations of images is a central issue to improve 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 nding 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.Keywords
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