Emerging applications of geometric multiscale analysis

@misc{citeulike:1379223, abstract = {Classical multiscale analysis based on wavelets has a number of successful applications, e.g. in data compression, fast algorithms, and noise removal. Wavelets, however, are adapted to point singularities, and many phenomena in several variables exhibit intermediate-dimensional singularities, such as edges, filaments, and sheets. This suggests that in higher dimensions, wavelets ought to be replaced in certain applications by multiscale analysis adapted to intermediate-dimensional singularities. My lecture described various initial attempts in this direction. In particular, I discussed two approaches to geometric multiscale analysis originally arising in the work of Harmonic Analysts Hart Smith and Peter Jones (and others): (a) a directional wavelet transform based on parabolic dilations; and (b) analysis via anistropic strips. Perhaps surprisingly, these tools have potential applications in data compression, inverse problems, noise removal, and signal detection; applied mathematicians, statisticians, and engineers are eagerly pursuing these leads.}, author = {Donoho, David L. }, citeulike-article-id = {1379223}, eprint = {math.ST/0212395}, keywords = {geometry, multiscale}, month = {Dec}, posted-at = {2007-06-11 20:38:51}, priority = {2}, title = {Emerging applications of geometric multiscale analysis}, url = {http://arxiv.org/abs/math.ST/0212395}, year = {2002} }

TY - ELEC ID - citeulike:1379223 L3 - citeulike-article-id:1379223 TI - Emerging applications of geometric multiscale analysis N2 - Classical multiscale analysis based on wavelets has a number of successful applications, e.g. in data compression, fast algorithms, and noise removal. Wavelets, however, are adapted to point singularities, and many phenomena in several variables exhibit intermediate-dimensional singularities, such as edges, filaments, and sheets. This suggests that in higher dimensions, wavelets ought to be replaced in certain applications by multiscale analysis adapted to intermediate-dimensional singularities. My lecture described various initial attempts in this direction. In particular, I discussed two approaches to geometric multiscale analysis originally arising in the work of Harmonic Analysts Hart Smith and Peter Jones (and others): (a) a directional wavelet transform based on parabolic dilations; and (b) analysis via anistropic strips. Perhaps surprisingly, these tools have potential applications in data compression, inverse problems, noise removal, and signal detection; applied mathematicians, statisticians, and engineers are eagerly pursuing these leads. KW - geometry KW - multiscale AU - Donoho, David PY - 2002/Dec/01/ UR - http://arxiv.org/abs/math.ST/0212395 ER -