Emerging applications of geometric multiscale analysis
Emerging applications of geometric multiscale analysis
复制标题
几何多尺度分析的新兴应用
DOI：
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发表时间：
2002
期刊：
影响因子：
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通讯作者：
D. Donoho
中科院分区：
文献类型：
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作者：
D. Donoho
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 phenom ena 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 partic ular, 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 po tential applications in data compression, inverse problems, noise removal, and signal detection; applied mathematicians, statisticians, and engineers are ea gerly pursuing these leads. Note: Owing to space constraints, the article is a severely compressed version of the talk. An extended version of this article, with figures used in the presentation, is available online at: http .-//www- stat. Stanford. ed«/~ donoho /Lectures/ICM2002
