2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/130485Classical 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.Statistics Theory41A30, 41A58, 41A63, 62G07, 62G08, 94A08, 94A11, 94A12, 94A29text