Nonlinear wavelet methods for recovery of signals, densities, and spectra from indirect and noisy data
David L. Donoho · Proceedings of symposia in applied mathematics · 1993
. We describe wavelet methods for recovery of objects from noisy and incomplete data. The common themes: (a) the new methods utilize nonlinear operations in the wavelet domain; (b) they accomplish tasks which are not possible by traditional linear/Fourier approaches to such problems. We attempt to indicate the heuristic principles, theoretical foundations, and possible application areas for these methods. Areas covered: (1) Wavelet De-Noising. (2) Wavelet Approaches to Linear Inverse Problems. (4) Wavelet Packet De-Noising. (5) Segmented MultiResolutions. (6) Nonlinear Multi-resolutions. 1. Introduction. With the rapid development of computerized scientific instruments comes a wide variety of interesting problems for data analysis and signal processing. In fields ranging from Extragalactic Astronomy to Molecular Spectroscopy to Medical Imaging to Computer Vision, one must recover a signal, curve, image, spectrum, or density from incomplete, indirect, and noisy data. What can wavelets ...