Discrete Representation of Signals from Infinite Dimensional Hilbert Spaces with Application to Noise Suppression and Compression.

摘要

Addressed in this thesis is the issue of representing signals from infinite dimensional Hilbert spaces in a discrete form. The discrete representations which are studied come from the irregular samples of a signal dependent transform called the group representation transform, e.g., the wavelet and Gabor transforms. The main issues dealt with are (i) the recoverability of a signal from its discrete representation, (ii) the suppression of noise in a corrupted signal, and (iii) compression through efficient discrete representation.