Orthogonal Sub-band Image Transforms

Eero P Simoncelli

Published as:

Masters Thesis
Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology
May, 1988

This paper proposes a class of linear transformations which are particularly well suited for image processing tasks such as data compression, progressive transmission, and machine vision. The basis functions of these transformations form a complete orthogonal set and are localized in both the spatial and spatial frequency domains. In addition, they may be implemented efficiently using cascaded convolutions with relatively small filters. Formulation of the problem is discussed in both the spatial frequency and spatial domains. Frequency domain formulation allows the isolation of aliasing errors and simple analysis of cascaded systems. Spatial domain formulation simplifies the problem of transform inversion, and provides a more obvious interpretation of the issues involved in filter design. Two simple design methods are proposed: a general spatial domain technique which is easily extended to multiple dimensions, and a frequency domain technique for the design of one-dimensional transforms. Examples of data compression and progressive transmission are given, and the extension of the results to two and three dimensions with arbitrary sampling geometries is discussed.

for a hardcopy / EPS Web-Available Publications / Home Page