Analysis of fractals, image compression, entropy encoding, Karhunen-Loève transforms
This interesting paper considers the mathematical formulation of problems in signal transmission, coding, and image processing on the one hand, and techniques from operator theory and functional analysis used to study relations on finite sets of operators on Hilbert space on the other. The formulation in Hilbert space gives a unified approach to a diverse array of problems that admit multiple scales, including entropic coding, the Karhunen--Loève analysis of correlation matrices, fractional Brownian motion, wavelet expansions, the geometry of self-similar fractals, and so on. Throughout the emphasis is both on formulating some problems motivated by engineering in a precise mathematical way, and then in drawing out the common underlying features using the language of Hilbert space.
scientific article; zbMATH DE number 5659975
scientific article