Stable construction of multiscale fuzzy-wavelet system for image recovery and compression

Abstract

This paper describes a convergent algorithms that is able to construct a multi-scale fuzzy-wavelet system for efficient image recovery and compression. Given only part of the original image and a prescribed compression error bound, a fuzzy system is firstly constructed at the coarsest scale. The fuzzy rules and corresponding membership functions can be stably extracted, and linguistic knowledge can also be combined with numerical one to make the scheme more flexible. Residual based wavelet system is then built to refine the performance by reaching certain fine scales. To increase the compression ratio, a reduction technique is developed to delete redundant fuzzy rules and wavelet nodes to make the whole fuzz-wavelet system as small as possible. The resulting image representation of the given image from coarse to fine scale is suitable for progressive transmission and video indexing purposes. An illustrative example is used to demonstrate the effectiveness of the scheme.