Supremal Multiscale Signal Analysis

Abstract

We introduce a novel approach to nonlinear signal analysis, which is referred to as supremal multiscale analysis. The proposed approach provides a rigorous mathematical foundation for a class of nonlinear multiscale signal analysis schemes and leads to a decomposition that can effectively be used in signal processing and analysis. Moreover, it is related to the supremal scale-spaces proposed by Heijmans and van den Boomgaard and is similar in flavor to the well-known linear multiresolution theory of Mallat and Meyer. In this framework, linear concepts such as vector spaces, projections, and linear operators are replaced by conceptually analogous nonlinear notions. We use supremal multiscale analysis to construct a multiscale image decomposition scheme based on two mathematical concepts that play a key role in the analysis and interpretation of images by vision systems, namely, regional maxima and connectivity. The resulting scheme is referred to as skyline supremal multiscale analysis and satisfies severa...