Topological Signal Processing

This book surveys topological methods in signal processing which address uncertainty in deterministic fashion. The author offers an efficient treatment of cellular sheaves, showing how their use is decisive in treating difficult problems in signal processing.

Signal processing is the discipline of extracting information from collections of measurements. To be effective, the measurements must be organized and then filtered, detected, or transformed to expose the desired information. Distortions caused by uncertainty, noise, and clutter degrade the performance of practical signal processing systems. In aggressively uncertain situations, the full truth about an underlying signal cannot be known. This book develops the theory and practice of signal processing systems for these situations that extract useful, qualitative information using the mathematics of topology -- the study of spaces under continuous transformations. Since the collection of continuous transformations is large and varied, tools which are topologically-motivated are automatically insensitive to substantial distortion. The target audience comprises practitioners as well as researchers, but the book may also be beneficial for graduate students.

Presents a systematic treatment of the common research threads on the interface between topology and signal processing Includes relevant background materials as well as case studies of topological signal processing applied to actual data Written by an expert in the field Includes supplementary material: sn.pub/extras

Inhalt

Introduction and informal discussion.- Parametrization.- Signals.- Detection.- Transforms.- Noise.