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Topological Signal Processing
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517 b
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This authored monograph presents a topological approach to signal processing. Topology is the study of space under continuous transformations. In engineering, continuous distortions arise when there is significant uncertainty. Rather than taking a stochastic approach, recent progress in topological methods allows practitioners in signal processing to address uncertainty in a deterministic fashion. To this end, one uses local data to make global inferences; a hallmark of the mathematics of sheaves. This book provides an efficient treatment of cellular sheaves, and explains how their use is decisive in treating difficult problems in signal processing. The target audience comprises practitioners as well as researchers, but the book may also be beneficial for graduate students.
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