TL;DR
This paper explores the topological structure of signal spaces under sampling equivalences and analyzes the properties of semi-tensor product based compressed sensing, including the construction of sensing matrices using BIBD.
Contribution
It introduces a quotient space framework for signals with different sampling schemes and analyzes the properties of STP-CS within this framework, including sensing matrix construction.
Findings
Signal space modeled as a quotient space with topological properties.
Characteristics of STP-CS revealed through this framework.
Construction of sensing matrices based on BIBD systematically analyzed.
Abstract
Under the assumption that a finite signal with different sampling lengths or different sampling frequencies is considered as equivalent, the signal space is considered as the quotient space of over equivalence. The topological structure and the properties of signal space are investigated. Using them some characteristics of semi-tensor product based compressed sensing (STP-CS) are revealed. Finally, a systematic analysis of the construction of sensing matrix based on balanced incomplete block design (BIBD) is presented.
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Taxonomy
TopicsComputability, Logic, AI Algorithms