A system/graph theoretical analysis of attractor coders

• Published in: 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing Vol. 4; pp. 2705 - 2708 vol.4
• Main Authors: Gharavi-Alkhansari, M., Huang, T.S.
• Format: Conference Proceeding
• Language: English
• Published: Washington DC IEEE 1997; IEEE Computer Society Press
• Subjects: Applied sciences; Constraint theory; Convergence; Decoding; Eigenvalues and eigenfunctions; Exact sciences and technology; Fractals; Image coding; Image processing; Information, signal and communications theory; Linear systems; Signal design; Signal processing; Sparse matrices; Stability; Telecommunications and information theory; Signal compression; Graph theory; Systems theory; Image processing; Coding
• ISBN: 0818679190; 9780818679193
• ISSN: 1520-6149
• DOI: 10.1109/ICASSP.1997.595347

This paper provides links between the young field of attractor coding and the well-established fields of systems theory and graph theory. Attractor decoders are modeled as linear systems whose stability is both necessary and sufficient for convergence of the decoder. This stability is dictated by the location of the eigenvalues of the sparse state transition matrix of the system. The relationship between these eigenvalues, spatial causality of the system, and the patterns of interdependency between signal elements (or image pixels) is investigated for several cases using concepts from graph and matrix theory.