Decomposition of the nodal conductance matrix of a planar resistive grid and derivation of its eigenvalues and eigenvectors using the kronecker product and sum with application to cnn image filters

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Tarih

2016-12

Dergi Başlığı

Dergi ISSN

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Yayıncı

IEEE

Erişim Hakkı

info:eu-repo/semantics/closedAccess

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Özet

It is shown that an (M× N)-node planar resistive grid can be decomposed into two sub-grids; one made up of M N-node horizontal and the other of N M-node vertical linear resistive grids which corresponds to decomposing its nodal conductance matrix (NCM) into the Kronecker sum of the NCMs of horizontal and vertical linear grids. This enables the analytical expressions of the eigenvalues and eigenvectors of the NCMs of the sub-grids as well as those of the planar resistive grid to be expressed in terms of those of the two linear grids, whose analytical expressions are well known. For a Cellular Neural Network (CNN) Gabor-type filter (GTF) we define generalized nodal conductance matrices (GNCMs) that correspond to the NCMs of the resistive sub-grids, show that each Kronecker decomposition has a counterpart in CNN GTF and prove that each GNCM, its counterpart NCM and the corresponding temporal state matrices are related through unitary diagonal similarity transformations. Consequently, we prove that the eigenvalues of the temporal state matrix of a spatial band-pass CNN GTF are the same as those of its counterpart spatial low-pass CNN image filter, hence their temporal transient behaviors are similar in settling to a forced response.

Açıklama

Anahtar Kelimeler

CNN low-pass and Gabor-type filters, Kronecker product, Nodal conductance matrix, Resistive grid, Bandpass filters, Cellular neural networks, Gabor filters, Linear transformations, Low pass filters, Matrix algebra, Analytical expressions, Conductance matrix, Eigenvalues and eigenvectors, Low-pass, Similarity transformation, Transient behavior, Eigenvalues and eigenfunctions

Kaynak

IEEE Transactions on Circuits and Systems I: Regular Papers

WoS Q Değeri

Q1

Scopus Q Değeri

Q1

Cilt

63

Sayı

12

Künye

Tavşanoğlu, A. V. (2016). Decomposition of the nodal conductance matrix of a planar resistive grid and derivation of its eigenvalues and eigenvectors using the kronecker product and sum with application to CNN image filters. IEEE Transactions on Circuits and Systems I: Regular Papers, 63(12), 2169-2179. doi:10.1109/TCSI.2016.2617918