P. Garcia-martinez et Hh. Arsenault, A correlation matrix representation using sliced orthogonal nonlinear generalized decomposition, OPT COMMUN, 172(1-6), 1999, pp. 181-192
A new sliced orthogonal nonlinear generalized (SONG) decomposition for imag
e processing can be useful for image representation. We examine the use of
this representation for two-class pattern recognition in the presence of no
ise. The SONG correlation is defined and expressed by means of a diagonal m
atrix representation. Common linear correlation, binary correlation and mor
phological correlation, among others, can be described in terms of the SONG
representation. This matrix allows the investigation of some interesting p
roperties of auto-correlation and cross-correlation operations. The discrim
ination capability and noise robustness of the SONG correlation are investi
gated and compared with those of other methods. Experimental results establ
ish the stability of the SONG process at Gaussian noise levels high enough
for the other methods to break down. Although the pattern recognition metho
d is nonlinear, the elementary correlation operations are linear and so the
method is suitable for optical implementation. (C) 1999 Elsevier Science B
.V. All rights reserved.