Page 158 - Introduction to Information Optics

2.9. Processing with Neural Networks

LCTVl
Jocoherent & Lens let Imaging
Light Source Diffoser Array Lens
LCTV2 CCD
Camera

Fig. 2.51. A hybrid optical neural network.

2.9.2. HOLPFIELD MODEL

One of the most frequently used neural network models is the Hopfield
model, which allows the desired output pattern to be retrieved from a distorted
or partial input pattern. The model utilizes an associative memory retrieval
process equivalent to an iterative thresholded matrix-vector outer-product
expression, as given by

V = (2.136)
0, K-+0, <0

where V t and Vj are binary output and binary input patterns, respectively, and
the associative memory matrix is written as

(2.137)
0,

where V™ and V™ are ith and /th elements of the wth binary vectory.
The Hopfield model depends on the outer-product operation for construct-
ing the associated memory, which severely limits the storage capacity and often
causes failure in retrieving similar patterns. To overcome these shortcomings,
neural network models, such as back propagation, orthogonal projection, and
others have been used. One of the important aspects of neural computing is