Optical neural network based on the fractional Fourier transform (FRT) has a simple optical architecture and it is suitable for a large-scale optical implementation. The FRT neural network with the mean square error has been proposed but its performance has not been examined in detail. In this dissertation the performance of this neural network is systematically analyzed in a pattern classification problem and its improvements are realized by the following methods. The mean square error is replaced with the log-likelihood in the FRT neural network and the parallelism is introduced for a significant improvement in performance. Then, the FRT neural network using two cylindrical lenses is proposed and its performance is analyzed. Finally, the optimization of fractional order, which is important in the pattern classification of the FRT neural network, is solved by evolutionary programming.
First, the performance of the FRT neural network is analyzed and improved as follows. Seven alphabet patterns (A, B, C, D, E, F, and, G) with 16 x 16 pixels have been classified by the FRT neural network, and then its recall rate is tested with the noisy patterns. However, it is found the classification performance of the FRT neural network with the mean square error is limited for a practical application. To improve both the learning convergence and the recall rate of neural network, the mean square error is replaced with the log-likelihood. To study the effect of parallelism on the FRT neural network, the parallelism is introduced to the FRT neural network with the mean square error. It initially improves the learning convergence but slightly diminishes its recall rate. It has been found that the combination of FRT, log-likelihood, and parallelism significantly improves both the learning convergence and the recall rate of neural network.
Second, the fractional orders associated with the horizontal axis and the vertical axis are independently controlled to classify various types of patterns. The proposed FRT neural network uses two cylindrical lenses instead of a spherical lens and this neural network classifies the elongated patterns better than the FRT neural network with a spherical lens.
Finally, the optimization of the fractional order of the FRT neural network, which is important for the good classification performance, is achieved by employing the evolutionary programming. Namely the fractional orders are successfully optimized in numeral pattern classifications using the FRT neural network with a spherical lens and the FRT neural network with two cylindrical lenses, respectively.
