植基於退火粒子群最佳化演算法之奇異質分解於二維濾波器之設計

2-D Filters Designed by Usingsingular-Value Decomposition Based on An Annealed Particleswarm Optimization

本論文旨在提出以退火粒子群最佳化 （Annealed particle swarm optimization,APSO） 演算法求得不等距取樣點之空間頻率取代傳統等距取樣點空間頻率，以產生平面響應矩陣。粒子群最佳化演算法是一種具有群體智慧概念、屬於演化計算領域的一種計算方法，在決策過程中利用個體所擁有的經驗以及他人的經驗，經由考慮這二項資訊，來做最佳的決策。當不等距取樣點之空間頻率取得後，再以奇異值分解法 （Singular value decomposition, SVD） 求得多級可分離之一維濾波器；最後以這些一維濾波器組合成二維濾波器。由實驗數據可看出，以粒子群演算法求得不等取樣點之空間頻率，由奇異值分解法所設計出來之二維濾波器，比傳統等距取樣點空間頻率可得到較佳之增益響應。

In this paper, an annealed particle swarm optimization (APSO) is proposedto randomly select non-equal scaling spatial frequency points in orderto generate the spatial-response matrix for the singular-value decomposition(SVD) algorithm to a 2-D filter design. PSO is a swarm intelligentstrategy which also is a new evolutionary computation technique. In thedecision process, each particle adjusts its position to get a promising positionin accordance with its own flying experience and its companion’s flyingexperience. The SVD algorithm is used to get multiple separated 1-Dfilters after generating non-equal scaling spatial frequency points. Finally,we can combine these 1-D filters to construct a 2-D filter. From the experimentalresults, the non-equal scaling spatial frequency points randomlyselected by the PSO for the SVD algorithm to design a 2-D filter can get abetter frequency response than those gotten by the traditional method,which generates equal scaling spatial frequency points.