- 學位論文
以粒子群演算法為基礎之正交鏡像濾波器組設計
Design of Quadrature Mirror Filter banks based on Particle Swarm Optimization
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摘要
正交鏡像濾波器組(Quadrature Mirror Filter banks, QMF)為小波理論中的重要課題，也是影像處理及資料壓縮上的應用工具之一；傳統上使用具有線性相位有限脈衝(Linear Phase Finite Impulse Response)的高低通濾波器來建構QMF；近年來許多文獻以數位全通濾波器(Digital Allpass Filter, DAP)來實現QMF，這種設計架構除了可以消除濾波器組振幅失真的問題外，亦可使用較少的階數達成所需的規格要求。 在此架構下，我們面臨的最佳化問題為一個高度非線性之環境；解決此問題的演算法一般而言有兩種；第一是列舉法(Enumeration)，也就是在所有可行解空間中，將所有可行解列舉出並逐一檢驗，再從中挑選出最佳解。此解法的優點在於保證可以找到全域最佳解(Global Optimum)，然而所需的運算時間與運算量極大，並不符合實際需求；第二種是線性近似化(linearized algorithm)演算法，將原先所面臨的高度非線性化的問題做線性近似，以期望能在較短的搜索時間內找到最佳解；此解法的優點在於運算時間短且運算量較小，卻容易陷於局部最佳解(Local Optimum)。因此，本論文中提出使用粒子群演算法作為最佳化法則，期望能在列舉法與線性近似法中取得平衡，並讓搜尋過程不容易受限於局部最佳解，並且能找出優於線性近似演算法的解。
並列摘要
Quadrature Mirror Filter banks is an important topic of wavelet theory, image processes and data compression; Traditionally a linear-phase finite impulse response(LP-FIR) low-pass filter and high-pass filter are used to construct QMF, recently several reports suggest that implement QMF by using IIR digital allpass filter, this structure could solve some problem such as amplitude distortion, also, be able to achieve the same specifications as using FIR filter with less filter order. Under this structure, the design problem we face is a highly nonlinear optimization problem. In general, there are two traditional algorithms to solve this problem. The first one is called enumeration, it lists all the feasible solutions in the search space and test them, select the best solution from all the candidates. The advantage of enumeration is that it is guaranteed to find the global optimum; however, it costs too much search time and computation loading. The second is linearized algorithm, which linearized the nonlinear problem so that less computation time and loading are needed, at the same time, it is easier trapped in local optimum. Based on the above concept, in this paper we propose a type of evolution algorithm—Particles Swarm Optimization (PSO) algorithm to be optimizer, which is expected be balanced between enumeration and linearized algorithm, not to trapped in local optimum and find a better solution than the solution solved by linearized algorithm.
參考文獻
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