在本論文中，我們提出兩種適應性濾波器設計方法，分別為複數類神經模糊系統(Complex Neuro-Fuzzy System, CNFS)濾波器與自我組織複數類神經模糊系統(Self-Organizing Complex Neuro-Fuzzy System, SOCNFS)濾波器，並將它們應用於解決適應性影像雜訊消除(adaptive image noise cancelling, AINC)的問題上。在濾波器設計上，我們主要分為兩個部份進行探討，第一部份為濾波器系統建構，第二部份為系統參數調整。系統建構方面，我們以Takagi-Sugeno (T-S) 模糊If-Then規則作為CNFS與SOCNFS的系統架構，並以複數模糊集合(Complex Fuzzy Set, CFS)做為模糊規則的歸屬函數。系統參數調整方面，我們進一步設計了一種PSO-RLSE複合式學習方法用於調整濾波器內的參數，此方法結合了著名的粒子群最佳化(Particle Swarm Optimization, PSO)方法與遞迴最小平方估計法(Recursive Least-Square Estimation, RLSE)。PSO用來調整濾波器的前鑑部參數，RLSE則用於調整濾波器的後鑑部參數。PSO-RLSE學習方法具有快速的學習能力與高度的執行效率。而我們所提出的CNFS與SOCNFS濾波器對於非線性函數均具有絕佳的映射能力。SOCNFS則是基於CNFS的概念並結合自我組織機制所設計出來的。將用來訓練SOCNFS的訓練數據進行分群，透過分群結果自動決定系統中的規則數以及初始化的系統參數。這種方式不僅可以減少人為介入因素，同時也為系統內模糊規則數的制定提出了有力的數理依據。
在AINC應用中，我們所提出的CNFS濾波器與SOCNFS濾波器會以間接函數逼近(indirect function approximation)的方式進行雜訊通道的動態行為模擬。經由這種方式，受汙染的影像將可被復原成極近似於原始影像的乾淨影像。我們分別以數張影像與四個範例測試CNFS與SOCNFS濾波器的雜訊消除效果，並得到出色的復原影像品質。

In this thesis, we propose two novel adaptive filters, complex neuro-fuzzy system (CNFS) and self-organizing complex neuro-fuzzy system (SOCNFS), and apply them to the problem of adaptive image noise cancelling (AINC). Complex fuzzy sets (CFS) and Takagi-Sugeno (T-S) fuzzy If-Then rules are used to shape the structure of both the CNFS and SOCNFS. A CFS is the fuzzy set whose membership is complex-valued state within the unit disk in complex plane. We devise a hybrid optimization method to adapt the adaptive filters for the AINC problem. The hybrid learning method is called the PSO-RLSE method, including the well-known particle swarm optimization (PSO) method and the famous recursive least square estimation (RLSE) method. They cooperate in hybrid way during the learning process for the adaptive filters. The PSO is used to update the parameters of premise part of the filters while the consequent part is updated by the RLSE. The PSO-RLSE learning method is very efficient for fast learning. The proposed CNFS and SOCNFS filters possess excellent nonlinear mapping ability because CFS can bring in complex memberships in fuzzy inference computing for input-output mapping capability. On the other hand, with the mechanism of self-organization, the SOCNFS can generate fuzzy rules in the form of clusters and learn its parameters by the stimulation of input/output training data to have its initial If–Then rules for application. In the AINC application, the proposed CNFS and SOCNFS can perform indirect function approximation to mimic the dynamic behaviour of unknown noise channel in such a way that a corrupted image may be adaptively restored as clear to its original version as possible. Few examples with several images are used to test the proposed approachs, by which excellent performance for image restoration has been observed.

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