臺灣博碩士論文加值系統

在類神經網路的運算中，堆疊濾波器（Stack Filters）之「假記憶」
（ False Memory ）是一個訊號（或圖樣）的集合，其元素為所有非不
是期望但在被濾波後郤依舊保根（ the Root Preservation ）的訊號。
然而不論期望與否，當一個訊號在濾波之後被保根，其即為該濾波器固定
點集合（ Root Set ）的元素之一。在傳統的設計中，「假記憶」確切存
在，且使得堆疊濾波器本身混淆而難以辨明什麼訊號是它所期望的，什麼
不是。在以往的研究論文中，曾提出一種靈感演算法（ Heuristic
Algorithm ）去找尋「近最佳」（ Near Optimal ）的堆疊濾波器使得
「假記憶」接近於最少。但它卻仍是遍尋了所有可能，以致於相當耗時。
在本篇論文中，我們導入了兩層堆疊濾波器的觀念，並經由使用不同大小
的滑動視窗（ Sliding　 Windows ）與各種型態的一層堆疊濾波器串連
，研究兩層堆疊濾波器的效率及效能。此外，在運作時，兩層堆疊濾波器
是由兩個易於導出及分析的濾波器組合,去完成較為複雜的工作。同時，
我們導出了幾類建構於以（ 2N+1 ）─　單調訊號為期望固定點的兩層
堆疊濾波器，進而研究它們的固定點結構（ Root Structures ）及濾波
行為（ Filtering Behavior ）。經由分析，選擇兩層堆疊濾波器相較於
一層可驗證為較佳的決策。而最佳的組合也被提出且證明。

In the neural network computing, the false memory of a Stack
Filter is defined a signal or pattern set in which each
element is undesired but still preserved by that filter.
Whatever desired or undesired a signal ( or pattern ) is
preserved, it is a root signal ( or pattern ) of the root set
for its corresponding Stack Filters -- even it is an element of
the false memory, it is still a root signal. In traditional
designs, false memory definitely occurred and it made much
more confusion and waste for Stack Filters to recognize what
they want. In previous research, people have devoted to
deriving a heuristic algorithm to finding a near optimal Stack
Filter. However, it is considerably time consuming based on
brute force to exhaust all the possible to obtain the near
optimal solution. The notion of Two-Layer Stack Filters are
thus introduced in this thesis to survey their efficiency
and performance by different width of sliding windows and
various types of cascades of One-Layer Stack Filters. They
are proposed to be implemented by the combinations of simple
One-Layer Stack Filters to accomplish more complicated work
with nice gains. In this thesis we build some classes os
Two-Layer Stack Filters based on (2N+1)-monotonic
signals, and survey their root structures and filtering
behaviors. All of these Two-Layer Stack Filters are proven
better than their corresponding One-Layer Stack Filters by
means of rigorous approaches and the best combinations are
also proposed and proved.