On the Existence and Design of the Best Stack Filter Based Associative Memory

The associative memory of a stack filter is defined to be the set of root signals of that filter. If the root sets of two stack filters both contain a desired set of patterns, but one filter’s root set is smaller than the other, then the filter with the smaller root set is said to be better for that set of patterns. Any filter which has the smallest number of roots containing the specified set of patterns is said to be a best filter. The configuration of the family of best filters is described via a graphical approach which specifies an upper and lower bound for the subset of possible best filters which are furthest from the sets of type-1 and type-2 stack filters. Knowledge of this configuration leads to an algorithm which can produce a near-best filter. This new method of constructing associative memories does not require the desired set of patterns to be independent and it can construct a much better filter than the methods in [I]

Analysis and Implementation of Median Type Filters

Median filters are a special class of ranked order filters used for smoothing signals. These filters have achieved- success in speech processing, image processing, and other impulsive noise environments where linear filters have proven inadequate. Although the implementation of a median filter requires only a simple digital operation, its properties are not easily analyzed. Even so, a number of properties have been exhibited in the literature. In this thesis, a new tool, known as threshold decomposition is introduced for the analysis and implementation of median type filters. This decomposition of multi-level signals into sets of binary signals has led to significant theoretical and practical breakthroughs in the area of median filters. A preliminary discussion on using the threshold decomposition as an algorithm for a fast and parallel VLSI Circuit implementation of ranked filters is also presented* In addition, the theory is developed both for determining the number of signals which are invariant to arbitrary window width median filters when any number of quantization levels are allowed and for counting or estimating the number of passes required to produce a root- i.e. invariant signal, for binary signals. Finally, the analog median filter is defined and proposed for analysis of the standard discrete median filter in cases with a large sample size or when the associated statistics would be simpler in the continuu