Signal Processing Based on Maximum Likelihood Selection and Linear Filtering

Abstract

In this paper we describe a class of non-linear digital maximum likelihood filters that consist of a linear system and a selection element. The data is input to the linear element which has several outputs. The selection element chooses one of these to be the final filter output. The output is chosen so that assuming an exponential input distribution it is the sample most likely to be the correct signal level. The median filter is a special case in this filter class.

Selection rules are derived for both scalar and multispectral samples. In the multispectral case the concept of vector median filters is described. The structure and purpose of the linear system is discussed. The root signals of the filters are studied. Examples of the filter performance are given and applications to image processing are shown in the areas of image smoothing and coding and edge detection.

Indexing terms:

• Digital maximum likelihood filter
• Signal processing