Partition-based weighted sum filters for image restoration

In this work, me develop the concept of partitioning the observation space to build a general class of filters referred to as partition-based weighted sum (PWS) filters. In the general framework, each observation vector is ma pped to one of M partitions comprising the observation space, and each part ition has an associated filtering function. Here, we focus on partitioning the observation space utilizing vector quantization and restrict the filter ing function within each partition to be linear. In this formulation, a wei ghted sum of the observation samples forms the estimate, where the weights are allowed to be unique within each partition. The partitions are selected and weights tuned by training on a representative set of data. It is shown that the proposed data adaptive processing allows for greater detail prese rvation when encountering nonstationarities in the data and yields superior results compared to several previously defined filters. Optimization of th e PWS filters is addressed and experimental results are provided illustrati ng the performance of PWS filters in the restoration of images corrupted by Gaussian noise.