A nonlinear scale-space filter by physical computation

Using the maximum entropy principle and statistical mechanics, the author derives and demonstrates a nonlinear scale-space filter. For each datum in a signal, a neighborhood of weighted data is used for scale-space clustering. The cluster center becomes the filter output. The filter is governed by a single scale parameter which dictates the spatial extent of nearby data used for clustering. This, together with the local characteristic of the signal, determine the scale parameter in the output space, which dictates the influences of these data on the output. This filter is thus completely unsupervised and data-driven. It provides a mechanism for a) removing noise; b) preserving edges and c) improved smoothing of nonimpulsive noise