The performance of a designed digital filter is measured by the sum of the errors of the optimal filter and the estimation error. Viewing an image at a high resolution results in optimal filters having smaller errors than at lower resolutions; however, higher resolutions bring increased estimation error. Hence, choosing an appropriate resolution for filter design is important. This paper discusses estimation of optimal filters in a pyramidal multiresolution framework. To take advantage of data at all resolutions, one can use a hybrid multiresolution design. In hybrid design, a sequence of filters is designed using data at increasing resolutions. With hybrid multiresolution design, the value of the designed filter at a given observation is based on the highest resolution at which conditioning by the observation is considered significant.
