Design of optimal binary filters under joint multiresolution-envelope constraint

This paper examines binary filter design by jointly applying multiresolution design and envelope constraint. In multiresolution design, the value of the designed filter for a configuration is defined at a resolution sufficiently low to have observed the configuration. Preference is given to higher resolutions, but the number of training observations is taken into account. In envelope design, the designed filter is constrained to lie in the envelope between two humanly designed filters. For small samples, the envelope-designed filter has the benefit of being in accord with expert knowledge, whereas for large samples statistical training provides more accurate filter design. To obtain the advantages of both approaches, they can be applied in combination. This can be done in more than a single way. This paper explores joint multiresolution–envelope design, extends the basic propositions for envelope design to the multiresolution setting, considers design consistency, and provides experimental support for the joint approach. 2002 Elsevier Science B.V. All rights reserved.