Hybrid human-machine non-linear filter design using envelopes

Machine design of a signal or image operator involves estimating the optimal filter from sample data. In principle, relative to the error measure used, the optimal filter is best; however, owing to design error, the designed filter might not perform well. In general it is suboptimal. The envelope constraint involves using two humanly designed filters that form a lower and upper bound for the designed operator. The method has been employed for binary operators. The paper considers envelope design for gray-scale filters, in particular, aperture filters. Some basic theoretical properties are stated, including optimality of the design method relative to the constraint imposed by the envelope. Examples are given for noise reduction and de-blurring.