Aperture filters

Except in the case of very low-bit signals (images), unconstrained design o f mean-square-error optimal digital window-based filters from sample signal s is hampered by the inability to obtain sufficient data to make acceptably precise estimates of the large number of conditional expectations required for the filter. Even under typical nonlinear constraints such as increasin gness or iterative decomposition, estimation remains intractable. This pape r mitigates the estimation dilemma by windowing in the range, as well as in the domain. At each point, the signal is viewed through an aperture, which is the product between a domain window and a gray-range window that is cho sen according to the signal values in the domain window. Signal values abov e and below the range window are projected into the top and bottom of the a perture, respectively. This projection compresses the probability mass of t he observed signal into a smaller set of variables in such a way as not to alter the mass of observations within the aperture (which carry the most ma ss) and minimally alter the mass of those outside the aperture. Experiments show that, as opposed to commonly employed increasing nonlinear filters, a perture filters can outperform linear filters for deblurring, especially in the restoration of edges. This paper addresses several issues concerning a perture filters: positioning of the aperture, the effect of range constrain t on probability mass, the size of the aperture relative to estimation prec ision and the amount of training data, estimation of conditional probabilit ies, and representation by decision trees. A sampling is provided of the ma ny experiments carried out to study the effects of aperture filters on corr uption by additive noise and blurring. (C) 2000 Elsevier Science B.V. All r ights reserved.