Fast adaptive stack filtering and perceptually optimal restoration of images
Abstract
Stack filters are a class of discrete-time, nonlinear filters which are defined in terms of positive Boolean functions and a weak superposition property called the threshold decomposition. Algorithms for determining a stack filter which minimizes the Mean Absolute Error (MAE) criterion have been developed and applied to such problems as edge detection and noise reduction in images. Unfortunately, present algorithms for designing stack filters can only be used for small window sizes because of either their computational overhead or their serial nature. A new adaptive algorithm is presented for determining a stack filter that minimizes the mean absolute error criterion. It retains the iterative nature of many current adaptive stack filtering algorithms, but significantly reduces the number of iterations required to converge to an optimal filter. The new algorithms is faster than all currently available stack filter design algorithms, is simple to implement, and is shown in this thesis to always converge to an optimal stack filter. Also, due to the parallel nature of the new algorithm, the training processing is much faster when it is implemented on the MasPar MP-1 parallel computer. One difficulty with this theory of MMAE stack filtering is that filters with large windows are often needed to produce the desired visual result in image processing applications. The hypothesis is that this difficulty is due to the error criterion that is used, not to fundamental limitations of stack filters. Thus, a new stack filter design algorithm is developed. It is based upon a Weighted Mean Absolute Error (WMAE) criterion instead of the traditional MAE criterion that assigns the same weights to all errors. The weights in this WMAE criterion are designed with the aid of the Visible Differences Predictor (VDP), which can estimate the sensitivity of the human visual system to changes in black and white images. Experiments with this perception-based WMAE approach show that the stark filters it produces perform significantly better in image processing applications than those designed with the MAE approach. This approach to the design of an analytically tractable, yet visually meaningful error criterion, can be used for any class of filters.
Degree
Ph.D.
Advisors
Coyle, Purdue University.
Subject Area
Electrical engineering
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