Computing the output distribution and selection probabilities of a stack filter from the DNF of its positive Boolean function

Many nonlinear filters used in practise are stack filters. An algorithm is presented which calculates the output distribution of an arbitrary stack filter S from the disjunctive normal form (DNF) of its underlying positive Boolean function. The so called selection probabilities can be computed along the way.Comment: This is the version published in Journal of Mathematical Imaging and Vision, online first, 1 august 201

On generalized adaptive neural filter

Linear filters have historically been used in the past as the most useful tools for suppressing noise in signal processing. It has been shown that the optimal filter which minimizes the mean square error (MSE) between the filter output and the desired output is a linear filter provided that the noise is additive white Gaussian noise (AWGN). However, in most signal processing applications, the noise in the channel through which a signal is transmitted is not AWGN; it is not stationary, and it may have unknown characteristics. To overcome the shortcomings of linear filters, nonlinear filters ranging from the median filters to stack filters have been developed. They have been successfully used in a number of applications, such as enhancing the signal-to-noise ratio of the telecommunication receivers, modeling the human vocal tract to synthesize speech in speech processing, and separating out the maternal and fetal electrocardiogram signals to diagnose prenatal ailments. In particular, stack filters have been shown to provide robust noise suppression, and are easily implementable in hardware, but configuring an optimal stack filter remains a challenge. This dissertation takes on this challenge by extending stack filters to a new class of nonlinear adaptive filters called generalized adaptive neural filters (GANFs). The objective of this work is to investigate their performance in terms of the mean absolute error criterion, to evaluate and predict the generalization of various discriminant functions employed for GANFs, and to address issues regarding their applications and implementation. It is shown that GANFs not only extend the class of stack filters, but also have better performance in terms of suppressing non-additive white Gaussian noise. Several results are drawn from the theoretical and experimental work: stack filters can be adaptively configured by neural networks; GANFs encompass a large class of nonlinear sliding-window filters which include stack filters; the mean absolute error (MAE) of the optimal GANF is upper-bounded by that of the optimal stack filter; a suitable class of discriminant functions can be determined before a training scheme is executed; VC dimension (VCdim) theory can be applied to determine the number of training samples; the algorithm presented in configuring GANFs is effective and robust

Visualization of smoke stack plume

System consists of ultraviolet vidicon tube, interference and color filters, ultraviolet telephoto lens, monitor, and waveform analyzer to extract information from video scene, stack plume viewed against sky. System will view SO2 and any other element which absorbs light at wavelength used

Assessment of SAR Image Filtering using Adaptive Stack Filters

Stack filters are a special case of non-linear filters. They have a good performance for filtering images with different types of noise while preserving edges and details. A stack filter decomposes an input image into several binary images according to a set of thresholds. Each binary image is then filtered by a Boolean function, which characterizes the filter. Adaptive stack filters can be designed to be optimal; they are computed from a pair of images consisting of an ideal noiseless image and its noisy version. In this work we study the performance of adaptive stack filters when they are applied to Synthetic Aperture Radar (SAR) images. This is done by evaluating the quality of the filtered images through the use of suitable image quality indexes and by measuring the classification accuracy of the resulting images

Simplification of the generalized adaptive neural filter and comparative studies with other nonlinear filters

Recently, a new class of adaptive filters called Generalized Adaptive Neural Filters (GANFs) has emerged. They share many characteristics in common with stack filters, include all stack filters as a subset. The GANFs allow a very efficient hardware implementation once they are trained. However, there are some problems associated with GANFs. Three of these arc slow training speeds and the difficulty in choosing a filter structure and neural operator. This thesis begins with a tutorial on filtering and traces the GANF development up through its origin -- the stack filter. After the GANF is covered in reasonable depth, its use as an image processing filter is examined. Its usefulness is determined based on simulation comparisons with other common filters. Also, some problems of GANFs are looked into. A brief study which investigates different types of neural networks and their applicability to GANFs is presented. Finally, some ideas on increasing the speed of the GANF are discussed. While these improvements do not completely solve the GANF\u27s problems, they make a measurable difference and bring the filter closer to reality

On the Existence and Design of the Best Stack Filter Based Associative Memory

The associative memory of a stack filter is defined to be the set of root signals of that filter. If the root sets of two stack filters both contain a desired set of patterns, but one filter’s root set is smaller than the other, then the filter with the smaller root set is said to be better for that set of patterns. Any filter which has the smallest number of roots containing the specified set of patterns is said to be a best filter. The configuration of the family of best filters is described via a graphical approach which specifies an upper and lower bound for the subset of possible best filters which are furthest from the sets of type-1 and type-2 stack filters. Knowledge of this configuration leads to an algorithm which can produce a near-best filter. This new method of constructing associative memories does not require the desired set of patterns to be independent and it can construct a much better filter than the methods in [I]

Constant-time filtering using shiftable kernels

It was recently demonstrated in [5] that the non-linear bilateral filter [14] can be efficiently implemented using a constant-time or O(1) algorithm. At the heart of this algorithm was the idea of approximating the Gaussian range kernel of the bilateral filter using trigonometric functions. In this letter, we explain how the idea in [5] can be extended to few other linear and non-linear filters [14, 17, 2]. While some of these filters have received a lot of attention in recent years, they are known to be computationally intensive. To extend the idea in [5], we identify a central property of trigonometric functions, called shiftability, that allows us to exploit the redundancy inherent in the filtering operations. In particular, using shiftable kernels, we show how certain complex filtering can be reduced to simply that of computing the moving sum of a stack of images. Each image in the stack is obtained through an elementary pointwise transform of the input image. This has a two-fold advantage. First, we can use fast recursive algorithms for computing the moving sum [15, 6], and, secondly, we can use parallel computation to further speed up the computation. We also show how shiftable kernels can also be used to approximate the (non-shiftable) Gaussian kernel that is ubiquitously used in image filtering.Comment: Accepted in IEEE Signal Processing Letter

Design of Computer Experiments: a powerful tool for the numerical design of BAW filters

We apply Design of Computer Experiments methods to the simulation of piezoelectric stacks and the design of BAW resonators and filters. Through the example of DCS filters with two different technologies (Iridium and Molybdenum electrodes), we show that the definition and the exploitation of a metamodel can accurately replace acoustic simulations and allows therefore a much faster material stack desig