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32
From Boolean to Probabilistic Boolean Networks as Models of Genetic Regulatory Networks
 Proc. IEEE
, 2002
"... Mathematical and computational modeling of genetic regulatory networks promises to uncover the fundamental principles governing biological systems in an integrarive and holistic manner. It also paves the way toward the development of systematic approaches for effective therapeutic intervention in di ..."
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Cited by 85 (16 self)
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Mathematical and computational modeling of genetic regulatory networks promises to uncover the fundamental principles governing biological systems in an integrarive and holistic manner. It also paves the way toward the development of systematic approaches for effective therapeutic intervention in disease. The central theme in this paper is the Boolean formalism as a building block for modeling complex, largescale, and dynamical networks of genetic interactions. We discuss the goals of modeling genetic networks as well as the data requirements. The Boolean formalism is justified from several points of view. We then introduce Boolean networks and discuss their relationships to nonlinear digital filters. The role of Boolean networks in understanding cell differentiation and cellular functional states is discussed. The inference of Boolean networks from real gene expression data is considered from the viewpoints of computational learning theory and nonlinear signal processing, touching on computational complexity of learning and robustness. Then, a discussion of the need to handle uncertainty in a probabilistic framework is presented, leading to an introduction of probabilistic Boolean networks and their relationships to Markov chains. Methods for quantifying the influence of genes on other genes are presented. The general question of the potential effect of individual genes on the global dynamical network behavior is considered using stochastic perturbation analysis. This discussion then leads into the problem of target identification for therapeutic intervention via the development of several computational tools based on firstpassage times in Markov chains. Examples from biology are presented throughout the paper. 1
Order statistics in digital image processing
 Proc. IEEE 80
, 1992
"... In recent years significant advances have been made in the development of nonlinear image processing techniques. Such techniques are used in digital image filtering, image enhancement, and edge detection. One of the most important families of nonlinear image filters is based on order shztktics. The ..."
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Cited by 53 (14 self)
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In recent years significant advances have been made in the development of nonlinear image processing techniques. Such techniques are used in digital image filtering, image enhancement, and edge detection. One of the most important families of nonlinear image filters is based on order shztktics. The widely used median filter is the best known filter of this family. Nonlinear filters based on order statistics have excellent robustness properties in the presence of impulsive noise. They tend to preserve edge information, which is very important to human perception. Their computation is relatively easy and fast compared with some linear filters. All these features make them very popular in the imageprocessing community. Their theoretical analysis is relatively difficult compared with that of the linear filters. However, several new tools have been developed in recent years that make this analysis easier. In this review paper an analysis of their properties as well as their algorithmic computation will be presented. I.
Motion Picture Restoration
, 1993
"... This dissertation presents algorithms for restoring some of the major corruptions observed in archived film or video material. The two principal problems of impulsive distortion (Dirt and Sparkle or Blotches) and noise degradation are considered. There is also an algorithm for suppressing the inter ..."
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Cited by 52 (9 self)
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This dissertation presents algorithms for restoring some of the major corruptions observed in archived film or video material. The two principal problems of impulsive distortion (Dirt and Sparkle or Blotches) and noise degradation are considered. There is also an algorithm for suppressing the interline jitter common in images decoded from noisy video signals. In the case of noise reduction and Blotch removal the thesis considers image sequences to be three dimensional signals involving evolution of features in time and space. This is necessary if any process presented is to show an improvement over standard twodimensional techniques. It is important to recognize that consideration of image sequences must involve an appreciation of the problems incurred by the motion of objects in the scene. The most obvious implication is that due to motion, useful three dimensional processing does not necessarily proceed in a direction `orthogonal' to the image frames. Therefore, attention is giv...
Minimum Mean Absolute Error Stack Filtering with Structural Constraints and Goals
, 1990
"... Two approaches have been used in the past to design or choose a rankorder based filter to estimate a signal from a noisecorrupted observation of that signal: the structural approach and the estimation approach. In the structural approach, the goal is to find a filter which preserves those shapes ..."
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Cited by 23 (12 self)
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Two approaches have been used in the past to design or choose a rankorder based filter to estimate a signal from a noisecorrupted observation of that signal: the structural approach and the estimation approach. In the structural approach, the goal is to find a filter which preserves those shapes that are part of the signal while removing those that are part of the noise. In the estimation approach, the goal is to find a filter which best estimates the desired signal given the noisecorrupted version of the signal as the filter’s input. This paper develops a theory for the structural behavior of stack filters. This theory provides a test which can determine if a given stack filter has any root signals; a method for classifying the root signal behavior of any stack filter found to have roots; and, perhaps what is most important, a method for designing stack filters with specific root signals or other structural behavior. This theory of root signals for stack filters is then combined with the theory of minimum mean absolute error stack filtering. This new, unified theory allows the designer to pick a filter which minimizes noise subject to constraints on its structural behavior.
An Overview of Median and Stack Filtering
 Circuits, Systems, and Signal Processing, Special issue on Median and Morphological Filtering
, 1992
"... Abstract. Within the last two decades a small group of researchers has built a useful, nontrivial theory of nonlinear signal processing around the medianrelated filters known as rankorder filters, orderstatistic filters, weighted median filters, and stack filters. This required significant effort ..."
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Cited by 10 (2 self)
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Abstract. Within the last two decades a small group of researchers has built a useful, nontrivial theory of nonlinear signal processing around the medianrelated filters known as rankorder filters, orderstatistic filters, weighted median filters, and stack filters. This required significant effort to overcome the bias, both in education and research, toward linear theory, which has been dominant since the days of Fourier, Laplace, and "Convolute." We trace the development of this theory of nonlinear filtering from its beginnings in the study of noiseremoval properties and structural behavior of the median filter to the recently developed theory of optimal stack filtering. The theory of stack filtering provides a point of view which unifies many different filter classes, including morphological filters, so it is discussed in detail. Of particular importance is the way this theory has brought together, in a single analytical framework, both the estimationbased and the structuralbased approaches to the design of these filters. Some recent applications of median and stack filters are provided to demonstrate the effectiveness of this approach to nonlinear filtering. They include: the design of an optimal stack filter for image restoration; the use of vector median filters to attenuate impulsive noise in color images and to eliminate cross luminance and cross color in TV images; and the use of medianbased filters for image sequence coding, reconstruction, and scan rate conversion in normal TV and HDTV systems. 1.
Selection Weighted Vector Directional Filters
"... In this paper, a class of Weighted Vector Directional Filters (WVDFs) based on the selection of the output sample from the multichannel input set is analyzed and optimized. The WVDF output minimizes the sum of weighted angular distances to other input samples from the filtering window. Dependent o ..."
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Cited by 8 (2 self)
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In this paper, a class of Weighted Vector Directional Filters (WVDFs) based on the selection of the output sample from the multichannel input set is analyzed and optimized. The WVDF output minimizes the sum of weighted angular distances to other input samples from the filtering window. Dependent on the weighting coefficients, the class of the WVDFs can be designed to perform a number of smoothing operations with different properties, which can be applied for specific filtering scenarios. In order to adapt the weighting coefficients to varying noise and image statistics, we introduce a methodology, which achieves an optimal tradeoff between smoothing and detail preserving characteristics. The proposed angular optimization algorithms take advantage of adaptive stack filters design and weighted median filtering framework. The optimized WVDFs are able to remove image noise, while maintaining excellent signaldetail preservation capabilities and sufficient robustness for a variety of signal and noise statistics.
Eye movements of younger and older drivers
 Human Factors
, 1999
"... This 2part study focuses on eye movements to explain drivingrelated visual performance in younger and older subjects. In the first task, subjects ’ eye movements were monitored as they viewed a traffic scene image with a numeric overlay, and visually located the numbers in their sequential order. ..."
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Cited by 6 (1 self)
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This 2part study focuses on eye movements to explain drivingrelated visual performance in younger and older subjects. In the first task, subjects ’ eye movements were monitored as they viewed a traffic scene image with a numeric overlay, and visually located the numbers in their sequential order. The results showed that older subjects had significantly longer search episodes than younger subjects, and their visual search was characterized by more fixations and shorter saccades, although the average fixation durations remained the same. In the second task the subjects viewed pictures of traffic scenes photographed from the driver's perspective, and the task was to assume the role of the driver and regard the image accordingly. Results in the second task showed that older subjects allocated a larger percentage of their visual scan time to a small subset of areas in the image, while younger subjects scanned the images more evenly. Also, older subjects revisited the same areas and younger subjects did not. The results suggest how aging might affect the efficacy of visual information processing.
Permutation Filters: A Class of NonLinear Filters Based on Set Permutations
 IEEE Transactions on Signal Processing
, 1994
"... In this paper we introduce and analyze a new class of nonlinear filters which have their roots in permutation theory. We show that a large body of nonlinear filters proposed to date constitute a proper subset of Permutation Filters (P Filters). In particular, rankorder filters, weighted rank ..."
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Cited by 6 (3 self)
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In this paper we introduce and analyze a new class of nonlinear filters which have their roots in permutation theory. We show that a large body of nonlinear filters proposed to date constitute a proper subset of Permutation Filters (P Filters). In particular, rankorder filters, weighted rankorder filters, and stack filters embody limited permutation transformations of a set. Indeed, by using the full potential of a permutation group transformation we can design very efficient estimation algorithms. Permutation groups inherently utilize both rankorder and temporalorder information; thus, the estimation of nonstationary processes in Gaussian/nonGaussian environments with frequency selection can be effectively addressed. An adaptive design algorithm which minimizes the mean absolute error criterion is described as well as a more flexible adaptive algorithm which attains the optimal permutation filter under a deterministic least normed error criterion. Simulation results ar...
The Viterbi Optimal RunlengthConstrained Approximation Nonlinear Filter
, 1995
"... Simple nonlinear filters are often used to enforce "hard" syntactic constraints while remaining close to the observation data; e.g., in the binary case it is common practice to employ iterations of a suitable median, or a onepass recursive median, openclose, or closopen filter to impose a ..."
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Cited by 6 (3 self)
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Simple nonlinear filters are often used to enforce "hard" syntactic constraints while remaining close to the observation data; e.g., in the binary case it is common practice to employ iterations of a suitable median, or a onepass recursive median, openclose, or closopen filter to impose a minimum symbol runlength constraint while remaining "faithful" to the observation. Unfortunately, these filters are  in general  suboptimal. Motivated by this observation, we pose the following optimization: Given a finitealphabet sequence of finite extent, y = fy(n)g N \Gamma1 n=0 , find a sequence, b x = fbx(n)g N \Gamma1 n=0 , which minimizes d(x; y) = P N \Gamma1 n=0 dn (y(n); x(n)) subject to: x is piecewise constant of plateau runlength M . We show how a suitable reformulation of the problem naturally leads to a simple and efficient Viterbitype optimal algorithmic solution. We call the resulting nonlinear inputoutput operator the Viterbi Optimal RunlengthConstrained Approximation...
VLSI Architectures for Weighted Order Statistic (WOS) Filters
 In Proc. of the IEEE Winter Workshop on Nonlinear Digital Signal Processing
, 1993
"... The class of median filters has been extended to include weighted order statistics (WOS) filters, to improve the flexibility of the filtering operation. The WOS filter weights each input within a sample window, and thus retains the original temporal order information. In this paper, we present effic ..."
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Cited by 6 (1 self)
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The class of median filters has been extended to include weighted order statistics (WOS) filters, to improve the flexibility of the filtering operation. The WOS filter weights each input within a sample window, and thus retains the original temporal order information. In this paper, we present efficient VLSI architectures for WOS filters which maintain a weighted rank for each sample in the sample window and update the weighted ranks for each window shift. We present novel (i) array architectures (ii) stack filter architectures and (iii) sorting network architectures for nonrecursive and recursive WOS filters which implement the above procedure. Our analysis shows that the bitserial stack filter implementation is the one with the smallest area while the bitparallel stack filter is the one with the smallest inputoutput latency. The sorting network architecture (based on updating a sorted list) has the best areatime performance. Physical implementations verify our analysis. 1 The ...