Distance Measures for Reduced Ordering Based Vector Filters

Reduced ordering based vector filters have proved successful in removing long-tailed noise from color images while preserving edges and fine image details. These filters commonly utilize variants of the Minkowski distance to order the color vectors with the aim of distinguishing between noisy and noise-free vectors. In this paper, we review various alternative distance measures and evaluate their performance on a large and diverse set of images using several effectiveness and efficiency criteria. The results demonstrate that there are in fact strong alternatives to the popular Minkowski metrics

Impulsive noise removal from color images with morphological filtering

This paper deals with impulse noise removal from color images. The proposed noise removal algorithm employs a novel approach with morphological filtering for color image denoising; that is, detection of corrupted pixels and removal of the detected noise by means of morphological filtering. With the help of computer simulation we show that the proposed algorithm can effectively remove impulse noise. The performance of the proposed algorithm is compared in terms of image restoration metrics and processing speed with that of common successful algorithms.Comment: The 6th international conference on analysis of images, social networks, and texts (AIST 2017), 27-29 July, 2017, Moscow, Russi

Reduced Complexity Filtering with Stochastic Dominance Bounds: A Convex Optimization Approach

This paper uses stochastic dominance principles to construct upper and lower sample path bounds for Hidden Markov Model (HMM) filters. Given a HMM, by using convex optimization methods for nuclear norm minimization with copositive constraints, we construct low rank stochastic marices so that the optimal filters using these matrices provably lower and upper bound (with respect to a partially ordered set) the true filtered distribution at each time instant. Since these matrices are low rank (say R), the computational cost of evaluating the filtering bounds is O(XR) instead of O(X2). A Monte-Carlo importance sampling filter is presented that exploits these upper and lower bounds to estimate the optimal posterior. Finally, using the Dobrushin coefficient, explicit bounds are given on the variational norm between the true posterior and the upper and lower bounds

DDP-GCN: Multi-Graph Convolutional Network for Spatiotemporal Traffic Forecasting

Traffic speed forecasting is one of the core problems in Intelligent Transportation Systems. For a more accurate prediction, recent studies started using not only the temporal speed patterns but also the spatial information on the road network through the graph convolutional networks. Even though the road network is highly complex due to its non-Euclidean and directional characteristics, previous approaches mainly focus on modeling the spatial dependencies only with the distance. In this paper, we identify two essential spatial dependencies in traffic forecasting in addition to distance, direction and positional relationship, for designing basic graph elements as the smallest building blocks. Using the building blocks, we suggest DDP-GCN (Distance, Direction, and Positional relationship Graph Convolutional Network) to incorporate the three spatial relationships into prediction network for traffic forecasting. We evaluate the proposed model with two large-scale real-world datasets, and find 7.40% average improvement for 1-hour forecasting in highly complex urban networks

Mode-coupling theory for multiple-time correlation functions of tagged particle densities and dynamical filters designed for glassy systems

The theoretical framework for higher-order correlation functions involving multiple times and multiple points in a classical, many-body system developed by Van Zon and Schofield [Phys. Rev. E 65, 011106 (2002)] is extended here to include tagged particle densities. Such densities have found an intriguing application as proposed measures of dynamical heterogeneities in structural glasses. The theoretical formalism is based upon projection operator techniques which are used to isolate the slow time evolution of dynamical variables by expanding the slowly-evolving component of arbitrary variables in an infinite basis composed of the products of slow variables of the system. The resulting formally exact mode-coupling expressions for multiple-point and multiple-time correlation functions are made tractable by applying the so-called N-ordering method. This theory is used to derive for moderate densities the leading mode coupling expressions for indicators of relaxation type and domain relaxation, which use dynamical filters that lead to multiple-time correlations of a tagged particle density. The mode coupling expressions for higher order correlation functions are also succesfully tested against simulations of a hard sphere fluid at relatively low density.Comment: 15 pages, 2 figure

Data Assimilation by Conditioning on Future Observations

Conventional recursive filtering approaches, designed for quantifying the state of an evolving uncertain dynamical system with intermittent observations, use a sequence of (i) an uncertainty propagation step followed by (ii) a step where the associated data is assimilated using Bayes' rule. In this paper we switch the order of the steps to: (i) one step ahead data assimilation followed by (ii) uncertainty propagation. This route leads to a class of filtering algorithms named \emph{smoothing filters}. For a system driven by random noise, our proposed methods require the probability distribution of the driving noise after the assimilation to be biased by a nonzero mean. The system noise, conditioned on future observations, in turn pushes forward the filtering solution in time closer to the true state and indeed helps to find a more accurate approximate solution for the state estimation problem