We consider multiscale stochastic systems that are partially observed at discrete points of the slow time scale. We introduce a particle filter that takes advantage of the multiscale structure of the system to efficiently approximate the optimal filter.

Most analysts start with an overview of the data before gradually refining their view to be more focused and detailed. Multiscale pan-and-zoom systems are effective because they directly support this approach. However, generating abstract overviews of large data sets is difficult and most systems take advantage of only one type of abstraction: visual abstraction. Furthermore, these existing sys...

This paper presents a generative model based approach to man-made structure detection in 2D natural images. The proposed approach uses a causal multiscale random field suggested in [3] as a prior model on the class labels on the image sites. However, instead of assuming the conditional independence of the observed data, we propose to capture the local dependencies in the data using a multiscale...

The development of accurate mathematical models describing the flow of groundwater is an important problem due to the prevalence of contaminants in or near groundwater supplies. An important parameter of these models is hydraulic conductivity, which describes the ability of the subsurface geology to conduct water flow. Because hydraulic conductivity is a function of the earth's subsurface, dire...

Since meshfree particle methods have advantages on simulating the problems involving extremely large deformations, fractures etc., they become attractive options to be used in the hierarchical multiscale modeling to approximate a large number of atoms. We propose a nanoscale meshfree particle method with the implementation of the quasicontinuum technique in this paper. The intrinsic properties ...

We present a new method for robustly decomposing a 3D voxel shape into disjoint segments using the medial surface, also called surface skeleton. The boundaries of the simplified foreand background skeletons map one-to-one to increasingly fuzzy, soft convex, respectively concave, edges of the shape. Using this property, we build a method for segmentation of 3D shapes which has several desirable ...

This paper presents a multiscale-based analysis of the statistical dependencies between the wavelet coefficients of random fields. In particular, in contrast to common decorrelated-coefficient models, we find that the correlation between wavelet scales can be surprisingly substantial, even across several scales. In this paper we investigate eight possible choices of statistical-interaction mode...

Many important problems in engineering and science are well-modeled by Poisson processes. In many applications it is of great interest to accurately estimate the intensities underlying observed Poisson data. In particular, this work is motivated by photon-limited imaging problems. This paper studies a new Bayesian approach to Poisson intensity estimation based on the Haar wavelet transform. It ...

This paper considers the problem of determining which set of 2P leaf nodes on a binary multiscale tree model of depth N ( N > p ) gives the best linear minimum mean-squared estimator of the tree root. We find that the best-case and worst-case sanipling choices depend on the correlation structure of the tree. This problem arises in Internet traffic estimation. where the goal is to estimate the a...

Suppose that one observes pairs (x1, Y1), (x2, Y2), . . . , (xn, Yn), where x1 ≤ x2 ≤ · · · ≤ xn are fixed numbers, and Y1, Y2, . . . , Yn are independent random variables with unknown distributions. The only assumption is that Median(Yi) = f(xi) for some unknown convex function f . We present a confidence band for this regression function f using suitable multiscale signtests. While the exact ...