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Classical image filters, such as those for averaging or differencing, are carefully normalized to ensure consistency, interpretability, and to avoid artifacts like intensity shifts, halos, or ringing. In contrast, convolutional filters…

Multiresolution Matrix Factorization (MMF) is unusual amongst fast matrix factorization algorithms in that it does not make a low rank assumption. This makes MMF especially well suited to modeling certain types of graphs with complex…

Convolutional neural network (CNN), with ability of feature learning and nonlinear mapping, has demonstrated its effectiveness in prognostics and health management (PHM). However, explanation on the physical meaning of a CNN architecture…

We introduce WaveSim, a multi-scale similarity metric for the evaluation of spatial fields in weather and climate applications. WaveSim exploits wavelet transforms to decompose input fields into scale-specific wavelet coefficients. The…

We explored the statistics of filtering of simple patterns on a number of deterministic and random graphs as a tractable simple example of information processing in complex systems. In this problem, multiple inputs map to the same output,…

Spatio-temporal data sets are rapidly growing in size. For example, environmental variables are measured with ever-higher resolution by increasing numbers of automated sensors mounted on satellites and aircraft. Using such data, which are…

Due to their adaptive nature, empirical wavelets had several successes in many fields from engineering, science, medical signal/image processing. Recently, a general theoretical framework has been developed in the one-dimensional case,…

In the framework of wave packet analysis, finite wavelet systems are particular classes of finite wave packet systems. In this paper, using a scaling matrix on a permuted version of the discrete Fourier transform (DFT) of system generator,…

The filters work in many areas of technology. There constructions are different and substances under filtration are different. It is necessary in some cases to take into account forming of sediments on the walls of the filter since they can…

This paper presents numerical and analytical investigation of gas flow in gas-dynamic filter - a device for cleaning gas from solid particles with counter flow of large water particles in order to prevent their release to the atmosphere.…

Implicit particle filters for data assimilation update the particles by first choosing probabilities and then looking for particle locations that assume them, guiding the particles one by one to the high probability domain. We provide a…

In a traditional convolutional layer, the learned filters stay fixed after training. In contrast, we introduce a new framework, the Dynamic Filter Network, where filters are generated dynamically conditioned on an input. We show that this…

Inspired by the key principle behind the EM algorithm, we propose a general methodology for conducting wavelet estimation with irregularly-spaced data by viewing the data as the observed portion of an augmented regularly-spaced data set. We…

Reduction of combinatorial filters involves compressing state representations that robots use. Such optimization arises in automating the construction of minimalist robots. But exact combinatorial filter reduction is an NP-complete problem…

A Schmidt filter is a modification of the Kalman filter that allows to append system parameters as states and considers their uncertainty effect in the filtering process without attempting to estimate such parameters. The states that are…

A dynamic dictionary is a data structure that maintains sets of cardinality at most $n$ from a given universe and supports insertions, deletions, and membership queries. A filter approximates membership queries with a one-sided error that…

Connected operators are filtering tools that act by merging elementary regions of an image. A popular strategy is based on tree-based image representations: for example, one can compute an attribute on each node of the tree and keep only…

In this paper, we propose a meshfree approximation method for the implicit filter developed in [2], which is a novel numerical algorithm for nonlinear filtering problems. The implicit filter approximates conditional distributions in the…

Bayesian filtering is a well-known problem that aims to estimate plausible states of a dynamical system from observations. Among existing approaches to solve this problem, particle filters are theoretically exact for non-linear dynamics and…

In the paper, effective filtering for a type of slow-fast data assimilation systems in Hilbert spaces is considered. Firstly, the system is reduced to a system on a random invariant manifold. Secondly, nonlinear filtering of the origin…