Related papers: Wavelet filter functions, the matrix completion pr…
The application of the continuous wavelet transform to study of a wide class of physical processes with oscillatory dynamics is restricted by large central frequencies due to the admissibility condition. We propose an alternative…
We present a general setting where wavelet filters and multiresolution decompositions can be defined, beyond the classical $\mathbf L^2(\mathbb R,dx)$ setting. This is done in a framework of {\em iterated function system} (IFS) measures;…
Let $k$ be a commutative Noetherian ring. In this paper we consider filtered modules of the category FI firstly introduced by Nagpal. We show that a finitely generated FI-module $V$ is filtered if and only if its higher homologies all…
We introduce the notion of $\mathcal{C}$-system of filters, generalizing the standard definitions of both extenders and towers of normal ideals. This provides a framework to develop the theory of extenders and towers in a more general and…
Matrix completion is a classical problem in data science wherein one attempts to reconstruct a low-rank matrix while only observing some subset of the entries. Previous authors have phrased this problem as a nuclear norm minimization…
The purpose of this work is the design of FIR QMF (Quadrature Mirror Filters) filters of perfect reconstruction and odd number of coefficients (even order). By design, these filters will have linear phase and integer delay. These filter…
In the present paper the notion of continuous frames is introduced and some results of these frames are proved. Next, we give the concept of duals of continuous frames in Hilbert C*-modules and investigate some properties of them.
The spectral properties of the Ruelle transfer operator which arises from a given polynomial wavelet filter are related to the convergence question for the cascade algorithm for approximation of the corresponding wavelet scaling function.
The Correlation Filter is an algorithm that trains a linear template to discriminate between images and their translations. It is well suited to object tracking because its formulation in the Fourier domain provides a fast solution,…
We investigate the "theta-deformed spheres" C(S^{3}_{theta}) and C(S^{4}_{theta}), where theta is any real number. We show that all finitely-generated projective modules over C(S^{3}_{theta}) are free, and that C(S^{4}_{theta}) has the…
The filter quotient construction is a particular instance of a filtered colimit of categories. It has primarily been considered in the context of categorical logic, where it has been used effectively to construct non-trivial models, for…
We consider the problem of imaging extended reflectors in terminating waveguides. We form the image by back-propagating the array response matrix projected on the waveguide's non-evanescent modes. The projection is adequately defined for…
In previous work, we related homotopy types of finite $(G,n)$-complexes when $G$ has periodic cohomology to projective $\mathbb{Z} G$-modules representing the Swan finiteness obstruction. We use this to determine when $X \vee S^n \simeq Y…
Compressed sensing (CS) using overcomplete wavelet dictionaries has been a well-investigated topic in the recent times for image and vision applications. In this paper, different overcomplete wavelet transforms have been studied to estimate…
We develop the notion of a "filtered cospan" as an algebraic object that stands in the same relation to interlevel persistence modules as filtered chain complexes stand with respect to sublevel persistence modules. This relation is…
The perfectly matched layers (PMLs), as a boundary termination over an unbounded spatial domain, are widely used in numerical simulations of wave propagation problems. Given a set of discretization parameters, a procedure to select the PML…
For an arbitrary matrix dilation, any integer n and any integer/semi-integer c, we describe all masks that are symmetric with respect to the point c and have sum rule of order n. For each such mask, we give explicit formulas for wavelet…
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…
We introduce continuous supersymmetric transformations to manipulate the modal content in systems of optical waveguides, providing a systematic method to design efficient and robust integrated devices such as tapered waveguides,…
In this paper we introduce a new linear filtering technique, the so-called matrix filters, that maximizes the signal-to-interference ratio of compact sources of unknown intensity embedded in a set of images by taking into account the…