Related papers: Weaving Information Packets
Inspired by the work of Bemrose et al. \cite{Be16}, we delve into the study of weaving frames in Krein spaces. This paper presents a comprehensive exploration of various properties and characterizations of Krein space weaving frames. In…
Fusion frames are a very active area of research today because of their myriad of applications in pure mathematics, applied mathematics, engineering, medicine, signal and image processing and much more. They provide a great flexibility for…
Certain signal classes such as audio signals call for signal representations with the ability to adapt to the signal's properties. In this article we introduce the new concept of quilted frames, which aim at adaptivity in time-frequency…
Weaving frames have potential applications in wireless sensor networks that require distributed processing of signal under different frames. In this paper, we study some new properties of weaving generalized frames (or $g$-frames) and…
This work shows the use of a two-dimensional Gabor wavelets in image processing. Convolution with such a two-dimensional wavelet can be separated into two series of one-dimensional ones. The key idea of this work is to utilize a Gabor…
In this note, we first introduce the notation of weaving cfusion frames in separable Hilbert spaces. After reviewing the conditions for maintaining the weaving c-fusion frames under the bounded linear operator and also, removing vectors…
In this note, we prove some results related to small perturbations of a frame for a Hilbert space $\mathcal{H}$ in order to have a woven pair for $\mathcal{H}$. Our results complete those known in the literature. In addition we study a…
Matching, a task to optimally assign limited resources under constraints, is a fundamental technology for society. The task potentially has various objectives, conditions, and constraints; however, the efficient neural network architecture…
We introduce and develop the concept of oblique duality for fusion frames. This concept provides a mathematical framework to deal with problems in distributed signal processing where the signals, considered as elements in a Hilbert space…
In this paper, we first introduce the notion of controlled weaving K-g-frames in Hilbert spaces. Then, we present sufficient conditions for controlled weaving K-g-frames in separable Hilbert spaces. Also, a characterization of controlled…
The scattering transform is a wavelet-based model of Convolutional Neural Networks originally introduced by S. Mallat. Mallat's analysis shows that this network has desirable stability and invariance guarantees and therefore helps explain…
So far there has not been paid attention to frames that are balanced, i.e. those frames which sum is zero. In this paper we consider balanced frames, and in particular balanced unit norm tight frames, in finite dimensional Hilbert spaces.…
In solving scientific, engineering or pure mathematical problems one is often faced with a need to approximate the function of a given class by the linear combination of a preferably small number of functions that are localised one way or…
Finite frame theory has become a powerful tool for many applications of mathematics. In this paper we introduce a new area of research in frame theory: Integer frames. These are frames having all integer coordinates with respect to a fixed…
Single photon interference due to passage through a periodic grating is considered in a novel proposal for processing D-dimensional quantum systems (quDits) encoded in the spatial degrees of freedom of light. We show that free space…
In this paper, we study nonhomogeneous wavelet systems which have close relations to the fast wavelet transform and homogeneous wavelet systems. We introduce and characterize a pair of frequency-based nonhomogeneous dual wavelet frames in…
We introduce the notion of weaving continuous controlled K-g-fusion frame in Hilbert space. Some characterizations of weaving continuous controlled K-g-fusion frame have been presented. We extend some of the recent results of woven…
Collections of time- and frequency-shifts of suitably chosen generators (Alltop or random vectors) proved successful for many applications in sparse recovery and related fields. It was shown in \cite{xia2005achieving} that taking a…
This chapter is dedicated to recent developments in the field of wavelet analysis for scattered data. We introduce the concept of samplets, which are signed measures of wavelet type and may be defined on sets of arbitrarily distributed data…
This research proposes a language independent intra-process framework for object based composition of unmodified code modules. Intuitively, the two major programming models, threads and processes, can be considered as extremes along a…