Related papers: On Weaving Generalized Frames and Generalized Ries…
In this paper we will consider, in the abstract setting of rigged Hilbert spaces, distribution valued functions and we will investigate, in particular, conditions for them to constitute a "continuous basis" for the smallest space $\mathcal…
We characterize Riesz frames and frames with the subframe property and use this to answer most of the questions from the literature concerning these properties and their relationships to the projection methods etc.
Region-of-Interest (ROI)-based image compression allocates bits unevenly according to the semantic importance of different regions. Such differentiated coding typically induces a sharp-peaked and heavy-tailed distribution. This distribution…
In wireless sensors networks, integrating localization and communications techniques is crucial for efficient spectrum and hardware utilization. In this paper, we present a novel framework of unmanned aerial vehicle (UAV)-aided localization…
In this paper a large class of universal windows for Gabor frames (Weyl-Heisenberg frames) is constructed. These windows have the fundamental property that every overcritical rectangular lattice generates a Gabor frame. Likewise, every…
We study the problem of regularization of inverse problems adopting a purely data driven approach, by using the similarity to the method of regularization by projection. We provide an application of a projection algorithm, utilized and…
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…
Given a positive weight function and an isometry map on a Hilbert spaces $\mathcal{H}$, we study a class of linear maps which is a $g$-frame, $g$-Riesz basis and a $g$-orthonormal basis for $\mathcal{H}$ with respect to $\mathbb{C}$ in…
Video frame interpolation aims at synthesizing intermediate frames from nearby source frames while maintaining spatial and temporal consistencies. The existing deep-learning-based video frame interpolation methods can be roughly divided…
Mesoscale simulations of woven composites using parameterized analytical geometries offer a way to connect constituent material properties and their geometric arrangement to effective composite properties and performance. However, the…
With the rapid development of Generative Artificial Intelligence (GAI) technology, Generative Diffusion Models (GDMs) have shown significant empowerment potential in the field of wireless networks due to advantages, such as noise…
Multipliers have been recently introduced by P. Balazs as operators for Bessel sequences and frames in Hilbert spaces. These are operators that combine (frame-like) analysis, a multiplication with a fixed sequence (called the symbol) and…
The problem of distributed or decentralized detection and estimation in applications such as wireless sensor networks has often been considered in the framework of parametric models, in which strong assumptions are made about a statistical…
We study the problem of decentralized interferometric imaging over networks, where agents have access to a subset of local radar measurements and can compute pair-wise correlations with their neighbors. We propose a primal-dual distributed…
We introduce probabilistic frames to study finite frames whose elements are chosen at random. While finite tight frames generalize orthonormal bases by allowing redundancy, independent, uniformly distributed points on the sphere…
Wireless signals are integral to modern society, enabling both communication and increasingly, environmental sensing. While various propagation models exist, ranging from empirical methods to full-wave simulations, the phenomenon of…
Graph neural networks are widely used tools for graph prediction tasks. Motivated by their empirical performance, prior works have developed generalization bounds for graph neural networks, which scale with graph structures in terms of the…
The focus of this work is on the analysis of transmit beamforming schemes with a low-rate feedback link in wireless sensor/relay networks, where nodes in the network need to implement beamforming in a distributed manner. Specifically, the…
In this paper, we propose the geometric algebra-informed neural radiance fields (GAI-NeRF), a novel framework for wireless channel prediction that leverages geometric algebra attention mechanisms to capture ray-object interactions in…
We provide a detailed analysis of the obstruction (studied first by S. Durand and later by R. Yin and one of us) in the construction of multidirectional wavelet orthonormal bases corresponding to any admissible frequency partition in the…