Related papers: Weaving Hilbert space fusion frames
In this work, we analyze Gabor frames for the Weyl--Heisenberg group and wavelet frames for the extended affine group. Firstly, we give necessary and sufficient conditions for the existence of nonstationary frames of translates. Using these…
In this article we consider the problems of distributed detection and estimation in wireless sensor networks. In the first part, we provide a general framework aimed to show how an efficient design of a sensor network requires a joint…
An active-sensing-based learning algorithm is proposed to solve the near-field beam alignment problem with the aid of wavenumber-domain transform matrices (WTMs). Specifically, WTMs can transform the antenna-domain channel into a sparse…
We present a general approach to a modular frame theory in C*-algebras and Hilbert C*-modules. The investigations rely on the idea of geometric dilation to standard Hilbert C*-modules over unital C*-algebras that possess orthonormal Hilbert…
In this paper we characterize and construct novel oversampled filter banks implementing fusion frames. A fusion frame is a sequence of orthogonal projection operators whose sum can be inverted in a numerically stable way. When properly…
Beamforming techniques have been widely used in the millimeter wave (mmWave) bands to mitigate the path loss of mmWave radio links as the narrow straight beams by directionally concentrating the signal energy. However, traditional mmWave…
We study embeddings and norm estimates for tensor products of weighted reproducing kernel Hilbert spaces. These results lead to a transfer principle that is directly applicable to tractability studies of multivariate problems as integration…
The Riesz transform is a natural multi-dimensional extension of the Hilbert transform, and it has been the object of study for many years due to its nice mathematical properties. More recently, the Riesz transform and its variants have been…
Generative Artificial Intelligence (GenAI) has made significant advancements in fields such as computer vision (CV) and natural language processing (NLP), demonstrating its capability to synthesize high-fidelity data and improve…
Operator-valued frames (or g-frames) are generalizations of frames and fusion frames and have been used in packets encoding, quantum computing, theory of coherent states and more. In this paper, we give a new formula for operator-valued…
The concept of smart wireless environments envisions dynamic programmable propagation of information-bearing signals through the deployment of Reconfigurable Intelligent Surfaces (RISs). Typical RIS implementations include metasurfaces with…
Weighted and controlled frames have been introduced recently to improve the numerical efficiency of iterative algorithms for inverting the frame operator. In this paper we develop systematically these notions, including their mutual…
We introduce the notion of a continuous biframe in a Hilbert space which is a generalization of discrete biframe in Hilbert space. Representation theorem for this type of generalized frame is verified and some characterizations of this…
A definition of frames in Krein spaces is stated and a complete characterization is given by comparing them to frames in the associated Hilbert space. The basic tools of frame theory are described in the formalism of Krein spaces. It is…
We consider a wireless sensor network consisting of multiple nodes that are coordinated by a fusion center (FC) in order to estimate a common signal of interest. In addition to being coordinated, the sensors are also able to collaborate,…
Wireless embedded edge devices are ubiquitous in our daily lives, enabling them to gather immense data via onboard sensors and mobile applications. This offers an amazing opportunity to train machine learning (ML) models in the realm of…
A general class of unidirectional transforms is presented that can be computed in a distributed manner along an arbitrary routing tree. Additionally, we provide a set of conditions under which these transforms are invertible. These…
We introduce a new basis for the gauge-invariant Hilbert space of lattice gauge theory and loop quantum gravity in $(2+1)$ dimensions, the fusion basis. In doing so, we shift the focus from the original lattice (or spin-network) structure…
Digital twins (DTs) are promising for wireless deployment, optimization, and data generation, but building a propagation-faithful twin from sparse real measurements remains difficult. This paper proposes a wireless environment digital twin…
Distributed computing platforms typically assume the availability of reliable and dedicated connections among the processors. This work considers an alternative scenario, relevant for wireless data centers and federated learning, in which…