Related papers: Weaving Hilbert space fusion frames
The concept of a bi-g-fusion frame for a Hilbert space, which is a generalizations of a controlled g-fusion frame, is introduced and an example is given. Finally, bi-g-fusion frame in tensor product of Hilbert spaces is considered.
Breakthroughs in information and power transfer for wireless networks are imperative in order to satisfy the requirement of wireless nodes for energy sustainability. To this end, significant research efforts in academia and industry have…
Development and testing of multi-robot systems employing wireless signal-based sensing requires access to suitable hardware, such as channel monitoring WiFi transceivers, which can pose significant limitations. The WiFi Sensor for Robotics…
Programmable, intelligent surfaces can manipulate electromagnetic waves impinging upon them, producing arbitrarily shaped reflection, refraction and diffraction, to the benefit of wireless users. Moreover, in their recent form of…
The construction of highly incoherent frames, sequences of vectors placed on the unit hyper sphere of a finite dimensional Hilbert space with low correlation between them, has proven very difficult. Algorithms proposed in the past have…
Unsupervised change detection techniques are generally constrained to two multi-band optical images acquired at different times through sensors sharing the same spatial and spectral resolution. This scenario is suitable for a straight…
The growing demand for accurate, continuous, and non-invasive health monitoring has propelled multi-sensor data fusion to the forefront of healthcare technology. This review aims to provide an overview of the development of fusion…
Presented is a novel way to combine snapshot compressive imaging and lateral shearing interferometry in order to capture the spatio-spectral phase of an ultrashort laser pulse in a single shot. A deep unrolling algorithm is utilised for the…
Denoising diffusion models are a novel class of generative algorithms that achieve state-of-the-art performance across a range of domains, including image generation and text-to-image tasks. Building on this success, diffusion models have…
A linear operator in a Hilbert space defined through the form of Riesz representation naturally introduces a reproducing kernel Hilbert space structure over the range space. Such formulation, called H-HK formulation in this paper, possesses…
Accurate and robust navigation in unstructured environments requires fusing data from multiple sensors. Such fusion ensures that the robot is better aware of its surroundings, including areas of the environment that are not immediately…
We present a novel generative modeling framework,Wavelet-Fourier-Diffusion, which adapts the diffusion paradigm to hybrid frequency representations in order to synthesize high-quality, high-fidelity images with improved spatial…
In this article we develop a theory for frames in tensor product of Hilbert spaces. We show that like bases if Y_1, Y_2, \cdot \cdot \cdot, Y_n are frames for H_1,H_2, \cdot \cdot \cdot, H_n, respectively, then…
We propose Fiber Bundle Networks (FiberNet), a novel machine learning framework integrating differential geometry with machine learning. Unlike traditional deep neural networks relying on black-box function fitting, we reformulate…
Wireless communication systems exhibit structural and functional similarities to neural networks: signals propagate through cascaded elements, interact with the environment, and undergo transformations. Building upon this perspective, we…
4D millimeter-wave (mmWave) radar has been widely adopted in autonomous driving and robot perception due to its low cost and all-weather robustness. However, point-cloud-based radar representations suffer from information loss due to…
In this article we obtain families of frames for the space B_\omega of functions with band in [-\omega,\omega] by using the theory of shift-invariant spaces. Our results are based on the Gramian analysis of A. Ron and Z. Shen and a variant,…
The notion of controlled frames for Hilbert spaces were introduced by Balazs, Antoine and Grybos to improve the numerical efficiency of iterative algorithms for inverting the frame operator. Controlled Frame Theory has a great revolution in…
The use of unitary invariant subspaces of a Hilbert space $\mathcal{H}$ is nowadays a recognized fact in the treatment of sampling problems. Indeed, shift-invariant subspaces of $L^2(\mathbb{R})$ and also periodic extensions of finite…
With the rapid development of wireless communication technology, wireless access points (AP) and internet of things (IoT) devices have been widely deployed in our surroundings. Various types of wireless signals (e.g., Wi-Fi, LoRa, LTE) are…