Related papers: On Weaving Generalized Frames and Generalized Ries…
Woven fabrics are widely used in applications of realistic rendering, where real-time capability is also essential. However, rendering realistic woven fabrics in real time is challenging due to their complex structure and optical…
Finding the optimal dual frame and optimal dual pair for signal reconstruction, which can minimize the reconstruction error when erasure occurs during data transmission, is a deep rooted problem from the perspective of frame theory. In this…
In this paper we develop the analytical framework for a novel Wireless signal-based Sensing capability for Robotics (WSR) by leveraging robots' mobility. It allows robots to primarily measure relative direction, or Angle-of-Arrival (AOA),…
Non-orthogonal communication is a promising technique for future wireless networks (e.g., 6G and Wi-Fi 7). In the vector channel model, designing efficient non-orthogonal communication schemes amounts to the following extremum problem: \[…
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…
Multiple concepts for future generations of wireless communication standards utilize coherent processing of signals from many distributed antennas. Names for these concepts include distributed MIMO, cell-free massive MIMO, XL-MIMO, and…
In this paper we give new characterizations of Riesz and conditional Riesz frames in terms of the properties of the nullspace of their synthesis operators. On the other hand, we also study the oblique dual frames whose coefficients in the…
Wireless physical layer assessment, such as measuring antenna radiation patterns, is complex and cost-intensive. Researchers often require a stationary setup with antennas surrounding the device under test. There remains a need for more…
One of a key problems in signal reconstruction process with the use of frames is to find a dual frame. Typically, a canonical dual frame is used. However, there are many applications where this choice appears to be unfortunate. Due to that…
The systems based on intelligent sensors are currently expanding, due to theirs functions and theirs performances of intelligence: transmitting and receiving data in real-time, computation and processing algorithms, metrology remote,…
We study the relationship between operators, orthonormal basis of subspaces and frames of subspaces (also called fusion frames) for a separable Hilbert space $\mathcal{H}$. We get sufficient conditions on an orthonormal basis of subspaces…
The propagation and divergence properties of beams carrying orbital angular momentum (OAM) play a crucial role in many applications. Here we present a general study on the divergence of optical beams with OAM. We show that the mean absolute…
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…
In this paper, we study multiwindow discrete Gabor $(M-D-G)$ systems $\mathcal{G}(g,L,M,N)$ on discrete periodic sets $\mathbb{S}$ and give some necessary and/or sufficient matrix-conditions for a $M-D-G$ system in $\ell^2(\mathbb{S})$ to…
Wavelet frames have become a useful tool in time freqency analysis and image processing. Many authors worked in the field of wavelet frames and obtained various necessary and sufficient conditions. Ron and Shen [17] gave a charactarization…
We propose a novel method for large-scale image stitching that is robust against repetitive patterns and featureless regions in the imagery. In such cases, state-of-the-art image stitching methods easily produce image alignment artifacts,…
Wireless sensor networks (WSNs) have attracted considerable attention in recent years and motivate a host of new challenges for distributed signal processing. The problem of distributed or decentralized estimation has often been considered…
In this work we study families of pairs of window functions and lattices which lead to Gabor frames which all possess the same frame bounds. To be more precise, for every generalized Gaussian $g$, we will construct an uncountable family of…
Finding corresponding pixels within a pair of images is a fundamental computer vision task with various applications. Due to the specific requirements of different tasks like optical flow estimation and local feature matching, previous…
Generalized fusion frame and some of their properties in tensor product of Hilbert spaces are described. Also, the canonical dual g-fusion frame in tensor product of Hilbert spaces is considered. Finally, the frame operator for a pair of…