Related papers: A note on weaving fusion frames
Hilbert space fusion frames are a natural extension of Hilbert space frames, extending the notion from a set of vectors in a Hilbert space to a set of subspaces of a Hilbert space with analogous notions of overcompleteness and boundedness.…
Let $\{W_i\}_{i\in I}$ be a (redundant) sequence of subspaces each being endowed with a weight $v_i$, and let $\mathcal{H}$ be the closed linear span of the $W_i$'s, a composite Hilbert space. Provided that $\{(W_i,v_i)\}_{i \in I}$…
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…
Networks of multiple radars are typically used for improving the coverage and tracking accuracy. Recently, such networks have facilitated deployment of commercial radars for civilian applications such as healthcare, gesture recognition,…
The fusion techniques that utilize multiple feature sets to form new features that are often more robust and contain useful information for future processing are referred to as feature fusion. The term data fusion is applied to the class of…
Sparse representations have emerged as a powerful tool in signal and information processing, culminated by the success of new acquisition and processing techniques such as Compressed Sensing (CS). Fusion frames are very rich new signal…
Unit norm finite frames are generalizations of orthonormal bases with many applications in signal processing. An important property of a frame is its coherence, a measure of how close any two vectors of the frame are to each other. Low…
Deep unfolding is a method of growing popularity that fuses iterative optimization algorithms with tools from neural networks to efficiently solve a range of tasks in machine learning, signal and image processing, and communication systems.…
In this paper we extend the notion of approximate dual to fusion frames and present some approaches to obtain dual and approximate alternate dual fusion frames. Also, we study the stability of dual and approximate alternate dual fusion…
Finite frames, or spanning sets for finite-dimensional Hilbert spaces, are a ubiquitous tool in signal processing. There has been much recent work on understanding the global structure of collections of finite frames with prescribed…
Weaving frames are powerful tools in wireless sensor networks and pre-processing signals. In this paper, we introduce the concept of weaving for g-frames in Hilbert spaces. We first give some properties of weaving g-frames and present two…
Recently, fusion frames and frames for operators were considered as generalizations of frames in Hilbert spaces. In this paper, we generalize some of the known results in frame theory to fusion frames related to a linear bounded operator K…
Fusion frames are valuable generalizations of discrete frames. Most concepts of fusion frames are shared by discrete frames. However, the dual setting is so complicated. In particular, unlike discrete frames, two fusion frames are not dual…
In this work we deal with the recently introduced concept of weaving frames. We extend the concept to include multi-window frames and present the first sufficient criteria for a family of multi-window Gabor frames to be woven. We give a…
We consider the recovery of sparse signals that share a common support from multiple measurement vectors. The performance of several algorithms developed for this task depends on parameters like dimension of the sparse signal, dimension of…
Transmitted data may be corrupted by both noise and data loss. Grassmannian frames are in some sense optimal representations of data transmitted over a noisy channel that may lose some of the transmitted coefficients. Fusion frame (or frame…
A proper fusion of complex data is of interest to many researchers in diverse fields, including computational statistics, computational geometry, bioinformatics, machine learning, pattern recognition, quality management, engineering,…
Vertex-frequency analysis, particularly the windowed graph Fourier transform (WGFT), is a significant challenge in graph signal processing. Tight frame theories is known for its low computational complexity in signal reconstruction, while…
Image decomposition is a crucial subject in the field of image processing. It can extract salient features from the source image. We propose a new image decomposition method based on convolutional neural network. This method can be applied…
Quality is one of the important things to be maintained in a weaving industry. Along with the times, technological developments in the field of image processing and computing have changed the old method of visual evaluation of woven fabric…