Related papers: A Survey of Fusion Frames in Hilbert Spaces
K-fusion frames are generalizations of fusion frames in frame theory. This article characterizes various kinds of property of K-fusion frames. Several perturbation results on K-fusion frames are formulated and analyzed.
We study the duality of reconstruction systems, which are $g$-frames in a finite dimensional setting. These systems allow redundant linear encoding-decoding schemes implemented by the so-called dual reconstruction systems. We are…
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…
In this paper we generalize a strategy recently proposed by the author concerning intertwining operators. In particular we discuss the possibility of extending our previous results in such a way to construct (almost) isospectral…
Coupling separately developed codes offers an attractive method for increasing the accuracy and fidelity of the computational models. Examples include the earth sciences and fusion integrated modeling. This paper describes the Framework…
Approximately dual frames as a generalization of duality notion in Hilbert spaces have applications in Gabor systems, wavelets, coorbit theory and sensor modeling. In recent years, the computing of the associated deviations of the canonical…
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,…
We study several interesting examples of Biangular Tight Frames (BTFs) - basis-like sets of unit vectors admitting exactly two distinct frame angles (ie, pairwise absolute inner products) - and examine their relationships with Equiangular…
Large collections of high-dimensional data have become nearly ubiquitous across many academic fields and application domains, ranging from biology to the humanities. Since working directly with high-dimensional data poses challenges, the…
In this paper we investigate a new notion of bases in Hilbert spaces and similar to fusion frame theory we introduce fusion bases theory in Hilbert spaces. We also introduce a new definition of fusion dual sequence associated with a fusion…
Although large-scale visual foundation models (VFMs) achieve remarkable performance in semantic understanding, they still underperform in instance-aware dense prediction tasks. They exhibit different biases in representation: for instance,…
The human visual perception system has strong robustness in image fusion. This robustness is based on human visual perception system's characteristics of feature selection and non-linear fusion of different features. In order to simulate…
We study an intriguing question in frame theory we call "Weaving Frames" that is partially motivated by preprocessing of Gabor frames. Two frames $\{\varphi_i\}_{i\in I}$ and $\{\psi_i \}_{i\in I}$ for a Hilbert space ${\mathbb H}$ are…
Transformers are widely used for solving tasks in natural language processing, computer vision, speech, and music domains. In this paper, we talk about the efficiency of transformers in terms of memory (the number of parameters),…
Feature alignment serves as the primary mechanism for fusing multimodal data. We put forth a feature alignment approach that achieves full integration of multimodal information. This is accomplished via an alternating process of shifting…
As a result of several successful applications in computer vision and image processing, sparse representation (SR) has attracted significant attention in multi-sensor image fusion. Unlike the traditional multiscale transforms (MSTs) that…
Let $I\subseteq \Bbb N$ be a finite or infinite set and let ${(x_n)_{n\in I}}$ be a frame for a separable Hilbert space $\mathcal{H}$. Consider transmission of a signal $h\in\mathcal{H}$ where a finite subset $(\langle h,x_n\rangle)_{n\in…
Modern datasets across many disciplines increasingly consist of time-evolving, potentially infinite-dimensional random objects, such as dynamic functional data, which are naturally modeled in Hilbert spaces. In these settings,…
We introduce the notion of weaving continuous controlled K-g-fusion frame in Hilbert space. Some characterizations of weaving continuous controlled K-g-fusion frame have been presented. We extend some of the recent results of woven…
Glass is very common in the real world. Influenced by the uncertainty about the glass region and the varying complex scenes behind the glass, the existence of glass poses severe challenges to many computer vision tasks, making glass…