Related papers: Fusion Frames: Existence and Construction

Aiming at the problems that the convolutional neural networks neglect to capture the inherent attributes of natural images and extract features only in a single scale in the field of image super-resolution reconstruction, a network…

Integral transforms are invaluable mathematical tools to map functions into spaces where they are easier to characterize. We introduce the hyperdimensional transform as a new kind of integral transform. It converts square-integrable…

Fusion is a common tool for the analysis and utilization of available datasets and so an essential part of data mining and machine learning processes. However, a clear definition of the type of fusion is not always provided due to…

Improving and extending the concept of dual for frames, fusion frames and continuous frames, the notion of dual for continuous fusion frames in Hilbert spaces will be studied. It will be shown that generally the dual of c-fusion frames may…

A persistence module $M$, with coefficients in a field $\mathbb{F}$, is a finite-dimensional linear representation of an equioriented quiver of type $A_n$ or, equivalently, a graded module over the ring of polynomials $\mathbb{F}[x]$. It is…

Deep learning-based image fusion approaches have obtained wide attention in recent years, achieving promising performance in terms of visual perception. However, the fusion module in the current deep learning-based methods suffers from two…

Intermediate feature representations represent the backbone for the expressivity and adaptability of deep neural networks. However, their geometric structure remains poorly understood. In this submission, we provide indirect insights into…

Retaining spatial characteristics of panchromatic image and spectral information of multispectral bands is a critical issue in pansharpening. This paper proposes a pyramid based deep fusion framework that preserves spectral and spatial…

The paper presents a survey over frame multipliers and related concepts. In particular, it includes a short motivation of why multipliers are of interest to consider, a review as well as extension of recent results, devoted to the…

Fusion frames, and, more generally, operator-valued frame sequences are generalizations of classical frames, which are today a standard notion when redundant, yet stable sequences are required. However, the question of stability of duals…

Vision Foundation Models (VFMs) have become the cornerstone of modern computer vision, offering robust representations across a wide array of tasks. While recent advances allow these models to handle varying input sizes during training,…

This paper presents Neural Mesh Fusion (NMF), an efficient approach for joint optimization of polygon mesh from multi-view image observations and unsupervised 3D planar-surface parsing of the scene. In contrast to implicit neural…

Traditional nonnegative matrix factorization (NMF) learns a new feature representation on the whole data space, which means treating all features equally. However, a subspace is often sufficient for accurate representation in practical…

A frame is an overcomplete set that can represent vectors(signals) faithfully and stably. Two frames are equivalent if signals can be essentially represented in the same way, which means two frames differ by a permutation, sign change or…

Due to the lack of a definitive ground truth for the image fusion problem, the loss functions are structured based on evaluation metrics, such as the structural similarity index measure (SSIM). However, in doing so, a bias is introduced…

In this work, we introduce a new generalized integral transform involving many potentially known or new transforms as special cases. Basic properties of the new integral transform, that investigated in this work, include the existence…

Image fusion methods and metrics for their evaluation have conventionally used pixel-based or low-level features. However, for many applications, the aim of image fusion is to effectively combine the semantic content of the input images.…

In many applications, we desire neural networks to exhibit invariance or equivariance to certain groups due to symmetries inherent in the data. Recently, frame-averaging methods emerged to be a unified framework for attaining symmetries…

Feature Structures (FSs) are a widespread tool used for decompositional frameworks of Attribute-Value associations. Even though they thrive in simple systems, they lack a way of representing higher-order entities and relations. This is…

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…