Related papers: A Survey of Fusion Frames in Hilbert Spaces
The objective of this paper is to improve the customary definition of redundancy by providing quantitative measures in its place, which we coin upper and lower redundancies, that match better with an intuitive understanding of redundancy…
Multi-modality is widely used in medical imaging, because it can provide multiinformation about a target (tumor, organ or tissue). Segmentation using multimodality consists of fusing multi-information to improve the segmentation. Recently,…
Recent studies have indicated that foundation models, such as BERT and GPT, excel in adapting to a variety of downstream tasks. This adaptability has established them as the dominant force in building artificial intelligence (AI) systems.…
In this paper, we study the Hilbert$-$Schmidt frame (HS-frame) theory for separable Hilbert spaces. We first present some characterizations of HS-frames and prove that HS-frames share many important properties with frames. Then, we show how…
Lidars and cameras play essential roles in autonomous driving, offering complementary information for 3D detection. The state-of-the-art fusion methods integrate them at the feature level, but they mostly rely on the learned soft…
We develope a local theory for frames on finite dimensional Hilbert spaces. In particular, a bounded frame on a finite dimensional Hilbert space contains a subset which is a good Riesz basis for a percentage (arbitrarily close to one) of…
Infrared and visible images, as multi-modal image pairs, show significant differences in the expression of the same scene. The image fusion task is faced with two problems: one is to maintain the unique features between different…
We discuss the concepts of pseudo-dual frames and approximately dual frames, and illuminate their relationship to classical frames. Approximately dual frames are easier to construct than the classical dual frames, and might be tailored to…
Frame theory provides a robust method for recovering vectors in a Hilbert space from inner product data, though the associated decomposition formula can be computationally demanding. We relax the frame condition by studying sequences that…
We derive necessary conditions for localization of continuous frames in terms of generalized Beurling densities. As an important application we provide necessary density conditions for sampling and interpolation in a very large class of…
The state of the art in 3D object detection using sensor fusion heavily relies on calibration quality, which is difficult to maintain in large scale deployment outside a lab environment. We present the first calibration-free approach for 3D…
Let $K$ be a compact group, and let $\rho$ be a representation of $K$ on a Hilbert space $\mathcal{H}_\rho$. We classify invariant subspaces of $\mathcal{H}_\rho$ in terms of range functions, and investigate frames of the form $\{\rho(\xi)…
Two-dimensional patterns are used in many research areas in computer science, ranging from image processing to specification and verification of complex software systems (via scenarios). The contribution of this paper is twofold. First, we…
Interaction frames play an important role in describing and understanding experimental schemes in magnetic resonance. They are often used to eliminate dominating parts of the spin Hamiltonian, e.g., the Zeeman Hamiltonian in the usual…
In this paper we present the construction of an exact dual frame under specific structural assumptions posed on the dual frame. When given a frame $F$ for a finite dimensional Hilbert space, and a set of vectors $H$ that is assumed to be a…
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…
The construction of Parseval fusion frames is highly desirable in a wide range of signal processing applications. In this paper, we study the problem of modifying the weights of a fusion frame in order to generate a Parseval fusion frame.…
This paper proposes a Hilbert space embedding for Dirichlet Process mixture models via a stick-breaking construction of Sethuraman. Although Bayesian nonparametrics offers a powerful approach to construct a prior that avoids the need to…
The advent of Deep Neural Networks (DNNs) has driven remarkable progress in low-light image enhancement (LLIE), with diverse architectures (e.g., CNNs and Transformers) and color spaces (e.g., sRGB, HSV, HVI) yielding impressive results.…
Optical interferometric imaging enables astronomical observation at extremely high angular resolution. The necessary optical information for imaging, such as the optical path differences and visibilities, is easy to extract from fringes…