We study some equivalency relations between Hilbert frames and closed subspaces of l2(I). We define also a distance between frames and we establish the geometric meaning of this metric. Finally we find the closest and respectively the nearest tight frame to a given frame.

X-ray computed tomography (CT) is widely used in medical applications, where many efforts have been made for decades to eliminate artifacts caused by incomplete projection. In this paper, we propose a new CT image reconstruction model based on nonlocal low-rank regularity and data-driven tight frame (NLR-DDTF). Unlike the Spatial-Radon domain regularization, proposed NLR-DDTF uses an asymmetric...

We consider the variational problem of cross-entropy loss with n feature vectors on a unit hypersphere in Rd. prove that when d≥n−1, global minimum is given by simplex equiangular tight frame, which justifies neural collapse behavior. also that, as n→∞ fixed d, minimizing points will distribute uniformly and show connection frame potential Benedetto & Fickus.

A homeomorphism of a compact metric space is tight provided every non-degenerate compact connected (not necessarily invariant) subset carries positive entropy. It is shown that every C diffeomorphism of a closed surface factors to a tight homeomorphism of a generalized cactoid (roughly, a surface with nodes) by a semi-conjugacy whose fibers carry zero entropy. Stony Brook IMS Preprint #2002/04 ...

Multi-modal image fusion can provide more information, which improves the quality for subsequent processing tasks. Because images acquired using photon counting devices always suffer from Poisson noise, this paper proposes a new three-step method based on fractional-order variational and data-driven tight frame to solve problem of multi-modal corrupted by noise. Thus, article obtains fused high...

Brain magnetic resonance images (MRIs) tissue segmentation is one of the most important parts of the clinical diagnostic tools. Pixel classification methods have been frequently used in the image segmentation with two supervised and unsupervised approaches up to now. Supervised segmentation methods lead to high accuracy, but they need a large amount of labeled data, which is hard, expensive, an...

We present a novel open-source Python framework called NanoNET (Nanoscale Non-equilibrium Electron Transport) for modeling electronic structure and transport. Our method is based on the tight-binding non-equilibrium Green’s function theory. The core functionality of providing facilities efficient construction Hamiltonian matrices from list atomic coordinates lookup table two-center integrals in...