Related papers: Excess of Fusion Frames: A Comprehensive Approach
We provide formulas and algorithms for computing the excess numbers of certain ideals. The solution for monomial ideals is given by the mixed volumes of certain polytopes. These results enable us to design specific homotopies for numerical…
Fusion frames consist of a sequence of subspaces from a Hilbert space and corresponding positive weights so that the sum of weighted orthogonal projections onto these subspaces is an invertible operator on the space. Given a spectrum for a…
One can improve predictability in the unknown domain by combining forecasts of imperfect complex computational models using a Bayesian statistical machine learning framework. In many cases, however, the models used in the mixing process are…
Overranging or overscanning increases the dose delivered to patients undergoing helical Computed Tomography examinations. In order to reduce it, nowadays most of the multidetector tomographs close the X-ray beam aperture at the scan…
Frame permutation quantization (FPQ) is a new vector quantization technique using finite frames. In FPQ, a vector is encoded using a permutation source code to quantize its frame expansion. This means that the encoding is a partial ordering…
We extended the existing methodology in Bound-to-Bound Data Collaboration (B2BDC), an optimization-based deterministic uncertainty quantification (UQ) framework, to explicitly take into account model discrepancy. The discrepancy was…
Deep model fusion/merging is an emerging technique that merges the parameters or predictions of multiple deep learning models into a single one. It combines the abilities of different models to make up for the biases and errors of a single…
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…
Functions of one or more variables are usually approximated with a basis: a complete, linearly-independent system of functions that spans a suitable function space. The topic of this paper is the numerical approximation of functions using…
We derive various interesting properties of complex equiangular cyclic frames for many pairs (n, k) using Gauss sums and number theory. We further use these results to study the random and burst errors of some special cases of complex…
In this article, we present a constructive method for computing the frame coefficients of finite wavelet frames over prime fields using tools from computational harmonic analysis and group theory.
A widely used tool in the study of risk, insurance and extreme values is the mean excess plot. One use is for validating a generalized Pareto model for the excess distribution. This paper investigates some theoretical and practical aspects…
We present novel, exotic types of frame changes for the calculation of quantum evolution operators. We detail in particular the biframe, in which a physical system's evolution is seen in an equal mixture of two different standard frames at…
This paper proposes a novel luminance adjustment method based on automatic exposure compensation for multi-exposure image fusion. Multi-exposure image fusion is a method to produce images without saturation regions, by using photos with…
The aim of this paper is to give not only an explicit upper bound of the total Q-curvature but also an induced isoperimetric deficit formula for the complete conformal metrics on $\mathbb R^n$, $n\ge 3$ with scalar curvature being…
Exposure correction is one of the fundamental tasks in image processing and computational photography. While various methods have been proposed, they either fail to produce visually pleasing results, or only work well for limited types of…
An adjustable algorithm of exclusion of conditional equations with excessive residuals is proposed. The criteria applied in the algorithm use variable exclusion limits which decrease as the number of equations goes down. The algorithm is…
A finite-dimensional Hilbert space is usually described in terms of an orthonormal basis, but in certain approaches or applications a description in terms of a finite overcomplete system of vectors, called a finite tight frame, may offer…
We use recent duality results of Eisenbud--Ulrich to give tools to study quadratically enriched residual intersections when there is no excess bundle. We use this to prove a formula for the Witt-valued Euler number of an almost complete…
Multi-Focus Image Fusion seeks to improve the quality of an acquired burst of images with different focus planes. For solving the task, an activity level measurement and a fusion rule are typically established to select and fuse the most…