相关论文: Projection to the Set of Shift Orthogonal Function…
It is known that the weighted $L^2$ projection operator exhibits approximation properties different from those of the classical $L^2$ projection, in the sense that the $L^2$ error of the weighted $L^2$ projection of an $H^1$ function…
This paper gives an introduction to the theory of orthogonal projection of functions or signals. Several kinds of decomposition are explored: Fourier, Fourier-Legendre, Fourier-Bessel series for 1D signals, and Spherical Harmonic series for…
Adaptive sparse coding methods learn a possibly overcomplete set of basis functions, such that natural image patches can be reconstructed by linearly combining a small subset of these bases. The applicability of these methods to visual…
In this paper we explore orthogonal systems in $\mathrm{L}_2(\mathbb{R})$ which give rise to a skew-Hermitian, tridiagonal differentiation matrix. Surprisingly, allowing the differentiation matrix to be complex leads to a particular family…
An efficient algorithm to enumerate the vertices of a two-dimensional (2D) projection of a polytope, is presented in this paper. The proposed algorithm uses the support function of the polytope to be projected and enumerated for vertices.…
A powerful data transformation method named guided projections is proposed creating new possibilities to reveal the group structure of high-dimensional data in the presence of noise variables. Utilising projections onto a space spanned by a…
The increasing size of neural networks has led to a growing demand for methods of efficient fine-tuning. Recently, an orthogonal fine-tuning paradigm was introduced that uses orthogonal matrices for adapting the weights of a pretrained…
The algorithm for finding the optimal consistent approximation of an inconsistent pairwise comparisons matrix is based on a logarithmic transformation of a pairwise comparisons matrix into a vector space with the Euclidean metric.…
This work aims at the precise and efficient computation of the x-ray projection of an image represented by a linear combination of general shifted basis functions that typically overlap. We achieve this with a suitable adaptation of ray…
Dual quaternions have gained significant attention due to their wide applications in areas such as multi-agent formation control, 3D motion modeling, and robotics. A fundamental aspect in dual quaternion research involves the projection…
This paper is concerned with the adaptation to hardware of methods for Euclidean norm projections onto the parity polytope and probability simplex. We first refine recent efforts to develop efficient methods of projection onto the parity…
We derive upper bounds on the difference between the orthogonal projections of a smooth function $u$ onto two finite element spaces that are nearby, in the sense that the support of every shape function belonging to one but not both of the…
The ordered weighted $\ell_1$ (OWL) norm is a newly developed generalization of the Octogonal Shrinkage and Clustering Algorithm for Regression (OSCAR) norm. This norm has desirable statistical properties and can be used to perform…
Orthogonal polynomials with respect to a weight function defined on a wedge in the plane are studied. A basis of orthogonal polynomials is explicitly constructed for two large class of weight functions and the convergence of Fourier…
We introduce the notion of order projections using the order unit property of a positive element in an order unit space and characterize them in terms of (geometric) orthogonality. We describe order projections of the order unit space…
We study approximation properties of weighted $\mathrm{L}^2$-orthogonal projectors onto spaces of polynomials of bounded degree in the Euclidean unit ball, where the weight is of the reflection-invariant form $(1-\lVert x \rVert^2)^\alpha…
This paper describes a very efficient algorithm for image signal extrapolation. It can be used for various applications in image and video communication, e.g. the concealment of data corrupted by transmission errors or prediction in video…
The mean shift algorithm is a non-parametric and iterative technique that has been used for finding modes of an estimated probability density function. It has been successfully employed in many applications in specific areas of machine…
We provide a robust and general algorithm for computing distribution functions associated to induced orthogonal polynomial measures. We leverage several tools for orthogonal polynomials to provide a spectrally-accurate method for a broad…
We provide a simple and efficient algorithm for the projection operator for weighted $\ell_1$-norm regularization subject to a sum constraint, together with an elementary proof. The implementation of the proposed algorithm can be downloaded…