Related papers: Compactly Supported Quasi-tight Multiframelets wit…
This paper introduces ItsOPT, an inexact two-level smoothing optimization framework designed to find first-order critical points of nonsmooth and nonconvex functions. The framework involves two levels of methodologies: at the upper level, a…
Although equirectangular projection (ERP) is a convenient form to store omnidirectional images (also known as 360-degree images), it is neither equal-area nor conformal, thus not friendly to subsequent visual communication. In the context…
$ \newcommand{\kalg}{{k_{\mathrm{alg}}}} \newcommand{\kopt}{{k_{\mathrm{opt}}}} \newcommand{\algset}{{T}} \renewcommand{\Re}{\mathbb{R}} \newcommand{\eps}{\varepsilon} \newcommand{\pth}[2][\!]{#1\left({#2}\right)} \newcommand{\npoints}{n}…
This paper presents a discussion on $p$-adic multiframe by means of its wavelet structure, called as multiframelet, which is build upon $p$-adic wavelet construction. Multiframelets create much excitement in mathematicians as well as…
Tight wavelet frames (TWFs) in \(L^2(\mathbb{R}^n)\) are versatile, and are practically useful due to their perfect reconstruction property. Nevertheless, existing TWF construction methods exhibit limitations, including a lack of specific…
We use hyperbolic wavelet regression for the fast reconstruction of high-dimensional functions having only low dimensional variable interactions. Compactly supported periodic Chui-Wang wavelets are used for the tensorized hyperbolic wavelet…
The construction of highly incoherent frames, sequences of vectors placed on the unit hyper sphere of a finite dimensional Hilbert space with low correlation between them, has proven very difficult. Algorithms proposed in the past have…
In this paper, we present a finite element method (FEM) framework enhanced by an operator-adapted wavelet decomposition algorithm designed for the efficient analysis of multiscale electromagnetic problems. Usual adaptive FEM approaches,…
Finite unit norm tight frames provide Parseval-like decompositions of vectors in terms of redundant components of equal weight. They are known to be exceptionally robust against additive noise and erasures, and as such, have great potential…
The Finite element method (FEM) has long served as the computational backbone for topology optimization (TO). However, for designing structures undergoing large deformations, conventional FEM-based TO often exhibits numerical instabilities…
Meshing complex engineering domains is a challenging task. Arbitrary polyhedral meshes can provide the much needed flexibility in automated discretization of such domains. The geometric property of the polyhedral meshes such as the…
Finite frames, or spanning sets for finite-dimensional Hilbert spaces, are a ubiquitous tool in signal processing. There has been much recent work on understanding the global structure of collections of finite frames with prescribed…
Sparsity constrained minimization captures a wide spectrum of applications in both machine learning and signal processing. This class of problems is difficult to solve since it is NP-hard and existing solutions are primarily based on…
A nearly optimal explicitly-sparse representation for oscillatory kernels is presented in this work by developing a curvelet based method. Multilevel curvelet-like functions are constructed as the transform of the original nodal basis. Then…
Typically, the sequence of points generated by an optimization algorithm may have multiple limit points. Under convexity assumptions, however, (sub)gradient methods are known to generate a convergent sequence of points. In this paper, we…
Many vision-related tasks benefit from reasoning over multiple modalities to leverage complementary views of data in an attempt to learn robust embedding spaces. Most deep learning-based methods rely on a late fusion technique whereby…
The paper presents a versatile library of quasi-analytic complex-valued wavelet packets (WPs) which originate from polynomial splines of arbitrary orders. The real parts of the quasi-analytic WPs are the regular spline-based orthonormal WPs…
A fruitful approach for solving signal deconvolution problems consists of resorting to a frame-based convex variational formulation. In this context, parallel proximal algorithms and related alternating direction methods of multipliers have…
A bi-level optimization framework (BiOPT) was proposed in [3] for convex composite optimization, which is a generalization of bi-level unconstrained minimization framework (BLUM) given in [20]. In this continuation paper, we introduce a…
Motivated by the challenge of nonstationarity in sequential decision making, we study Online Convex Optimization (OCO) under the coupling of two problem structures: the domain is unbounded, and the comparator sequence $u_1,\ldots,u_T$ is…