Related papers: Compactly Supported Quasi-tight Multiframelets wit…
This paper is concerned with the theory, construction and application of variable-stepsize implicit Peer two-step methods that are super-convergent for variable stepsizes, i.e., preserve their classical order achieved for uniform stepsizes…
Current state-of-the-art segmentation models encode entire images before focusing on specific objects. As a result, they waste computational resources - particularly when small objects are to be segmented in high-resolution scenes. We…
Numerical optimization is used to construct new orthonormal compactly supported wavelets with Sobolev regularity exponent as high as possible among those mother wavelets with a fixed support length and a fixed number of vanishing moments.…
X-ray computed tomography (CT) using sparse projection views is a recent approach to reduce the radiation dose. However, due to the insufficient projection views, an analytic reconstruction approach using the filtered back projection (FBP)…
Segmentation plays an important role in many preprocessing stages in image processing. Recently, convex relaxation methods for image multi-labeling were proposed in the literature. Often these models involve the total variation (TV)…
Dual pseudo splines constitute a new class of refinable functions with B-splines as special examples, which was introduced in \cite{DHSS}. In this paper, we shall construct Riesz wavelet associated with dual pseudo splines. Furthermore, we…
Unlike conventional mechanisms, compliant mechanisms produce the desired deformations by exploiting elastic strain and do not need, therefore, moving parts. The number of degrees of freedom of a conventional mechanism, also called mobility,…
An Equiangular tight frame (ETF) - also known as the Welch-bound-equality sequences - consists of a sequence of unit norm vectors whose absolute inner product is identical and minimal. Due to this unique property, these frames are preferred…
Optical coherence tomography (OCT) is an important interferometric diagnostic technique which provides cross-sectional views of the subsurface microstructure of biological tissues. However, the imaging quality of high-speed OCT is limited…
Multi-scale Vision Transformer (ViT) has emerged as a powerful backbone for computer vision tasks, while the self-attention computation in Transformer scales quadratically w.r.t. the input patch number. Thus, existing solutions commonly…
OMD and its variants give a flexible framework for OCO where the performance depends crucially on the choice of the mirror map. While the geometries underlying OPGD and OEG, both special cases of OMD, are well understood, it remains a…
The theory of (tight) wavelet frames has been extensively studied in the past twenty years and they are currently widely used for image restoration and other image processing and analysis problems. The success of wavelet frame based models,…
Spatially periodic elastic metamaterials, comprising hard inclusions within a soft matrix in $d$-dimensional space ($d\geq 2$), exhibit a rich spectrum of physical phenomena. This paper investigates such a model and presents the following…
To effectively capture singularities in high-dimensional data and functions, multivariate compactly supported tight framelets, having directionality and derived from refinable box splines, are of particular interest in both theory and…
Let $q\geq 2$ be an integer, and $\Bbb F_q^d$, $d\geq 1$, be the vector space over the cyclic space $\Bbb F_q$. The purpose of this paper is two-fold. First, we obtain sufficient conditions on $E \subset \Bbb F_q^d$ such that the inverse…
Vision Transformer (ViT) has prevailed in computer vision tasks due to its strong long-range dependency modelling ability. \textcolor{blue}{However, its large model size and weak local feature modeling ability hinder its application in real…
Constrained quasiconvex optimization problems appear in many fields, such as economics, engineering, and management science. In particular, fractional programming, which models ratio indicators such as the profit/cost ratio as fractional…
Achieving high-precision light manipulation is crucial for delivering information through complex media with high fidelity. However, existing spatial light modulation devices face a fundamental tradeoff between speed and accuracy. Digital…
We consider strongly-convex-strongly-concave saddle-point problems with general non-bilinear objective and different condition numbers with respect to the primal and the dual variables. First, we consider such problems with smooth composite…
Composite minimization is a powerful framework in large-scale convex optimization, based on decoupling of the objective function into terms with structurally different properties and allowing for more flexible algorithmic design. We…