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Fractal analysis has been widely used in computer vision, especially in texture image processing and texture analysis. The key concept of fractal-based image model is the fractal dimension, which is invariant to bi-Lipschitz transformation…
The resolving ability of widefield fluorescence microscopy is fundamentally limited by out-of-focus background owing to its low axial resolution, particularly for densely labeled biological samples. Although total internal reflection…
Super-resolved far-field microscopy has emerged as a powerful tool for investigating the structure of objects with resolution well below the diffraction limit of light. Nearly all super-resolution imaging techniques reported to date rely on…
The radial basis function (RBF) and quasi Monte Carlo (QMC) methods are two very promising schemes to handle high-dimension problems with complex and moving boundary geometry due to the fact that they are independent of dimensionality and…
Vision Foundation Models (VFMs) have become the cornerstone of modern computer vision, offering robust representations across a wide array of tasks. While recent advances allow these models to handle varying input sizes during training,…
The development of scalable and wavenumber-robust iterative solvers for Helmholtz problems is challenging but also relevant for various application fields. In this work, two-level Schwarz domain decomposition preconditioners are enhanced by…
The performance of single image super-resolution depends heavily on how to generate and complement high-frequency details to low-resolution images. Recently, diffusion-based DDPM models exhibit great potential in generating high-quality…
Multi-focus image fusion (MFIF) and super-resolution (SR) are the inverse problem of imaging model, purposes of MFIF and SR are obtaining all-in-focus and high-resolution 2D mapping of targets. Though various MFIF and SR methods have been…
This paper presents an innovative set of tools to support a methodology for the multichannel interpolation (MCI) of a discrete signal. It is shown that a bandlimited signal $f$ can be exactly reconstructed from finite samples of $g_k$…
In this article, we construct the multivariate fractal interpolation functions for a given data points and explore the existence of $\alpha$-fractal function corresponding to the multivariate continuous function defined on $[0,1]\times…
This research focuses on the discovery and localization of hidden objects in the wild and serves unmanned systems. Through empirical analysis, infrared and visible image fusion (IVIF) enables hard-to-find objects apparent, whereas…
In the process of measuring objects with local self-similarity, such as satellite images or coastlines, we obtain a data set with both local self-similarity and uncertainty. To better interpolate such data sets, an interpolation function…
Multi-modal image fusion aims to integrate complementary information from multiple source images to produce high-quality fused images with enriched content. Although existing approaches based on state space model have achieved satisfied…
Fourier Transform Interferometry (FTI) is an appealing Hyperspectral (HS) imaging modality for many applications demanding high spectral resolution, e.g., in fluorescence microscopy. However, the effective resolution of FTI is limited by…
Improving the resolution of fluorescence microscopy beyond the diffraction limit can be achievedby acquiring and processing multiple images of the sample under different illumination conditions.One of the simplest techniques, Random…
We consider the problem of reconstructing one-dimensional point sources from their Fourier measurements in a bounded interval $[-\Omega, \Omega]$. This problem is known to be challenging in the regime where the spacing of the sources is…
Applications in materials and biological imaging are limited by the ability to collect high-resolution data over large areas in practical amounts of time. One solution to this problem is to collect low-resolution data and interpolate to…
Recovering high-resolution structural and compositional information from coherent X-ray measurements involves solving coupled, nonlinear, and ill-posed inverse problems. Ptychography reconstructs a complex transmission function from…
Multispectral and Hyperspectral Image Fusion (MHIF) is a practical task that aims to fuse a high-resolution multispectral image (HR-MSI) and a low-resolution hyperspectral image (LR-HSI) of the same scene to obtain a high-resolution…
We identify multiresolution subspaces giving rise via Hankel transforms to Bessel functions. They emerge as orthogonal systems derived from geometric Hilbert-space considerations, the same way the wavelet functions from a multiresolution…