相关论文: A nonstandard higher-order variational model to sp…
High-precision numerical scheme for nonlinear hyperbolic evolution equations is proposed based on the spectral method. The detail discretization processes are discussed in case of one-dimensional Klein-Gordon equations. In conclusion, a…
We present topological derivative and energy based procedures for the imaging of micro and nanostructures using one beam of visible light of a single wavelength. Objects with diameters as small as 10 nm can be located, and their position…
We introduce a new non-smooth variational model for the restoration of manifold-valued data which includes second order differences in the regularization term. While such models were successfully applied for real-valued images, we introduce…
Two different Perfectly Matched Layer (PML) formulations with efficient pseudo-spectral numerical schemes are derived for the standard and non-relativistic nonlinear Klein-Gordon equations (NKGE). A pseudo-spectral explicit exponential…
This paper proposes a novel method which combines both median filter and simple standard deviation to accomplish an excellent edge detector for image processing. First of all, a denoising process must be applied on the grey scale image…
We propose a nonlocal operator method for solving partial differential equations (PDEs). The nonlocal operator is derived from the Taylor series expansion of the unknown field, and can be regarded as the integral form "equivalent" to the…
We develop a novel method for detection of signals and reconstruction of images in the presence of random noise. The method uses results from percolation theory. We specifically address the problem of detection of multiple objects of…
We present a new methodology for detecting out-of-distribution (OOD) images by utilizing norms of the score estimates at multiple noise scales. A score is defined to be the gradient of the log density with respect to the input data. Our…
In this article, we study the semi discrete and fully discrete formulations for a Kirchhoff type quasilinear integro-differential equation involving time-fractional derivative of order $\alpha \in (0,1) $. For the semi discrete formulation…
Image segmentation is an important median level vision topic. Accurate and efficient multiphase segmentation for images with intensity inhomogeneity is still a great challenge. We present a new two-stage multiphase segmentation method…
This paper proposes a method of estimating micro-motion of an object at each pixel that is too small to detect under a common setup of camera and illumination. The method introduces an active-lighting approach to make the motion visually…
In this paper we perform quantitative reconstruction of the electric susceptibility and the Gr\"uneisen parameter of a non-magnetic linear dielectric medium using measurement of a multi-modal photoacoustic and optical coherence tomography…
We discuss a general framework for recovering edges in piecewise smooth functions with finitely many jump discontinuities, where $[f](x):=f(x+)-f(x-) \neq 0$. Our approach is based on two main aspects--localization using appropriate…
Image segmentation and image restoration are two important topics in image processing with great achievements. In this paper, we propose a new multiphase segmentation model by combining image restoration and image segmentation models.…
In this paper, we present a deep learning-based numerical method for approximating high dimensional stochastic partial differential equations (SPDEs). At each time step, our method relies on a predictor-corrector procedure. More precisely,…
A novel high-order numerical scheme is proposed to compute the covariant derivative, particularly for divergence and curl, on any curved surface. The proposed scheme does not require the construction of a curved axis or metric tensor, which…
One of the major open problems in computer vision is detection of features in visually impaired images. In this paper, we describe a potential solution using Phase Stretch Transform, a new computational approach for image analysis, edge…
Elliptic partial differential equations arise in many fields of science and engineering such as steady state distribution of heat, fluid dynamics, structural/mechanical engineering, aerospace engineering and seismology etc. In three…
The detection of exoplanets in coronographic images is severely limited by residual starlight speckles. Dedicated post-processing can drastically reduce this "stellar leakage" and thereby increase the faintness of detectable exoplanets.…
$L^1$ based optimization is widely used in image denoising, machine learning and related applications. One of the main features of such approach is that it naturally provide a sparse structure in the numerical solutions. In this paper, we…