Related papers: A Convergent Overlapping Domain Decomposition Meth…
Compositional minimisation can be an effective technique to reduce the state space explosion problem. This technique considers a parallel composition of several processes. In its simplest form, each sequential process is replaced by an…
A rigorous mathematical framework is provided for a substructuring-based domain-decomposition approach for nonlocal problems that feature interactions between points separated by a finite distance. Here, by substructuring it is meant that a…
The fast Fourier transform (FFT) is undoubtedly an essential primitive that has been applied in various fields of science and engineering. In this paper, we present a decomposition method for parallelization of multi-dimensional FFTs with…
This paper presents four novel domain decomposition algorithms integrated with nonlinear mapping techniques to address collocation-based solutions of eigenvalue problems involving sharp interfaces or steep gradients. The proposed methods…
We address the problem of reconstructing a multi-band signal from its sub-Nyquist point-wise samples. To date, all reconstruction methods proposed for this class of signals assumed knowledge of the band locations. In this paper, we develop…
Hyperspectral imaging is an important tool having been applied in various fields, but still limited in observation of dynamic scenes. In this paper, we propose a snapshot hyperspectral imaging technique which exploits both spectral and…
The machine learning random Fourier feature method for data in high dimension is computationally and theoretically attractive since the optimization is based on a convex standard least squares problem and independent sampling of Fourier…
Efficiently utilizing discriminative features is crucial for convolutional neural networks to achieve remarkable performance in medical image segmentation and is also important for model generalization across multiple domains, where letting…
Total variation (TV) minimization is one of the most important techniques in modern signal/image processing, and has wide range of applications. While there are numerous recent works on the restoration guarantee of the TV minimization in…
We propose a simple domain decomposition method for $d$-dimensional elliptic PDEs which involves an overlapping decomposition into local subdomain problems and a global coarse problem. It relies on a space-filling curve to create equally…
Distributional shift between domains poses great challenges to modern machine learning algorithms. The domain generalization (DG) signifies a popular line targeting this issue, where these methods intend to uncover universal patterns across…
Segmentation of overlapping convex objects has various applications, for example, in nanoparticles and cell imaging. Often the segmentation method has to rely purely on edges between the background and foreground making the analyzed images…
Variational methods have become an important kind of methods in signal and image restoration - a typical inverse problem. One important minimization model consists of the squared $\ell_2$ data fidelity (corresponding to Gaussian noise) and…
A sequential piecewise linear programming method is presented where bounded domains of non-convex functions are successively contracted about the solution of a piecewise linear program at each iteration of the algorithm. Although…
This paper proposes a model order reduction method for a class of parametric dynamical systems. Using a temporal Fourier transform, we reformulate these systems into complex-valued elliptic equations in the frequency domain, containing…
In this paper we study the compressive sensing effects on 2D signals exhibiting sparsity in 2D DFT domain. A simple algorithm for reconstruction of randomly under-sampled data is proposed. It is based on the analytically determined…
Phase retrieval refers to a classical nonconvex problem of recovering a signal from its Fourier magnitude measurements. Inspired by the compressed sensing technique, signal sparsity is exploited in recent studies of phase retrieval to…
We propose a parallel algorithm for the numerical solution of a class of second order semi-linear equations coming from stochastic optimal control problems, by means of a dynamic domain decomposition technique. The new method is an…
The aim of this paper is to establish a nonlinear variational approach to the reconstruction of moving density images from indirect dynamic measurements. Our approach is to model the dynamics as a hyperelastic deformation of an initial…
Implicit neural representations (INRs) have emerged as a powerful tool for solving inverse problems in computer vision and computational imaging. INRs represent images as continuous domain functions realized by a neural network taking…