Related papers: Laplace-Beltrami based Multi-Resolution Shape Reco…

We recover the Riemannian gradient of a given function defined on interior points of a Riemannian submanifold in the Euclidean space based on a sample of function evaluations at points in the submanifold. This approach is based on the…

Multimodal MRI offers complementary multi-scale information to characterize the brain structure. However, it remains challenging to effectively integrate multimodal MRI while achieving neuroscience interpretability. Here we propose to use…

Three-dimensional point clouds can be viewed as discrete samples of smooth manifolds, allowing spectral analysis using the Laplace-Beltrami operator (LBO). However, the traditional point cloud manifold harmonic transform (PMHT) is limited…

We develop a new optimisation technique that combines multiresolution subdivision surfaces for boundary description with immersed finite elements for the discretisation of the primal and adjoint problems of optimisation. Similar to wavelets…

A practical solution for the mathematical problem of functional calculus with Laplace-Beltrami operator on surfaces with axial symmetry is found. A quantitative analysis of the spectrum is presented.

We are interested in generating surfaces with arbitrary roughness and forming patterns on the surfaces. Two methods are applied to construct rough surfaces. In the first method, some superposition of wave functions with random frequencies…

Inverse design of metasurfaces for the joint optimization of optical modulation and algorithmic decoding in computational optics presents significant challenges, especially in applications such as hyperspectral imaging. We introduce a…

The direct parametrisation method for invariant manifold is a model-order reduction technique that can be applied to nonlinear systems described by PDEs and discretised e.g. with a finite element procedure in order to derive efficient…

To develop an efficient motion-compensated reconstruction technique for free-breathing cardiac magnetic resonance imaging (MRI) that allows high-quality images to be reconstructed from multiple undersampled single-shot acquisitions. The…

We consider a compact Riemannian manifold with boundary and a metric that is singular at the boundary. The associated Laplace-Beltrami operator is of the form of a Grushin operator plus a singular potential. In a supercritical parameter…

We introduce the notion of a family of convolution operators associated with a given elliptic partial differential operator. Such a convolution structure is shown to exist for a general class of Laplace-Beltrami operators on two-dimensional…

The optical resolution of a digital camera is one of its most crucial parameters with broad relevance for consumer electronics, surveillance systems, remote sensing, or medical imaging. However, resolution is physically limited by the…

Magnetic Resonance Imaging (MRI) is widely used in clinical practice, but suffered from prolonged acquisition time. Although deep learning methods have been proposed to accelerate acquisition and demonstrate promising performance, they rely…

This paper presents a mixed basis approach for Laplace eigenvalue problems, which treats the boundary as a perturbation of the free Laplace operator. The method separates the boundary from the volume via a generic function that can be…

Optical interferometers provide multiple wavelength measurements. In order to fully exploit the spectral and spatial resolution of these instruments, new algorithms for image reconstruction have to be developed. Early attempts to deal with…

Modern reconstruction methods for magnetic resonance imaging (MRI) exploit the spatially varying sensitivity profiles of receive-coil arrays as additional source of information. This allows to reduce the number of time-consuming…

This paper investigates model-order reduction methods for geometrically nonlinear structures. The parametrisation method of invariant manifolds is used and adapted to the case of mechanical systems expressed in the physical basis, so that…

Meshless methods are often used in numerical simulations of systems of partial differential equations (PDEs), particularly those which involve complex geometries or free surfaces. Here we present a novel compact scheme based on the local…

Metasurfaces -- ultrathin structures composed of subwavelength optical elements -- have revolutionized light manipulation by enabling precise control over electromagnetic waves' amplitude, phase, polarization, and spectral properties.…

Three-dimensional segmentation in magnetic resonance images (MRI), which reflects the true shape of the objects, is challenging since high-resolution isotropic MRIs are rare and typical MRIs are anisotropic, with the out-of-plane dimension…