Related papers: Representations for multidimensional down-down dec…
Tsunamis are often generated by a moving sea bottom. This paper deals with the case where the tsunami source is an earthquake. The linearized water-wave equations are solved analytically for various sea bottom motions. Numerical results…
Wavelets are closely related to the Schr\"odinger's wave functions and the interpretation of Born. Similarly to the appearance of atomic orbital, it is proposed to combine anti-symmetric wavelets into orbital wavelets. The proposed approach…
Dynamic mode decomposition (DMD) has recently become a popular tool for the non-intrusive analysis of dynamical systems. Exploiting Proper Orthogonal Decomposition (POD) as a dimensionality reduction technique, DMD is able to approximate a…
Seeking the convex hull of an object is a very fundamental problem arising from various tasks. In this work, we propose two variational convex hull models using level set representation for 2-dimensional data. The first one is an exact…
We propose a novel approach for performing convolution of signals on curved surfaces and show its utility in a variety of geometric deep learning applications. Key to our construction is the notion of directional functions defined on the…
We predict that the interface of materials with defocusing thermal nonlinearities support stable fundamental and higher-order surface waves when the opposite edges of the medium are maintained at different temperatures. Such surface waves…
When representing a solid object there are alternatives to the use of traditional explicit (surface meshes) or implicit (zero crossing of implicit functions) methods. Skeletal representations encode shape information in a mixed fashion:…
The purpose of marine seismic experiments is to provide information of the structure and physical properties of the subsurface. The P-wave velocity distribution is the most commonly modelled property, usually by inversion of arrival times…
In order to meet the requirements of practical applications, a model of deforming manifold in the embedded space is proposed. The deforming vector and deforming field are presented to precisely describe the deforming process, which have…
We propose a convolutional neural network (CNN) denoising based method for seismic data interpolation. It provides a simple and efficient way to break though the lack problem of geophysical training labels that are often required by deep…
In this paper, we propose a novel lower dimensional representation of a shape sequence. The proposed dimension reduction is invertible and computationally more efficient in comparison to other related works. Theoretically, the differential…
The standard analytical approach for studying gravity free-surface waves generated by a moving body often relies upon a linearization of the physical geometry, where the body is considered asymptotically small in one or several of its…
Graph convolutions have gained popularity due to their ability to efficiently operate on data with an irregular geometric structure. However, graph convolutions cause over-smoothing, which refers to representations becoming more similar…
We propose Multiscale Flow, a generative Normalizing Flow that creates samples and models the field-level likelihood of two-dimensional cosmological data such as weak lensing. Multiscale Flow uses hierarchical decomposition of cosmological…
The dynamics of many-body systems can often be captured in terms of only a few relevant variables. Mathematical and numerical approaches exist to identify these variables by exploiting a separation of time scales between slow relevant and…
Several imaging algorithms including patch-based image denoising, image time series recovery, and convolutional neural networks can be thought of as methods that exploit the manifold structure of signals. While the empirical performance of…
We present in this paper new multiscale transforms on the sphere, namely the isotropic undecimated wavelet transform, the pyramidal wavelet transform, the ridgelet transform and the curvelet transform. All of these transforms can be…
In an underwater scene, wavelength-dependent light absorption and scattering degrade the visibility of images, causing low contrast and distorted color casts. To address this problem, we propose a convolutional neural network based image…
We present a progressive image decomposition method based on a novel non-linear filter named Sub-window Variance filter. Our method is specifically designed for image detail enhancement purpose; this application requires extraction of image…
Diffusion model-based approaches recently achieved re-markable success in MRI reconstruction, but integration into clinical routine remains challenging due to its time-consuming convergence. This phenomenon is partic-ularly notable when…