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The great advances of learning-based approaches in image processing and computer vision are largely based on deeply nested networks that compose linear transfer functions with suitable non-linearities. Interestingly, the most frequently…
Advances in data acquisition and numerical wave simulation have improved tomographic imaging techniques and results, but non-experts may find it difficult to understand which model is best for their needs. This paper is intended for these…
We demonstrate that the integration of the recently developed dynamic mode decomposition (DMD) with a multi-resolution analysis allows for a decomposition method capable of robustly separating complex systems into a hierarchy of…
In this work, we consider a certain multilayered (thick layer) wave--(thin layer) wave--heat (fluid) interactive PDE system. Such coupled PDE systems have been used in the literature to describe the blood transport process in mammalian…
This paper presents a survey of ocean simulation and rendering methods in computer graphics. To model and animate the ocean's surface, these methods mainly rely on two main approaches: on the one hand, those which approximate ocean dynamics…
Oceanic waves registered by satellite observations often have curvilinear fronts and propagate over various currents. In this paper, we study long linear and weakly-nonlinear ring waves in a stratified fluid in the presence of a…
Low-dimensional embeddings (LDEs) of high-dimensional data are ubiquitous in science and engineering. They allow us to quickly understand the main properties of the data, identify outliers and processing errors, and inform the next steps of…
Seismic data denoising is vital to geophysical applications and the transform-based function method is one of the most widely used techniques. However, it is challenging to design a suit- able sparse representation to express a…
We prove descent theorems for semiorthogonal decompositions using techniques from derived algebraic geometry. Our methods allow us to capture more general filtrations of derived categories and even marked filtrations, where one descends not…
We apply dynamic mode decomposition (DMD) and proper orthogonal decomposition (POD) methods to flows in highly-heterogeneous porous media to extract the dominant coherent structures and derive reduced-order models via Galerkin projection.…
Images of near-field SAR contains spatial-variant sidelobes and clutter, subduing the image quality. Current image restoration methods are only suitable for small observation angle, due to their assumption of 2D spatial-invariant…
For numerous earth observation applications, one may benefit from various satellite sensors to address the reconstruction of some process or information of interest. A variety of satellite sensors deliver observation data with different…
We present a versatile formulation of the convolution operation that we term a "mapped convolution." The standard convolution operation implicitly samples the pixel grid and computes a weighted sum. Our mapped convolution decouples these…
Nonlinear water waves interacting with quasi-one-dimensional, non-uniformly periodic bed profiles are studied numerically in the deep-water regime with the help of approximate equations for envelopes of the forward and backward waves.…
By considering the features of the airport runway image filtering, an improved bilateral filtering method was proposed which can remove noise with edge preserving. Firstly the steerable filtering decomposition is used to calculate the…
It has previously been hypothesized, and supported with some experimental evidence, that deeper representations, when well trained, tend to do a better job at disentangling the underlying factors of variation. We study the following related…
Developing deep learning techniques for geometric data is an active and fruitful research area. This paper tackles the problem of sphere-type surface learning by developing a novel surface-to-image representation. Using this representation…
Free-surface ghosts in marine seismic data are traditionally treated as artifacts that degrade bandwidth and temporal resolution and are mitigated through acquisition design or inverse filtering. This study proposes a processing-driven…
We study integral transforms mapping a function on the Euclidean space to the family of its integration on some hypersurfaces, that is, a function of hypersurfaces. The hypersurfaces are given by the graphs of functions with fixed axes of…
Seismic data processing involves techniques to deal with undesired effects that occur during acquisition and pre-processing. These effects mainly comprise coherent artefacts such as multiples, non-coherent signals such as electrical noise,…