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Convolutional Neural Network (CNN) is one of the most important architectures in deep learning. The fundamental building block of a CNN is a trainable filter, represented as a discrete grid, used to perform convolution on discrete input…

This paper introduces a meta-learning approach for parameterized pseudo-differential operators with deep neural networks. With the help of the nonstandard wavelet form, the pseudo-differential operators can be approximated in a compressed…

In end-to-end optimized learned image compression, it is standard practice to use a convolutional variational autoencoder with generalized divisive normalization (GDN) to transform images into a latent space. Recently, Operational Neural…

As deep neural networks are increasingly used in applications suited for low-power devices, a fundamental dilemma becomes apparent: the trend is to grow models to absorb increasing data that gives rise to memory intensive; however low-power…

When working with three-dimensional data, choice of representation is key. We explore voxel-based models, and present evidence for the viability of voxellated representations in applications including shape modeling and object…

In the study of condensed matter physics, spectral information plays an important role for understand the mechanism of materials. However, it is difficult to obtain the spectrum directly through experiments or simulation. For example, the…

We introduce a generative smoothness regularization on manifolds (SToRM) model for the recovery of dynamic image data from highly undersampled measurements. The model assumes that the images in the dataset are non-linear mappings of…

Motivated by the important archaeological application of exploring cultural heritage objects, in this paper we study the challenging problem of automatically segmenting curve structures that are very weakly stamped or carved on an object…

Physics-based models often involve large systems of parametrized partial differential equations, where design parameters control various properties. However, high-fidelity simulations of such systems on large domains or with high grid…

3D shape analysis is an important research topic in computer vision and graphics. While existing methods have generalized image-based deep learning to meshes using graph-based convolutions, the lack of an effective pooling operation…

Recently, there has been great success in applying deep neural networks on graph structured data. Most work, however, focuses on either node- or graph-level supervised learning, such as node, link or graph classification or node-level…

Deep neural networks have recently achieved state of the art performance thanks to new training algorithms for rapid parameter estimation and new regularization methods to reduce overfitting. However, in practice the network architecture…

Focused ultrasound (FUS) therapy is a promising tool for optimally targeted treatment of spinal cord injuries (SCI), offering submillimeter precision to enhance blood flow at injury sites while minimizing impact on surrounding tissues.…

There have been attempts to insert mathematical morphology (MM) operators into convolutional neural networks (CNN), and the most successful endeavor to date has been the morphological neural networks (MNN). Although MNN have performed…

We present a numerical framework for deep neural network (DNN) modeling of unknown time-dependent partial differential equations (PDE) using their trajectory data. Unlike the recent work of [Wu and Xiu, J. Comput. Phys. 2020], where the…

This work introduces the Topological CNN (TCNN), which encompasses several topologically defined convolutional methods. Manifolds with important relationships to the natural image space are used to parameterize image filters which are used…

Deconvolution of large survey images with millions of galaxies requires to develop a new generation of methods which can take into account a space variant Point Spread Function (PSF) and have to be at the same time accurate and fast. We…

Although deep convolutional neural network has been proved to efficiently eliminate coding artifacts caused by the coarse quantization of traditional codec, it's difficult to train any neural network in front of the encoder for gradient's…

Learning neural operators on heterogeneous and irregular geometries remains a fundamental challenge, as existing approaches typically rely on structured discretisations or explicit mappings to a shared reference domain. We propose a unified…

Cellular electron cryo-tomography enables the 3D visualization of cellular organization in the near-native state and at submolecular resolution. However, the contents of cellular tomograms are often complex, making it difficult to…