Related papers: Learning the geometry of wave-based imaging

This paper presents a neural network approach for solving two-dimensional optical tomography (OT) problems based on the radiative transfer equation. The mathematical problem of OT is to recover the optical properties of an object based on…

Transformers have emerged as the state of the art neural network architecture for natural language processing and computer vision. In the foundation model paradigm, large transformer models (BERT, GPT3/4, Bloom, ViT) are pre-trained on…

Deep learning technique has dramatically boosted the performance of face alignment algorithms. However, due to large variability and lack of samples, the alignment problem in unconstrained situations, \emph{e.g}\onedot large head poses,…

Full Waveform Inversion (FWI) is a highly nonlinear and ill-posed problem that aims to recover subsurface velocity maps from surface-recorded seismic waveforms data. Existing data-driven FWI typically uses small models, as available…

This paper provides a theoretical foundation for some common formulations of inverse problems in wave propagation, based on hyperbolic systems of linear integro-differential equations with bounded and measurable coefficients. The…

In this paper, we propose the $\textit{geometric invariance hypothesis (GIH)}$, which argues that the input space curvature of a neural network remains invariant under transformation in certain architecture-dependent directions during…

Diffeomorphic deformable image registration is one of the crucial tasks in medical image analysis, which aims to find a unique transformation while preserving the topology and invertibility of the transformation. Deep convolutional neural…

Deep neural networks have been applied successfully to a wide variety of inverse problems arising in computational imaging. These networks are typically trained using a forward model that describes the measurement process to be inverted,…

A physics assisted deep learning framework to perform accurate indoor imaging using phaseless Wi-Fi measurements is proposed. It is able to image objects that are large (compared to wavelength) and have high permittivity values, that…

Non-invasive subsurface imaging using full waveform inversion (FWI) has the potential to fundamentally change engineering site characterization by enabling the recovery of high resolution 2D/3D maps of subsurface stiffness. Yet, the…

Ultrafast optics is driven by a myriad of complex nonlinear dynamics. The ubiquitous presence of governing equations in the form of partial integro-differential equations (PIDE) necessitates the need for advanced computational tools to…

Image registration is an ill-posed inverse problem which often requires regularisation on the solution space. In contrast to most of the current approaches which impose explicit regularisation terms such as smoothness, in this paper we…

In this article we propose feature graph architectures (FGA), which are deep learning systems employing a structured initialisation and training method based on a feature graph which facilitates improved generalisation performance compared…

Full waveform inversion (FWI) is an advanced seismic inversion technique for quantitatively estimating subsurface properties. However, with FWI, it is hard to converge to a geologically-realistic subsurface model. Thus, we propose a…

Wave equations are fundamental to describing a vast array of physical phenomena, yet their simulation in inhomogeneous media poses a computational challenge due to the highly oscillatory nature of the solutions. To overcome the high costs…

Neural networks are seeing rapid adoption in purely inertial odometry, where accelerometer and gyroscope measurements from commodity inertial measurement units (IMU) are used to regress displacements and associated uncertainties. They can…

The goal of diffusion-weighted magnetic resonance imaging (DWI) is to infer the structural connectivity of an individual subject's brain in vivo. To statistically study the variability and differences between normal and abnormal brain…

We propose FiberNet, a method to estimate \emph{in-vivo} the cardiac fiber architecture of the human atria from multiple catheter recordings of the electrical activation. Cardiac fibers play a central role in the electro-mechanical function…

Although statistical learning theory provides a robust framework to understand supervised learning, many theoretical aspects of deep learning remain unclear, in particular how different architectures may lead to inductive bias when trained…

An accurate velocity model is essential to make a good seismic image. Conventional methods to perform Velocity Model Building (VMB) tasks rely on inverse methods, which, despite being widely used, are ill-posed problems that require intense…