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An analysis of high-dimensional data can offer a detailed description of a system but is often challenged by the curse of dimensionality. General dimensionality reduction techniques can alleviate such difficulty by extracting a few…
Diffusion models have recently emerged as powerful generative priors for solving inverse problems. However, training diffusion models in the pixel space are both data-intensive and computationally demanding, which restricts their…
We propose a multi-scale deep energy model that is strongly convex in the local neighbourhood around the data manifold to represent its probability density, with application in inverse problems. In particular, we represent the negative…
Deep Neural Networks (DNNs) demonstrate remarkable capabilities in learning complex hierarchical data representations, but the nature of these representations remains largely unknown. Existing global explainability methods, such as Network…
Magnetic Resonance Elastography (MRE) has become an essential tool in assessing the mechanical properties of soft tissues in-vivo, prompting significant progress in new inversion algorithms. This creates a need for a benchmarking framework…
We consider the problem of efficiently approximating and encoding high-dimensional data sampled from a probability distribution $\rho$ in $\mathbb{R}^D$, that is nearly supported on a $d$-dimensional set $\mathcal{M}$ - for example…
This paper deals with the solution of Maxwell's equations to model the electromagnetic fields in the case of a layered earth. The integrals involved in the solution are approximated by means of a novel approach based on the splitting of the…
Modern seismic and volcanic monitoring is increasingly shaped by continuous, multi-sensor observations and by the need to extract actionable information from nonstationary, noisy wavefields. In this context, machine learning has moved from…
High-dimensional big data appears in many research fields such as image recognition, biology and collaborative filtering. Often, the exploration of such data by classic algorithms is encountered with difficulties due to `curse of…
When modeling global satellite data to recover a planetary magnetic or gravitational potential field and evaluate it elsewhere, the method of choice remains their analysis in terms of spherical harmonics. When only regional data are…
Muography is an imaging tool based on the attenuation of cosmic muons to observe the density distribution of large objects, such as underground caves or fractured zones. Tomography based on muography measurements -- that is, three…
For many materials, macroscopic mechanical behavior is determined by an intricate microstructure. Understanding the relation between these two scales helps scientists and engineers design better materials. The relation which maps…
Among the biggest challenges we face in utilizing neural networks trained on waveform data (i.e., seismic, electromagnetic, or ultrasound) is its application to real data. The requirement for accurate labels forces us to develop solutions…
Multi-physical inversion plays a critical role in geophysics. It has been widely used to infer various physical properties~(such as velocity and conductivity). Among those inversion problems, some are explicitly governed by partial…
In the present paper we consider application of overcomplete dictionaries to solution of general ill-posed linear inverse problems. In the context of regression problems, there has been enormous amount of effort to recover an unknown…
We describe new results and algorithms for two different, but related, problems which deal with circulant matrices: learning shift-invariant components from training data and calculating the shift (or alignment) between two given signals.…
Geosystems are geological formations altered by humans activities such as fossil energy exploration, waste disposal, geologic carbon sequestration, and renewable energy generation. Geosystems also represent a critical link in the global…
Seismic velocity is one of the most important parameters used in seismic exploration. Accurate velocity models are key prerequisites for reverse-time migration and other high-resolution seismic imaging techniques. Such velocity information…
Geoelectrical techniques are widely used to monitor groundwater processes, while surprisingly few studies have considered audio (AMT) and radio (RMT) magnetotellurics for such purposes. In this numerical investigation, we analyze to what…
A dictionary is a database of standard vectors, so that other vectors / signals are expressed as linear combinations of dictionary vectors, and the task of learning a dictionary for a given data is to find a good dictionary so that the…