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In this work, we develop a Bayesian framework for solving inverse problems in which the unknown parameter belongs to a space of Radon measures taking values in a separable Hilbert space. The inherent ill-posedness of such problems is…

This short note modifies a reconstruction method by the author (Comm. PDE, 45(9):1118-1133, 2020), for reconstructing piecewise constant conductivities in the Calder\'on problem (electrical impedance tomography). In the former paper, a…

Physics-Informed Neural Networks (PINN) are a machine learning tool that can be used to solve direct and inverse problems related to models described by Partial Differential Equations. This paper proposes an adaptive inverse PINN applied to…

Many inverse problems have to deal with complex, evolving and often not exactly known geometries, e.g. as domains of forward problems modeled by partial differential equations. This makes it desirable to use methods which are robust with…

Inverse problems have many applications in science and engineering. In Computer vision, several image restoration tasks such as inpainting, deblurring, and super-resolution can be formally modeled as inverse problems. Recently, methods have…

We consider solving ill-posed imaging inverse problems without access to an image prior or ground-truth examples. An overarching challenge in these inverse problems is that an infinite number of images, including many that are implausible,…

Physics-driven deep learning methods have emerged as a powerful tool for computational magnetic resonance imaging (MRI) problems, pushing reconstruction performance to new limits. This article provides an overview of the recent developments…

Vision foundation models in remote sensing have been extensively studied due to their superior generalization on various downstream tasks. Synthetic Aperture Radar (SAR) offers all-day, all-weather imaging capabilities, providing…

Subsurface seismic velocity structure is essential for earthquake source studies, including hypocenter determination. Conventional hypocenter determination methods ignore the inherent uncertainty in seismic velocity structure models, and…

Integrated sensing and communication holds great promise for low-altitude economy applications. However, conventional downtilted base stations primarily provide sectorized forward lobes for ground services, failing to sense air targets due…

We introduce a new framework of numerical multiscale methods for advection-dominated problems motivated by climate sciences. Current numerical multiscale methods (MsFEM) work well on stationary elliptic problems but have difficulties when…

This paper presents a new family of localized orthonormal bases - sinlets - which are well suited for both signal and image processing and analysis. One-dimensional sinlets are related to specific solutions of the time-dependent harmonic…

Deep learning-based models have demonstrated remarkable success in solving illposed inverse problems; however, many fail to strictly adhere to the physical constraints imposed by the measurement process. In this work, we introduce a…

Parallel imaging is a commonly used technique to accelerate magnetic resonance imaging (MRI) data acquisition. Mathematically, parallel MRI reconstruction can be formulated as an inverse problem relating the sparsely sampled k-space…

We propose a neural inverse rendering pipeline called IRON that operates on photometric images and outputs high-quality 3D content in the format of triangle meshes and material textures readily deployable in existing graphics pipelines. Our…

Obtaining meaningful solutions for inverse problems has been a major challenge with many applications in science and engineering. Recent machine learning techniques based on proximal and diffusion-based methods have shown promising results.…

This is the report for the PRIM project in Telecom Paris. This report is about applications based on spatial-frequency transform and deep learning techniques. In this report, there are two main works. The first work is about the enhanced…

Resolving the diffusion coefficient is a key element in many biological and engineering systems, including pharmacological drug transport and fluid mechanics analyses. Additionally, these systems often have spatial variation in the…

Magnetic induction (MI) communication is an effective underground emergency communication technique after disasters such as landslides, mine collapses, and earthquakes, due to its advantages in mediums such as soil, concrete, and metals.…

This comprehensive review examines electrical and seismic refraction methods, emphasizing their advanced applications in electrical resistivity tomography (ERT) and seismic refraction tomography (SRT). These techniques are crucial for…