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Characterising the noise of an airborne electromagnetic (AEM) system is critical in correctly imaging the earth's subsurface conductivity. Deterministic and probabilistic geophysical inversion algorithms require foreknowledge of the system…
Diffusion models have been widely studied as effective generative tools for solving inverse problems. The main ideas focus on performing the reverse sampling process conditioned on noisy measurements, using well-established numerical…
Metasurfaces are subwavelength-structured artificial media that can shape and localize electromagnetic waves in unique ways. The inverse design of these devices is a non-convex optimization problem in a high dimensional space, making global…
Extracting subsurface velocity information from seismic data is mainly an undetermined problem that requires injecting a priori information to constrain the inversion process. Machine learning has offered a platform to do so through the…
We describe a new data collection scheme for optical diffusion tomography in which plane wave illumination is combined with multiple projections in the slab imaging geometry. Multiple projection measurements are performed by rotating the…
Unsupervised source separation involves unraveling an unknown set of source signals recorded through a mixing operator, with limited prior knowledge about the sources, and only access to a dataset of signal mixtures. This problem is…
The CLEAN algorithm, widely used in radio interferometry for the deconvolution of radio images, performs well only if the raw radio image (dirty image) is, to good approximation, a simple convolution between the instrumental point-spread…
We provide a framework for solving inverse problems with diffusion models learned from linearly corrupted data. Firstly, we extend the Ambient Diffusion framework to enable training directly from measurements corrupted in the Fourier…
It is well known that the modulus of the far-field pattern (or phaseless far-field pattern) is invariant under translations of the scattering obstacle if only one plane wave is used as the incident field, so the shape but not the location…
In this paper we consider the problem of reconstructing an image that is downsampled in the space of its $SE(2)$ wavelet transform, which is motivated by classical models of simple cells receptive fields and feature preference maps in…
A conditional latent-diffusion based framework for solving the electromagnetic inverse scattering problem associated with microwave imaging is introduced. This generative machine-learning model explicitly mirrors the non-uniqueness of the…
In this paper, we study both the direct and inverse random source problems associated with the multi-term time-fractional diffusion-wave equation driven by a fractional Brownian motion. Regarding the direct problem, the well-posedness is…
We consider an inverse source problem for partially coherent light propagating in the Fresnel regime. The data is the coherence of the field measured away from the source. The reconstruction is based on a minimum residue formulation, which…
Diffusion models (DMs) have demonstrated remarkable ability to generate diverse and high-quality images by efficiently modeling complex data distributions. They have also been explored as powerful generative priors for signal recovery,…
Material reconstruction from a photograph is a key component of 3D content creation democratization. We propose to formulate this ill-posed problem as a controlled synthesis one, leveraging the recent progress in generative deep networks.…
Incorporating a deep generative model as the prior distribution in inverse problems has established substantial success in reconstructing images from corrupted observations. Notwithstanding, the existing optimization approaches use gradient…
We propose a data-driven approach for intrinsic image decomposition, which is the process of inferring the confounding factors of reflectance and shading in an image. We pose this as a two-stage learning problem. First, we train a model to…
In this paper, we address the problem of generative dataset distillation that utilizes generative models to synthesize images. The generator may produce any number of images under a preserved evaluation time. In this work, we leverage the…
Since most inverse problems arising in scientific and engineering applications are ill-posed, prior information about the solution space is incorporated, typically through regularization, to establish a well-posed problem with a unique…
This paper is concerned with the multi-frequency factorization method for imaging the support of a wave-number-dependent source function. It is supposed that the source function is given by the inverse Fourier transform of some…