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Matrix recovery from sparse observations is an extensively studied topic emerging in various applications, such as recommendation system and signal processing, which includes the matrix completion and compressed sensing models as special…

This paper considers a noisy data structure recovery problem. The goal is to investigate the following question: Given a noisy observation of a permuted data set, according to which permutation was the original data sorted? The focus is on…

Geophysical inverse problems are often ill-posed and admit multiple solutions. Conventional discriminative methods typically yield a single deterministic solution, which fails to model the posterior distribution, cannot generate diverse…

We study, using simulated experiments inspired by thin film magnetic domain patterns, the feasibility of phase retrieval in X-ray diffractive imaging in the presence of intrinsic charge scattering given only photon-shot-noise limited…

For numerous earth observation applications, one may benefit from various satellite sensors to address the reconstruction of some process or information of interest. A variety of satellite sensors deliver observation data with different…

In urban areas, dense buildings frequently block and reflect global positioning system (GPS) signals, resulting in the reception of a few visible satellites with many multipath signals. This is a significant problem that results in…

Diffusion models provide powerful generative priors for solving inverse problems by sampling from a posterior distribution conditioned on corrupted measurements. Existing methods primarily follow two paradigms: direct methods, which…

This paper considers the problem of recovering a structured signal from a relatively small number of noisy measurements with the aid of a similar signal which is known beforehand. We propose a new approach to integrate prior information…

We explore a scheme that enables the training of a deep neural network in a Federated Learning configuration over an additive white Gaussian noise channel. The goal is to create a low complexity, linear compression strategy, called…

Quantifying the amount of polarization is crucial for understanding and studying political polarization in political and social systems. Several methods are used commonly to measure polarization in social networks by purely inspecting their…

In this chapter we provide a theoretically founded investigation of state-of-the-art learning approaches for inverse problems from the point of view of spectral reconstruction operators. We give an extended definition of regularization…

It is well known that there exists a four dimensional complex vector associated with a nondepolarizing Mueller matrix. In this note it is shown that this complex vector, which is isomorphic to the Jones matrix, can be obtained from the…

A supervised learning approach is proposed for regularization of large inverse problems where the main operator is built from noisy data. This is germane to superresolution imaging via the sampling indicators of the inverse scattering…

In this work, we investigate the use of normalizing flows to model conditional distributions. In particular, we use our proposed method to analyze inverse problems with invertible neural networks by maximizing the posterior likelihood. Our…

In the geophysical field, seismic noise attenuation has been considered as a critical and long-standing problem, especially for the pre-stack data processing. Here, we propose a model to leverage the deep-learning model for this task.…

We examine the optical properties of a system of nano and micro particles of varying size, shape, and material (including metals and dielectrics, and sub-wavelength and super-wavelength regimes). Training data is generated by numerically…

Score-based diffusion models learn to reverse a stochastic differential equation that maps data to noise. However, for complex tasks, numerical error can compound and result in highly unnatural samples. Previous work mitigates this drift…

Accurate interpolation of seismic data is crucial for improving the quality of imaging and interpretation. In recent years, deep learning models such as U-Net and generative adversarial networks have been widely applied to seismic data…

Accurate noise modelling is important for training of deep learning reconstruction algorithms. While noise models are well known for traditional imaging techniques, the noise distribution of a novel sensor may be difficult to determine a…

Compressive sensing is a method to recover the original image from undersampled measurements. In order to overcome the ill-posedness of this inverse problem, image priors are used such as sparsity in the wavelet domain, minimum…