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Diffusion models have recently attained significant interest within the community owing to their strong performance as generative models. Furthermore, its application to inverse problems have demonstrated state-of-the-art performance.…
For electrical impedance tomography (EIT), most practical reconstruction methods are based on linearizing the underlying non-linear inverse problem. Recently, it has been shown that the linearized problem still contains the exact shape…
Error Correcting Output Codes (ECOC) is a successful technique in multi-class classification, which is a core problem in Pattern Recognition and Machine Learning. A major advantage of ECOC over other methods is that the multi- class problem…
Traditional model-free feature selection methods treat each feature independently while disregarding the interrelationships among features, which leads to relatively poor performance compared with the model-aware methods. To address this…
Diffusion models have emerged as powerful generative tools with applications in computer vision and scientific machine learning (SciML), where they have been used to solve large-scale probabilistic inverse problems. Traditionally, these…
This EM review article focuses on parameter expansion, a simple technique introduced in the PX-EM algorithm to make EM converge faster while maintaining its simplicity and stability. The primary objective concerns the connection between…
We study an inverse problem for the time-dependent Maxwell system in an inhomogeneous and anisotropic medium. The objective is to recover the initial electric field $\mathbf{E}_0$ in a bounded domain $\Omega \subset \mathbb{R}^3$, using…
We introduce a new formulation of structural causal models for extremes, called the extremal structural causal model (eSCM). Unlike conventional structural causal models, where randomness is governed by a probability distribution, eSCMs use…
The task of conditional generation is one of the most important applications of generative models, and numerous methods have been developed to date based on the celebrated flow-based models. However, many flow-based models in use today are…
We develop a novel iterative direct sampling method (IDSM) for solving linear or nonlinear elliptic inverse problems with partial Cauchy data. It integrates three innovations: a data completion scheme to reconstruct missing boundary…
High-fidelity Monte Carlo simulations and complex inverse problems, such as mapping smeared experimental observations to ground-truth states, are computationally intensive yet essential for robust data analysis. Conditional Flow Matching…
The inverse acoustic scattering problems using multi-frequency backscattering far field patterns at isolated directions are studied. The underlying object could be point like scatterers, small scatterers, extended inhomogeneities and…
This work is dedicated to a novel sampling method for accurately reconstructing elastic and electromagnetic sources from the far field patterns. We show that the proposed indicators in the form of integrals with full far field patterns are…
In the present study the software CrackComput, based on the Xfem and Xcrack libraries has been used for three problems- to experiment on the convergence properties of the method applied to elasto-statics crack problems, comparison of stress…
We study Bayesian inverse problems with mixed noise, modeled as a combination of additive and multiplicative Gaussian components. While traditional inference methods often assume fixed or known noise characteristics, real-world…
In a recent paper an Inexact Restoration method for solving continuous constrained optimization problems was analyzed from the point of view of worst-case functional complexity and convergence. On the other hand, the Inexact Restoration…
Consider a problem where a set of feasible observations are provided by an expert and a cost function is defined that characterizes which of the observations dominate the others and are hence, preferred. Our goal is to find a set of linear…
As one of the most commonly seen data challenges, missing data, in particular, multiple, non-monotone missing patterns, complicates estimation and inference due to the fact that missingness mechanisms are often not missing at random, and…
The Stochastic Approximation EM (SAEM) algorithm, a variant stochastic approximation of EM, is a versatile tool for inference in incomplete data models. In this paper, we review the fundamental EM algorithm and then focus especially on the…
This paper is concerned with uniqueness, phase retrieval and shape reconstruction methods for solving inverse electromagnetic source scattering problems with multi-frequency sparse phased or phaseless far field data. With the phased data,…