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A general framework for solving image inverse problems is introduced in this paper. The approach is based on Gaussian mixture models, estimated via a computationally efficient MAP-EM algorithm. A dual mathematical interpretation of the…

We consider the inverse scattering problem for sparse scatterers. An image reconstruction algorithm is proposed that is based on a nonlinear generalization of iterative hard thresholding. The convergence and error of the method was analyzed…

In many contexts Gaussian Mixtures (GM) are used to approximate probability distributions, possibly time-varying. In some applications the number of GM components exponentially increases over time, and reduction procedures are required to…

We consider the tuning parameter selection rules for nuclear norm regularized multivariate linear regression (NMLR) in high-dimensional setting. High-dimensional multivariate linear regression is widely used in statistics and machine…

Gaussian process regression (GPR) is a powerful machine learning method which has recently enjoyed wider use, in particular in physical sciences. In its original formulation, GPR uses a square matrix of covariances among training data and…

Tuning a complex simulation code refers to the process of improving the agreement of a code calculation with respect to a set of experimental data by adjusting parameters implemented in the code. This process belongs to the class of inverse…

Gaussian processes (GPs) are popular as nonlinear regression models for expensive computer simulations, yet GP performance relies heavily on estimation of unknown covariance parameters. Maximum likelihood estimation (MLE) is common, but it…

Gradient-descent based iterative algorithms pervade a variety of problems in estimation, prediction, learning, control, and optimization. Recently iterative algorithms based on higher-order information have been explored in an attempt to…

Image research has shown substantial attention in deblurring networks in recent years. Yet, their practical usage in real-world deblurring, especially motion blur, remains limited due to the lack of pixel-aligned training triplets…

Iterative procedures for parameter estimation based on stochastic gradient descent allow the estimation to scale to massive data sets. However, in both theory and practice, they suffer from numerical instability. Moreover, they are…

Iterative thresholding algorithms are well-suited for high-dimensional problems in sparse recovery and compressive sensing. The performance of this class of algorithms depends heavily on the tuning of certain threshold parameters. In…

In this paper we present a bilevel optimization scheme for the solution of a general image deblurring problem, in which a parametric variational-like approach is encapsulated within a machine learning scheme to provide a high quality…

Image deblurring remains a central research area within image processing, critical for its role in enhancing image quality and facilitating clearer visual representations across diverse applications. This paper tackles the optimization…

This paper presents a new variable selection approach integrated with Gaussian process (GP) regression. We consider a sparse projection of input variables and a general stationary covariance model that depends on the Euclidean distance…

In this paper, we consider an LQR design problem for distributed control systems. For large-scale distributed systems, finding a solution might be computationally demanding due to communications among agents. To this aim, we deal with LQR…

Reconstructing dynamic 3D scenes from monocular video has broad applications in AR/VR, robotics, and autonomous navigation, but often fails due to severe motion blur caused by camera and object motion. Existing methods commonly follow a…

Estimating the values of unknown parameters from corrupted measured data faces a lot of challenges in ill-posed problems. In such problems, many fundamental estimation methods fail to provide a meaningful stabilized solution. In this work,…

This paper proposes a novel approach to regularize the ill-posed blind image deconvolution (blind image deblurring) problem using deep generative networks. We employ two separate deep generative models - one trained to produce sharp images…

Diffusion models have demonstrated impressive results in both data generation and downstream tasks such as inverse problems, text-based editing, classification, and more. However, training such models usually requires large amounts of clean…

Fast matrix algorithms have become the fundamental tools of machine learning in big data era. The generalized matrix regression problem is widely used in the matrix approximation such as CUR decomposition, kernel matrix approximation, and…