Related papers: A convergent Plug-and-Play Majorization-Minimizati…

Plug-and-Play (PnP) methods have become standard tools for solving imaging inverse problems by replacing the intractable maximum a posteriori (MAP) denoiser with the MMSE one. While this mismatch has been widely treated as unavoidable,…

We consider the minimum-norm-point (MNP) problem over polyhedra, a well-studied problem that encompasses linear programming. We present a general algorithmic framework that combines two fundamental approaches for this problem: active set…

We propose a new fast algorithm for solving one of the standard approaches to ill-posed linear inverse problems (IPLIP), where a (possibly non-smooth) regularizer is minimized under the constraint that the solution explains the observations…

Consider the problem of minimizing an expected logarithmic loss over either the probability simplex or the set of quantum density matrices. This problem includes tasks such as solving the Poisson inverse problem, computing the…

Much research has been devoted to the problem of restoring Poissonian images, namely for medical and astronomical applications. However, the restoration of these images using state-of-the-art regularizers (such as those based on multiscale…

Many material and biological samples in scientific imaging are characterized by non-local repeating structures. These are studied using scanning electron microscopy and electron tomography. Sparse sampling of individual pixels in a 2D image…

We propose a novel multi-layer neural network architecture that gives a promising neural network empowered optimization approach to the image restoration problem. The proposed architecture is motivated by the recent study of monotone…

This paper presents a quantum algorithm for solving the fractional Poisson equation \((-\Delta)^s u = f\) with \(s \in (0,1)\) on bounded domains. The proposed approach combines rational approximation techniques with quantum linear system…

Estimating a binary vector from noisy linear measurements is a prototypical problem for MIMO systems. A popular algorithm, called the box-relaxation decoder, estimates the target signal by solving a least squares problem with convex…

The Kullback-Leibler (KL) divergence is frequently used in data science. For discrete distributions on large state spaces, approximations of probability vectors may result in a few small negative entries, rendering the KL divergence…

This paper introduces a novel variational Bayesian method that integrates Tucker decomposition for efficient high-dimensional inverse problem solving. The method reduces computational complexity by transforming variational inference from a…

Deconvolution is a widely used strategy to mitigate the blurring and noisy degradation of hyperspectral images~(HSI) generated by the acquisition devices. This issue is usually addressed by solving an ill-posed inverse problem. While…

Alternating direction method of multiplier (ADMM) is a widely used algorithm for solving constrained optimization problems in image restoration. Among many useful features, one critical feature of the ADMM algorithm is its modular structure…

In this paper, a methodology is investigated for signal recovery in the presence of non-Gaussian noise. In contrast with regularized minimization approaches often adopted in the literature, in our algorithm the regularization parameter is…

Inverse optimization refers to the inference of unknown parameters of an optimization problem based on knowledge of its optimal solutions. This paper considers inverse optimization in the setting where measurements of the optimal solutions…

These lecture notes summarize various summer schools that I have given on the topic of solving inverse problems (state and parameter estimation) by combining optimally measurement observations and parametrized PDE models. After defining a…

Magnetic resonance imaging (MRI) plays an important role in modern medical diagnostic but suffers from prolonged scan time. Current deep learning methods for undersampled MRI reconstruction exhibit good performance in image de-aliasing…

In a particle beam microscope, a raster-scanned focused beam of particles interacts with a sample to generate a secondary electron (SE) signal pixel by pixel. Conventionally formed micrographs are noisy because of limitations on acquisition…

Existing physical model-based imaging methods for ultrasound elasticity reconstruction utilize fixed variational regularizers that may not be appropriate for the application of interest or may not capture complex spatial prior information…

In this paper we study algorithms to find a Gaussian approximation to a target measure defined on a Hilbert space of functions; the target measure itself is defined via its density with respect to a reference Gaussian measure. We employ the…