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Image super-resolution (SR) is an underdetermined inverse problem, where a large number of plausible high-resolution images can explain the same downsampled image. Most current single image SR methods use empirical risk minimisation, often…

In ill-posed inverse problems, it is commonly desirable to obtain insight into the full spectrum of plausible solutions, rather than extracting only a single reconstruction. Information about the plausible solutions and their likelihoods is…

Accelerating magnetic resonance imaging (MRI) remains challenging, particularly under realistic acquisition noise. While diffusion models have recently shown promise for reconstructing undersampled MRI data, many approaches lack an explicit…

We study the inverse problem of estimating a field $u$ from data comprising a finite set of nonlinear functionals of $u$, subject to additive noise; we denote this observed data by $y$. Our interest is in the reconstruction of piecewise…

Practical applications of microwave imaging often require the solution of inverse scattering problems with inhomogeneous backgrounds. Towards this end, a novel inversion strategy, which combines the multi-scaling (MS) regularization scheme…

Success of machine learning (ML) in the modern world is largely determined by abundance of data. However at many industrial and scientific problems, amount of data is limited. Application of ML methods to data-scarce scientific problems can…

A demanding challenge in Bayesian inversion is to efficiently characterize the posterior distribution. This task is problematic especially in high-dimensional non-Gaussian problems, where the structure of the posterior can be very chaotic…

Maximum A Posteriori (MAP) estimation is a cornerstone framework for blind inverse problems, where an image and a forward operator are jointly estimated as the maximizers of a posterior distribution. In this paper, we analyze the recovery…

In many inverse problems, model parameters cannot be precisely determined from observational data. Bayesian inference provides a mechanism for capturing the resulting parameter uncertainty, but typically at a high computational cost. This…

We present the marginal unbiased score expansion (MUSE) method, an algorithm for generic high-dimensional hierarchical Bayesian inference. MUSE performs approximate marginalization over arbitrary non-Gaussian latent parameter spaces,…

Current state-of-the-art generative models map noise to data distributions by matching flows or scores. A key limitation of these models is their inability to readily integrate available partial observations and additional priors. In…

Using diffusion priors to solve inverse problems in imaging have significantly matured over the years. In this chapter, we review the various different approaches that were proposed over the years. We categorize the approaches into the more…

Bayesian analysis enables combining prior knowledge with measurement data to learn model parameters. Commonly, one resorts to computing the maximum a posteriori (MAP) estimate, when only a point estimate of the parameters is of interest. We…

The inverse design of metasurfaces faces inherent challenges due to the nonlinear and highly complex relationship between geometric configurations and their electromagnetic behavior. Traditional optimization approaches often suffer from…

In this paper we present new algorithms and analysis for the linear inverse sensor placement and scheduling problems over multiple time instances with power and communications constraints. The proposed algorithms, which deal directly with…

We propose and show the efficacy of a new method to address generic inverse problems. Inverse modeling is the task whereby one seeks to determine the control parameters of a natural system that produce a given set of observed measurements.…

Inverse problems occur in a variety of parameter identification tasks in engineering. Such problems are challenging in practice, as they require repeated evaluation of computationally expensive forward models. We introduce a unifying…

This paper presents an improved implicit sampling method for hierarchical Bayesian inverse problems. A widely used approach for sampling posterior distribution is based on Markov chain Monte Carlo (MCMC). However, the samples generated by…

Inverse design has emerged as a transformative approach for photonic device optimization, enabling the exploration of high-dimensional, non-intuitive design spaces to create ultra-compact devices and advance photonic integrated circuits…

With the exponential growth of multimedia data, leveraging multimodal sensors presents a promising approach for improving accuracy in human activity recognition. Nevertheless, accurately identifying these activities using both video data…