Related papers: Wasserstein-based Projections with Applications to…

The main contribution of this paper is to develop a hierarchical Bayesian formulation of PINNs for linear inverse problems, which is called BPINN-IP. The proposed methodology extends PINN to account for prior knowledge on the nature of the…

In plug-and-play (PnP) regularization, the proximal operator in algorithms such as ISTA and ADMM is replaced by a powerful denoiser. This formal substitution works surprisingly well in practice. In fact, PnP has been shown to give…

Image restoration, the recovery of clean images from degraded measurements, has applications in various domains like surveillance, defense, and medical imaging. Despite achieving state-of-the-art (SOTA) restoration performance, existing…

Deep-unrolling and plug-and-play (PnP) approaches have become the de-facto standard solvers for single-pixel imaging (SPI) inverse problem. PnP approaches, a class of iterative algorithms where regularization is implicitly performed by an…

Image restoration schemes based on the pre-trained deep models have received great attention due to their unique flexibility for solving various inverse problems. In particular, the Plug-and-Play (PnP) framework is a popular and powerful…

Noisy labels often occur in vision datasets, especially when they are obtained from crowdsourcing or Web scraping. We propose a new regularization method, which enables learning robust classifiers in presence of noisy data. To achieve this…

Watermarking becomes one of the pivotal solutions to trace and verify the origin of synthetic images generated by artificial intelligence models, but it is not free of risks. Recent studies demonstrate the capability to forge watermarks…

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 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…

Inverse problems and regularization theory is a central theme in contemporary signal processing, where the goal is to reconstruct an unknown signal from partial indirect, and possibly noisy, measurements of it. A now standard method for…

Recently, deep unfolding methods that guide the design of deep neural networks (DNNs) through iterative algorithms have received increasing attention in the field of inverse problems. Unlike general end-to-end DNNs, unfolding methods have…

Deep learning-based models have demonstrated remarkable success in solving illposed inverse problems; however, many fail to strictly adhere to the physical constraints imposed by the measurement process. In this work, we introduce a…

Existing approaches to depth or disparity estimation output a distribution over a set of pre-defined discrete values. This leads to inaccurate results when the true depth or disparity does not match any of these values. The fact that this…

Optimal transportation theory and the related $p$-Wasserstein distance ($W_p$, $p\geq 1$) are widely-applied in statistics and machine learning. In spite of their popularity, inference based on these tools has some issues. For instance, it…

The squared Wasserstein distance is a natural quantity to compare probability distributions in a non-parametric setting. This quantity is usually estimated with the plug-in estimator, defined via a discrete optimal transport problem which…

In this paper, we focus on computational aspects of the Wasserstein barycenter problem. We propose two algorithms to compute Wasserstein barycenters of $m$ discrete measures of size $n$ with accuracy $\e$. The first algorithm, based on…

In this paper, we propose two algorithms for solving linear inverse problems when the observations are corrupted by noise. A proper data fidelity term (log-likelihood) is introduced to reflect the statistics of the noise (e.g. Gaussian,…

Wasserstein \textbf{D}istributionally \textbf{R}obust \textbf{O}ptimization (DRO) is concerned with finding decisions that perform well on data that are drawn from the worst-case probability distribution within a Wasserstein ball centered…

This brief note aims to introduce the recent paradigm of distributional robustness in the field of shape and topology optimization. Acknowledging that the probability law of uncertain physical data is rarely known beyond a rough…

This paper addresses a class of (non-)convex optimization problems subject to general convex constraints, which pose significant challenges for traditional methods due to their inherent non-convexity and diversity. Conventional convex…