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Inverse optimization (IO) is used to estimate unknown parameters of an optimization model from observed decisions. In the data-driven context, the estimated parameters are inherently uncertain, yet quantifying this uncertainty has received…
Bayesian hierarchical models have been demonstrated to provide efficient algorithms for finding sparse solutions to ill-posed inverse problems. The models comprise typically a conditionally Gaussian prior model for the unknown, augmented by…
We propose a Bayesian uncertainty quantification method for large-scale imaging inverse problems. Our method applies to all Bayesian models that are log-concave, where maximum-a-posteriori (MAP) estimation is a convex optimization problem.…
We consider the problem of exact recovery of a $k$-sparse binary vector from generalized linear measurements (such as logistic regression). We analyze the linear estimation algorithm (Plan, Vershynin, Yudovina, 2017), and also show…
The success of the compressed sensing paradigm has shown that a substantial reduction in sampling and storage complexity can be achieved in certain linear and non-adaptive estimation problems. It is therefore an advisable strategy for…
This paper addresses the problem of identifying a lower dimensional space where observed data can be sparsely represented. This under-complete dictionary learning task can be formulated as a blind separation problem of sparse sources…
There are two major routes to address the ubiquitous family of inverse problems appearing in signal and image processing, such as denoising or deblurring. A first route relies on Bayesian modeling, where prior probabilities are used to…
The L1-regularized Gaussian maximum likelihood estimator (MLE) has been shown to have strong statistical guarantees in recovering a sparse inverse covariance matrix, or alternatively the underlying graph structure of a Gaussian Markov…
We develop and apply an analytic method to predict peak counts in weak-lensing surveys. It is based on the theory of Gaussian random fields and suitable to quantify the level of spurious detections caused by chance projections of…
We consider the problem of estimating the parameters of a Gaussian or binary distribution in such a way that the resulting undirected graphical model is sparse. Our approach is to solve a maximum likelihood problem with an added l_1-norm…
We consider the inverse problem of recovering an unknown functional parameter $u$ in a separable Banach space, from a noisy observation $y$ of its image through a known possibly non-linear ill-posed map ${\mathcal G}$. The data $y$ is…
In this paper, we study weakly-supervised laparoscopic image segmentation with sparse annotations. We introduce a novel Bayesian deep learning approach designed to enhance both the accuracy and interpretability of the model's segmentation,…
Bayesian hierarchical models can provide efficient algorithms for finding sparse solutions to ill-posed inverse problems. The models typically comprise a conditionally Gaussian prior model for the unknown which is augmented by a generalized…
The available probes of the large scale structure in the Universe have distinct properties: galaxies are a high resolution but biased tracer of mass, while weak lensing avoids such biases but, due to low signal-to-noise ratio, has poor…
Compressed sensing deals with the reconstruction of sparse signals using a small number of linear measurements. One of the main challenges in compressed sensing is to find the support of a sparse signal. In the literature, several bounds on…
Crowd counting is a challenging yet critical task in computer vision with applications ranging from public safety to urban planning. Recent advances using Convolutional Neural Networks (CNNs) that estimate density maps have shown…
The problem of estimating a sparse signal from low dimensional noisy observations arises in many applications, including super resolution, signal deconvolution, and radar imaging. In this paper, we consider a sparse signal model with…
We consider the problem of recovering fusion frame sparse signals from incomplete measurements. These signals are composed of a small number of nonzero blocks taken from a family of subspaces. First, we show that, by using a-priori…
Computational imaging plays a pivotal role in determining hidden information from sparse measurements. A robust inverse solver is crucial to fully characterize the uncertainty induced by these measurements, as it allows for the estimation…
We develop a method for sparse image reconstruction from polychromatic computed tomography (CT) measurements under the blind scenario where the material of the inspected object and the incident-energy spectrum are unknown. We obtain a…