Related papers: Sparse modeling approach to analytical continuatio…

In the context of the compressed sensing problem, we propose a new ensemble of sparse random matrices which allow one (i) to acquire and compress a {\rho}0-sparse signal of length N in a time linear in N and (ii) to perfectly recover the…

Sparse linear inverse problems appear in a variety of settings, but often the noise contaminating observations cannot accurately be described as bounded by or arising from a Gaussian distribution. Poisson observations in particular are a…

The Extended Randomized Kaczmarz method is a well known iterative scheme which can find the Moore-Penrose inverse solution of a possibly inconsistent linear system and requires only one additional column of the system matrix in each…

So-called sparse estimators arise in the context of model fitting, when one a priori assumes that only a few (unknown) model parameters deviate from zero. Sparsity constraints can be useful when the estimation problem is under-determined,…

We develop diffusion-based samplers for target distributions known up to a normalising constant. To this end, we rely on the well-known diffusion path that smoothly interpolates between a simple base distribution and the target, popularised…

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,…

We propose and implement an approach to inference in linear instrumental variables models which is simultaneously robust and computationally tractable. Inference is based on self-normalization of sample moment conditions, and allows for…

We derive new explicit expressions for the components of Moore-Penrose inverses of symmetric difference matrices. These generalized inverses are applied in a new regularization approach for scattered data interpolation based on partial…

In this work, we investigate data fitting problems with random noises. A randomized progressive iterative regularization method is proposed. It works well for large-scale matrix computations and converges in expectation to the least-squares…

In electrocardiography, the "classic" inverse problem is the reconstruction of electric potentials at a surface enclosing the heart from remote recordings at the body surface and an accurate description of the anatomy. The latter being…

We study the maximum entropy (MaxEnt) approach for analytical continuation of spectral data from imaginary times to real frequencies. The total error is divided in a statistical error, due to the noise in the input data, and a systematic…

Independently estimating pixel values in Monte Carlo rendering results in a perceptually sub-optimal white-noise distribution of error in image space. Recent works have shown that perceptual fidelity can be improved significantly by…

This paper develops a new empirical Bayesian inference algorithm for solving a linear inverse problem given multiple measurement vectors (MMV) of under-sampled and noisy observable data. Specifically, by exploiting the joint sparsity across…

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…

We investigate implicit regularization schemes for gradient descent methods applied to unpenalized least squares regression to solve the problem of reconstructing a sparse signal from an underdetermined system of linear measurements under…

The identification of parameters in mathematical models using noisy observations is a common task in uncertainty quantification. We employ the framework of Bayesian inversion: we combine monitoring and observational data with prior…

Low-rank pseudoinverses are widely used to approximate matrix inverses in scalable machine learning, optimization, and scientific computing. However, real-world matrices are often observed with noise, arising from sampling, sketching, and…

We consider the inverse problem of recovering a continuous-domain function from a finite number of noisy linear measurements. The unknown signal is modeled as the sum of a slowly varying trend and a periodic or quasi-periodic seasonal…

Monte Carlo path tracer renders noisy image sequences at low sampling counts. Although great progress has been made on denoising such sequences, existing methods still suffer from spatial and temporary artifacts. In this paper, we tackle…

Monte Carlo sampling is a powerful toolbox of algorithmic techniques widely used for a number of applications wherein some noisy quantity, or summary statistic thereof, is sought to be estimated. In this paper, we survey the literature for…