Related papers: Bayesian Inversion via Probabilistic Cellular Auto…

In Bayesian inverse problems, the posterior distribution is used to quantify uncertainty about the reconstructed solution. In practice, Markov chain Monte Carlo algorithms often are used to draw samples from the posterior distribution.…

Fourier PCA is Principal Component Analysis of a matrix obtained from higher order derivatives of the logarithm of the Fourier transform of a distribution.We make this method algorithmic by developing a tensor decomposition method for a…

Markov Chain Monte Carlo (MCMC) algorithms are standard approaches to solve imaging inverse problems and quantify estimation uncertainties, a key requirement in absence of ground-truth data. To improve estimation quality, Plug-and-Play MCMC…

We consider the following multi-component sparse PCA problem: given a set of data points, we seek to extract a small number of sparse components with disjoint supports that jointly capture the maximum possible variance. These components can…

This paper presents a new accelerated proximal Markov chain Monte Carlo methodology to perform Bayesian inference in imaging inverse problems with an underlying convex geometry. The proposed strategy takes the form of a stochastic relaxed…

Machine learning methods for computational imaging require uncertainty estimation to be reliable in real settings. While Bayesian models offer a computationally tractable way of recovering uncertainty, they need large data volumes to be…

This work proposes a Processing-In-Sensor Accelerator, namely PISA, as a flexible, energy-efficient, and high-performance solution for real-time and smart image processing in AI devices. PISA intrinsically implements a coarse-grained…

A learning-based posterior distribution estimation method, Probabilistic Dipole Inversion (PDI), is proposed to solve quantitative susceptibility mapping (QSM) inverse problem in MRI with uncertainty estimation. A deep convolutional neural…

In this work, we are trying to extent the existing photometric redshift regression models from modeling pure photometric data back to the spectra themselves. To that end, we developed a PCA that is capable of describing the input…

A common task in inverse problems and imaging is finding a solution that is sparse, in the sense that most of its components vanish. In the framework of compressed sensing, general results guaranteeing exact recovery have been proven. In…

The idea of computer vision as the Bayesian inverse problem to computer graphics has a long history and an appealing elegance, but it has proved difficult to directly implement. Instead, most vision tasks are approached via complex…

We propose a novel adaptive importance sampling scheme for Bayesian inversion problems where the inference of the variables of interest and the power of the data noise is split. More specifically, we consider a Bayesian analysis for the…

We present a novel, general-purpose method for deconvolving and denoising images from gridded radio interferometric visibilities using Bayesian inference based on a Gaussian process model. The method automatically takes into account…

Principal component analysis (PCA) is a dimensionality reduction method in data analysis that involves diagonalizing the covariance matrix of the dataset. Recently, quantum algorithms have been formulated for PCA based on diagonalizing a…

Artificial neural networks that learn to perform Principal Component Analysis (PCA) and related tasks using strictly local learning rules have been previously derived based on the principle of similarity matching: similar pairs of inputs…

Patch-based low-rank minimization for image processing attracts much attention in recent years. The minimization of the matrix rank coupled with the Frobenius norm data fidelity can be solved by the hard thresholding filter with principle…

Bayesian Optimization (BO) is a surrogate-assisted global optimization technique that has been successfully applied in various fields, e.g., automated machine learning and design optimization. Built upon a so-called infill-criterion and…

We present an algorithm using Principal Component Analysis (PCA) to subtract galaxies from imaging data, and also two algorithms to find strong, galaxy-scale gravitational lenses in the resulting residual image. The combined method is…

We examine the problem of selecting a small set of linear measurements for reconstructing high-dimensional signals. Well-established methods for optimizing such measurements include principal component analysis (PCA), independent component…

Generative adversarial networks (GANs) have made great success in image inpainting yet still have difficulties tackling large missing regions. In contrast, iterative probabilistic algorithms, such as autoregressive and denoising diffusion…