Related papers: Bayesian Inversion via Probabilistic Cellular Auto…
Principal component analysis (PCA) plays an important role in the analysis of cryo-EM images for various tasks such as classification, denoising, compression, and ab-initio modeling. We introduce a fast method for estimating a compressed…
We study the problem of estimating a rank-$1$ signal in the presence of rotationally invariant noise-a class of perturbations more general than Gaussian noise. Principal Component Analysis (PCA) provides a natural estimator, and sharp…
Sparse versions of principal component analysis (PCA) have imposed themselves as simple, yet powerful ways of selecting relevant features of high-dimensional data in an unsupervised manner. However, when several sparse principal components…
The problem of Non-Gaussian Component Analysis (NGCA) is about finding a maximal low-dimensional subspace $E$ in $\mathbb{R}^n$ so that data points projected onto $E$ follow a non-gaussian distribution. Although this is an appropriate model…
A common approach to perform PCA on probability measures is to embed them into a Hilbert space where standard functional PCA techniques apply. While convergence rates for estimating the embedding of a single measure from $m$ samples are…
This paper presents a novel approach for denoising binary images using simulated annealing (SA), a global optimization technique that addresses the inherent challenges of non convex energy functions. Binary images are often corrupted by…
Bayesian optimization is an effective methodology for the global optimization of functions with expensive evaluations. It relies on querying a distribution over functions defined by a relatively cheap surrogate model. An accurate model for…
In a non supervised Bayesian estimation approach for inverse problems in imaging systems, one tries to estimate jointly the unknown image pixels $f$ and the hyperparameters $\theta$ given the observed data $g$ and a model $M$ linking these…
We present a Bayesian model selection approach to estimate the intrinsic dimensionality of a high-dimensional dataset. To this end, we introduce a novel formulation of the probabilisitic principal component analysis model based on a…
Neural Cellular Automata (NCA) offer a robust and interpretable approach to image classification, making them a promising choice for microscopy image analysis. However, a performance gap remains between NCA and larger, more complex…
The formulation of Bayesian inverse problems involves choosing prior distributions; choices that seem equally reasonable may lead to significantly different conclusions. We develop a computational approach to better understand the impact of…
Inverse problems exist in many domains such as phase imaging, image processing, and computer vision. These problems are often solved with application-specific algorithms, even though their nature remains the same: mapping input image(s) to…
Sparse principal component analysis (PCA) is a popular dimensionality reduction technique for obtaining principal components which are linear combinations of a small subset of the original features. Existing approaches cannot supply…
Principal component analysis (PCA) is very popular to perform dimension reduction. The selection of the number of significant components is essential but often based on some practical heuristics depending on the application. Only few works…
In order to solve tasks like uncertainty quantification or hypothesis tests in Bayesian imaging inverse problems, we often have to draw samples from the arising posterior distribution. For the usually log-concave but high-dimensional…
Posterior sampling has been shown to be a powerful Bayesian approach for solving imaging inverse problems. The recent plug-and-play unadjusted Langevin algorithm (PnP-ULA) has emerged as a promising method for Monte Carlo sampling and…
Motivated by the recently shown connection between self-attention and (kernel) principal component analysis (PCA), we revisit the fundamentals of PCA. Using the difference-of-convex (DC) framework, we present several novel formulations and…
We study self-similarity in one-dimensional probabilistic cellular automata (PCA) using the renormalization technique. We introduce a general framework for algebraic construction of renormalization groups (RG) on cellular automata and apply…
Deep neural networks have proven extremely efficient at solving a wide rangeof inverse problems, but most often the uncertainty on the solution they provideis hard to quantify. In this work, we propose a generic Bayesian framework…
A Cellular Automata (CA) is a computing model of complex System using simple rule. In CA the problem space into number of cell and each cell can be one or several final state. Cells are affected by neighbours' to the simple rule. Cellular…