Fully Adaptive Bayesian Algorithm for Data Analysis, FABADA

• URL: http://arxiv.org/abs/2201.05145v2
• Date: Thu, 6 Jul 2023 10:14:11 GMT
• Title: Fully Adaptive Bayesian Algorithm for Data Analysis, FABADA
• Authors: Pablo M Sanchez-Alarcon and Yago Ascasibar Sequeiros
• Abstract summary: This paper describes a novel non-parametric noise reduction technique from the point of view of Bayesian inference. It iteratively evaluates possible smoothed versions of the data, the smooth models, obtaining an estimation of the underlying signal. Iterations stop based on the evidence and the $chi2$ statistic of the last smooth model, and we compute the expected value of the signal.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The aim of this paper is to describe a novel non-parametric noise reduction technique from the point of view of Bayesian inference that may automatically improve the signal-to-noise ratio of one- and two-dimensional data, such as e.g. astronomical images and spectra. The algorithm iteratively evaluates possible smoothed versions of the data, the smooth models, obtaining an estimation of the underlying signal that is statistically compatible with the noisy measurements. Iterations stop based on the evidence and the $\chi^2$ statistic of the last smooth model, and we compute the expected value of the signal as a weighted average of the whole set of smooth models. In this paper, we explain the mathematical formalism and numerical implementation of the algorithm, and we evaluate its performance in terms of the peak signal to noise ratio, the structural similarity index, and the time payload, using a battery of real astronomical observations. Our Fully Adaptive Bayesian Algorithm for Data Analysis (FABADA) yields results that, without any parameter tuning, are comparable to standard image processing algorithms whose parameters have been optimized based on the true signal to be recovered, something that is impossible in a real application. State-of-the-art non-parametric methods, such as BM3D, offer slightly better performance at high signal-to-noise ratio, while our algorithm is significantly more accurate for extremely noisy data (higher than $20-40\%$ relative errors, a situation of particular interest in the field of astronomy). In this range, the standard deviation of the residuals obtained by our reconstruction may become more than an order of magnitude lower than that of the original measurements. The source code needed to reproduce all the results presented in this report, including the implementation of the method, is publicly available at https://github.com/PabloMSanAla/fabada

Related papers

• Linear Anchored Gaussian Mixture Model for Location and Width Computations of Objects in Thick Line Shape [1.7205106391379021]
  3D image gray level representation is considered as a finite mixture model of a statistical distribution. Expectation-Maximization algorithm (Algo1) using the original image as input data is used to estimate the model parameters. modified EM algorithm (Algo2) is detailed.
  arXiv  Detail & Related papers  (2024-04-03T20:05:00Z)
• Learning Unnormalized Statistical Models via Compositional Optimization [73.30514599338407]
  Noise-contrastive estimation(NCE) has been proposed by formulating the objective as the logistic loss of the real data and the artificial noise. In this paper, we study it a direct approach for optimizing the negative log-likelihood of unnormalized models.
  arXiv  Detail & Related papers  (2023-06-13T01:18:16Z)
• Optimal Algorithms for the Inhomogeneous Spiked Wigner Model [89.1371983413931]
  We derive an approximate message-passing algorithm (AMP) for the inhomogeneous problem. We identify in particular the existence of a statistical-to-computational gap where known algorithms require a signal-to-noise ratio bigger than the information-theoretic threshold to perform better than random.
  arXiv  Detail & Related papers  (2023-02-13T19:57:17Z)
• Curvature regularization for Non-line-of-sight Imaging from Under-sampled Data [5.591221518341613]
  Non-line-of-sight (NLOS) imaging aims to reconstruct the three-dimensional hidden scenes from the data measured in the line-of-sight. We propose novel NLOS reconstruction models based on curvature regularization. We evaluate the proposed algorithms on both synthetic and real datasets.
  arXiv  Detail & Related papers  (2023-01-01T14:10:43Z)
• Greedy versus Map-based Optimized Adaptive Algorithms for random-telegraph-noise mitigation by spectator qubits [6.305016513788048]
  In a scenario where data-storage qubits are kept in isolation as far as possible, noise mitigation can still be done using additional noise probes. We construct a theoretical model assuming projective measurements on the qubits, and derive the performance of different measurement and control strategies. We show, analytically and numerically, that MOAAAR outperforms the Greedy algorithm, especially in the regime of high noise sensitivity of SQ.
  arXiv  Detail & Related papers  (2022-05-25T08:25:10Z)
• Learning Summary Statistics for Bayesian Inference with Autoencoders [58.720142291102135]
  We use the inner dimension of deep neural network based Autoencoders as summary statistics. To create an incentive for the encoder to encode all the parameter-related information but not the noise, we give the decoder access to explicit or implicit information that has been used to generate the training data.
  arXiv  Detail & Related papers  (2022-01-28T12:00:31Z)
• Learning Optical Flow from a Few Matches [67.83633948984954]
  We show that the dense correlation volume representation is redundant and accurate flow estimation can be achieved with only a fraction of elements in it. Experiments show that our method can reduce computational cost and memory use significantly, while maintaining high accuracy.
  arXiv  Detail & Related papers  (2021-04-05T21:44:00Z)
• Learning based signal detection for MIMO systems with unknown noise statistics [84.02122699723536]
  This paper aims to devise a generalized maximum likelihood (ML) estimator to robustly detect signals with unknown noise statistics. In practice, there is little or even no statistical knowledge on the system noise, which in many cases is non-Gaussian, impulsive and not analyzable. Our framework is driven by an unsupervised learning approach, where only the noise samples are required.
  arXiv  Detail & Related papers  (2021-01-21T04:48:15Z)
• Active Model Estimation in Markov Decision Processes [108.46146218973189]
  We study the problem of efficient exploration in order to learn an accurate model of an environment, modeled as a Markov decision process (MDP) We show that our Markov-based algorithm outperforms both our original algorithm and the maximum entropy algorithm in the small sample regime.
  arXiv  Detail & Related papers  (2020-03-06T16:17:24Z)
• Statistical Outlier Identification in Multi-robot Visual SLAM using Expectation Maximization [18.259478519717426]
  This paper introduces a novel and distributed method for detecting inter-map loop closure outliers in simultaneous localization and mapping (SLAM) The proposed algorithm does not rely on a good initialization and can handle more than two maps at a time.
  arXiv  Detail & Related papers  (2020-02-07T06:34:44Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.