Bayesian Reconstruction of Fourier Pairs

Tobar, Felipe; Araya-Hernandez, Lerko; Huijse, P.; Djurić, Petar M.

doi:10.1109/tsp.2020.3038135

Cited by 7 publications

(3 citation statements)

References 31 publications

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“…the parameters of Kx and h, and the noise variance σ2. Depending on the application the filter might be known beforehand, for instance, in de-reverberation [42] h is given by the geometry of the room, whereas in astronomy h is given by the atmosphere and/or the telescope [43,44]. When h is unknown, a case referred to as blind deconvolution , its parameters have to be learned from data alongside the other hyperparameters.…”

Section: The Blind Deconvolution Casementioning

confidence: 99%

Gaussian process deconvolution

2023

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Let us consider the deconvolution problem, i.e. to recover a latent source x ( ⋅ ) from the observations y = [ y 1 , … , y N ] of a convolution process y = x ⋆ h + η , where η is an additive noise, the observations in y might have missing parts with respect to y , and the filter h could be unknown. We propose a novel strategy to address this task when x is a continuous-time signal: we adopt a Gaussian process prior on the source x , which allows for closed-form Bayesian non-parametric deconvolution. We first analyse the direct model to establish the conditions under which the model is well-defined. Then, we turn to the inverse problem, where we study (i) some necessary conditions under which Bayesian deconvolution is feasible and (ii) to which extent the filter h can be learned from data or approximated for the blind deconvolution case. The proposed approach, termed Gaussian process deconvolution, is compared to other deconvolution methods conceptually, via illustrative examples, and using real-world datasets.

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Section: The Blind Deconvolution Casementioning

confidence: 99%

Gaussian process deconvolution

2023

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“…The main setback of Model II, however, is that it requires the use of a specific prior. Future work includes: i) heuristics to determine the hyperparameters µ 0 , λ, α, β, ii) a quantitative assessment of the reduction in computational complexity provided by Model II, iii) a development of a hierarchical prior to simultaneously identify the AR model order (e.g., a Dirichlet prior), and iv) extensions to ARMA models to cater for moving-average spectral components and spectra with zeros, iv) comparisons against nonparametric models such as [18].…”

Section: Finding the Periodicity Of An Astronomical Time Seriesmentioning

confidence: 99%

Bayesian autoregressive spectral estimation

Cuevas¹,

Lopez²,

Mandic³

et al. 2021

Preprint

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Autoregressive (AR) time series models are widely used in parametric spectral estimation (SE), where the power spectral density (PSD) of the time series is approximated by that of the best-fit AR model, which is available in closed form. Since AR parameters are usually found via maximum-likelihood, least squares or the method of moments, AR-based SE fails to account for the uncertainty of the approximate PSD, and thus only yields point estimates. We propose to handle the uncertainty related to the AR approximation by finding the full posterior distribution of the AR parameters to then propagate this uncertainty to the PSD approximation by integrating out the AR parameters; we implement this concept by assuming two different priors over the model noise. Through practical experiments, we show that the proposed Bayesian autoregressive spectral estimation (BASE) provides point estimates that follow closely those of standard autoregressive spectral estimation (ASE), while also providing error bars. BASE is validated against ASE and the Periodogram on both synthetic and real-world signals.

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“…Lastly, for those of our graduates who pursue an academic career, the MSc thesis provides a fertile environment for theoretical research, where students join PhD students and postdocs to work under the close supervision of their mentors and, in most cases, successfully publish their findings (see, e.g., [29], [30], [31], [32], [33]).…”

Section: F Early Research Trainingmentioning

confidence: 99%

Data Science for Engineers: A Teaching Ecosystem

Tobar,

Bravo-Marquez,

Dunstan

et al. 2021

Preprint

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We describe an ecosystem for teaching data science (DS) to engineers which blends theory, methods, and applications, developed at the Faculty of Physical and Mathematical Sciences, Universidad de Chile, over the last three years. This initiative has been motivated by the increasing demand for DS qualifications both from academic and professional environments. The ecosystem is distributed in a collaborative fashion across three departments in the above Faculty and includes postgraduate programmes, courses, professional diplomas, data repositories, laboratories, trainee programmes, and internships. By sharing our teaching principles and the innovative components of our approach to teaching DS, we hope our experience can be useful to those developing their own DS programmes and ecosystems. The open challenges and future plans for our ecosystem are also discussed at the end of the article.

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Bayesian Reconstruction of Fourier Pairs

Cited by 7 publications

References 31 publications

Gaussian process deconvolution

Gaussian process deconvolution

Bayesian autoregressive spectral estimation

Data Science for Engineers: A Teaching Ecosystem

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