# Gaussian process deconvolution

arXiv: https://arxiv.org/abs/2305.04871 · HTML: https://mlsanity.com/paper/2305.04871/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 50 references that are in the map.
- First posted on arXiv 8 May 2023.

## Builds on (most cited first, 15 of 15)

- [Deep Kernel Learning](https://mlsanity.com/paper/1511.02222/) (2015)
- [Neural Blind Deconvolution Using Deep Priors](https://mlsanity.com/paper/1908.02197/) (2019)
- [Convolutional Gaussian Processes](https://mlsanity.com/paper/1709.01894/) (2017)
- [DWDN: Deep Wiener Deconvolution Network for Non-Blind Image Deblurring](https://mlsanity.com/paper/2103.09962/) (2021)
- [Spectral Mixture Kernels for Multi-Output Gaussian Processes](https://mlsanity.com/paper/1709.01298/) (2017)
- [Deep convolutional Gaussian processes](https://mlsanity.com/paper/1810.03052/) (2018)
- [Graph Convolutional Gaussian Processes](https://mlsanity.com/paper/1905.05739/) (2019)
- [The Wasserstein-Fourier Distance for Stationary Time Series](https://mlsanity.com/paper/1912.05509/) (2019)
- [Band-Limited Gaussian Processes: The Sinc Kernel](https://mlsanity.com/paper/1909.07279/) (2019)
- [Bayesian Nonparametric Spectral Estimation](https://mlsanity.com/paper/1809.02196/) (2018)
- [Complex-Valued Gaussian Processes for Regression](https://mlsanity.com/paper/1511.05710/) (2015)
- [Complex-valued Gaussian Process Regression for Time Series Analysis](https://mlsanity.com/paper/1611.10073/) (2016)
- [Recovering Latent Signals from a Mixture of Measurements using a Gaussian Process Prior](https://mlsanity.com/paper/1707.05909/) (2017)
- [Blind hierarchical deconvolution](https://mlsanity.com/paper/2007.11391/) (2020)
- [Bayesian Reconstruction of Fourier Pairs](https://mlsanity.com/paper/2011.04585/) (2020)

## Built on by (most cited first, 1 of 1)

- [Learning Point Spread Function Invertibility Assessment for Image Deconvolution](https://mlsanity.com/paper/2405.16343/) (2024)

## Abstract (arXiv)

Let us consider the deconvolution problem, that is, to recover a latent source x(·) from the observations y = [y1,ldots,yN] of a convolution process y = xstar 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 (GP) prior on the source x, which allows for closed-form Bayesian nonparametric 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 learnt from data or approximated for the blind deconvolution case. The proposed approach, termed Gaussian process deconvolution (GPDC) is compared to other deconvolution methods conceptually, via illustrative examples, and using real-world datasets.