A Bayesian Approach to Denoising of Single-Photon Binary Images

Yoann Altmann, Reuben Aspden, Miles Padgett, Steve McLaughlin

Research output: Contribution to journalArticle

Abstract

This paper discusses new methods for processing images in the photon-limited regime where the number of photons per pixel is binary. We present a new Bayesian denoising method for binary, single-photon images. Each pixel measurement is assumed to follow a Bernoulli distribution whose mean is related by a nonlinear function to the underlying intensity value to be recovered. Adopting a Bayesian approach, we assign the unknown intensity field a smoothness promoting spatial and potentially temporal prior while enforcing the positivity of the intensity. A stochastic simulation method is then used to sample the resulting joint posterior distribution and estimate the unknown intensity, as well as the regularization parameters. We show that this new unsupervised denoising method can also be used to analyze images corrupted by Poisson noise. The proposed algorithm is compared to state-of-the art denoising techniques dedicated to photon-limited images using synthetic and real single-photon measurements. The results presented illustrate the potential benefits of the proposed methodology for photon-limited imaging, in particular with non photonnumber resolving detectors.
Original languageEnglish
Pages (from-to)460-471
Number of pages12
JournalIEEE Transactions on Computational Imaging
Volume3
Issue number3
DOIs
Publication statusPublished - 12 May 2017

Fingerprint

Binary images
Photons
Pixels
Image processing
Detectors
Imaging techniques

Keywords

  • stat.ME

Cite this

@article{bd33aabf9d444a86bf2fa9c90c6cc4dc,
title = "A Bayesian Approach to Denoising of Single-Photon Binary Images",
abstract = "This paper discusses new methods for processing images in the photon-limited regime where the number of photons per pixel is binary. We present a new Bayesian denoising method for binary, single-photon images. Each pixel measurement is assumed to follow a Bernoulli distribution whose mean is related by a nonlinear function to the underlying intensity value to be recovered. Adopting a Bayesian approach, we assign the unknown intensity field a smoothness promoting spatial and potentially temporal prior while enforcing the positivity of the intensity. A stochastic simulation method is then used to sample the resulting joint posterior distribution and estimate the unknown intensity, as well as the regularization parameters. We show that this new unsupervised denoising method can also be used to analyze images corrupted by Poisson noise. The proposed algorithm is compared to state-of-the art denoising techniques dedicated to photon-limited images using synthetic and real single-photon measurements. The results presented illustrate the potential benefits of the proposed methodology for photon-limited imaging, in particular with non photonnumber resolving detectors.",
keywords = "stat.ME",
author = "Yoann Altmann and Reuben Aspden and Miles Padgett and Steve McLaughlin",
year = "2017",
month = "5",
day = "12",
doi = "10.1109/TCI.2017.2703900",
language = "English",
volume = "3",
pages = "460--471",
journal = "IEEE Transactions on Computational Imaging",
issn = "2333-9403",
publisher = "IEEE",
number = "3",

}

A Bayesian Approach to Denoising of Single-Photon Binary Images. / Altmann, Yoann; Aspden, Reuben; Padgett, Miles; McLaughlin, Steve.

In: IEEE Transactions on Computational Imaging, Vol. 3, No. 3, 12.05.2017, p. 460-471.

Research output: Contribution to journalArticle

TY - JOUR

T1 - A Bayesian Approach to Denoising of Single-Photon Binary Images

AU - Altmann, Yoann

AU - Aspden, Reuben

AU - Padgett, Miles

AU - McLaughlin, Steve

PY - 2017/5/12

Y1 - 2017/5/12

N2 - This paper discusses new methods for processing images in the photon-limited regime where the number of photons per pixel is binary. We present a new Bayesian denoising method for binary, single-photon images. Each pixel measurement is assumed to follow a Bernoulli distribution whose mean is related by a nonlinear function to the underlying intensity value to be recovered. Adopting a Bayesian approach, we assign the unknown intensity field a smoothness promoting spatial and potentially temporal prior while enforcing the positivity of the intensity. A stochastic simulation method is then used to sample the resulting joint posterior distribution and estimate the unknown intensity, as well as the regularization parameters. We show that this new unsupervised denoising method can also be used to analyze images corrupted by Poisson noise. The proposed algorithm is compared to state-of-the art denoising techniques dedicated to photon-limited images using synthetic and real single-photon measurements. The results presented illustrate the potential benefits of the proposed methodology for photon-limited imaging, in particular with non photonnumber resolving detectors.

AB - This paper discusses new methods for processing images in the photon-limited regime where the number of photons per pixel is binary. We present a new Bayesian denoising method for binary, single-photon images. Each pixel measurement is assumed to follow a Bernoulli distribution whose mean is related by a nonlinear function to the underlying intensity value to be recovered. Adopting a Bayesian approach, we assign the unknown intensity field a smoothness promoting spatial and potentially temporal prior while enforcing the positivity of the intensity. A stochastic simulation method is then used to sample the resulting joint posterior distribution and estimate the unknown intensity, as well as the regularization parameters. We show that this new unsupervised denoising method can also be used to analyze images corrupted by Poisson noise. The proposed algorithm is compared to state-of-the art denoising techniques dedicated to photon-limited images using synthetic and real single-photon measurements. The results presented illustrate the potential benefits of the proposed methodology for photon-limited imaging, in particular with non photonnumber resolving detectors.

KW - stat.ME

U2 - 10.1109/TCI.2017.2703900

DO - 10.1109/TCI.2017.2703900

M3 - Article

VL - 3

SP - 460

EP - 471

JO - IEEE Transactions on Computational Imaging

JF - IEEE Transactions on Computational Imaging

SN - 2333-9403

IS - 3

ER -