Journal of Mathematical Imaging and Vision

, Volume 48, Issue 2, pp 279–294 | Cite as

Poisson Noise Reduction with Non-local PCA

  • Joseph Salmon
  • Zachary Harmany
  • Charles-Alban Deledalle
  • Rebecca Willett


Photon-limited imaging arises when the number of photons collected by a sensor array is small relative to the number of detector elements. Photon limitations are an important concern for many applications such as spectral imaging, night vision, nuclear medicine, and astronomy. Typically a Poisson distribution is used to model these observations, and the inherent heteroscedasticity of the data combined with standard noise removal methods yields significant artifacts. This paper introduces a novel denoising algorithm for photon-limited images which combines elements of dictionary learning and sparse patch-based representations of images. The method employs both an adaptation of Principal Component Analysis (PCA) for Poisson noise and recently developed sparsity-regularized convex optimization algorithms for photon-limited images. A comprehensive empirical evaluation of the proposed method helps characterize the performance of this approach relative to other state-of-the-art denoising methods. The results reveal that, despite its conceptual simplicity, Poisson PCA-based denoising appears to be highly competitive in very low light regimes.


Image denoising PCA Gradient methods Newton’s method Signal representations 



Joseph Salmon, Zachary Harmany, and Rebecca Willett gratefully acknowledge support from DARPA grant no. FA8650-11-1-7150, AFOSR award no. FA9550-10-1-0390, and NSF award no. CCF-06-43947. The authors would also like to thank J. Boulanger and C. Kervrann for providing their SAFIR algorithm, Steven Reynolds for providing the spectral images from the supernova remnant G1.9+0.3, and an anonymous reviewer for proposing the improvement using the binning step.


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Joseph Salmon
    • 1
  • Zachary Harmany
    • 2
  • Charles-Alban Deledalle
    • 3
  • Rebecca Willett
    • 4
  1. 1.Department LTCI, CNRS UMR 5141Institut Mines-Télécom, Télécom ParisTechParisFrance
  2. 2.Department of Electrical and Computer EngineeringUniversity of Wisconsin-MadisonMadisonUSA
  3. 3.IMBCNRS-Université Bordeaux 1TalenceFrance
  4. 4.Department of Electrical and Computer EngineeringDuke UniversityDurhamUSA

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