Poisson Shot Noise Removal by an Oracular Non-Local Algorithm
| Autor: | Quansheng Liu, Ion Grama, Qiyu Jin |
|---|---|
| Přispěvatelé: | Inner Mongolia University, Laboratoire de Mathématiques de Bretagne Atlantique (LMBA), Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Centre National de la Recherche Scientifique (CNRS) |
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Statistics and Probability
Applied Mathematics Noise reduction Shot noise Estimator 02 engineering and technology Function (mathematics) Filter (signal processing) Condensed Matter Physics Poisson distribution [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] symbols.namesake Additive white Gaussian noise Rate of convergence Modeling and Simulation 0202 electrical engineering electronic engineering information engineering symbols 020201 artificial intelligence & image processing Geometry and Topology Computer Vision and Pattern Recognition Algorithm [SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing Mathematics |
| Zdroj: | Journal of Mathematical Imaging and Vision Journal of Mathematical Imaging and Vision, Springer Verlag, 2021, 63 (7), pp.855-874. ⟨10.1007/s10851-021-01033-3⟩ |
| ISSN: | 0924-9907 1573-7683 |
| DOI: | 10.1007/s10851-021-01033-3⟩ |
| Popis: | International audience; In this paper we address the problem of denoising images obtained under low light conditions for the Poisson shot noise model. Under such conditions the variance stabilization transform (VST) is no longer applicable, so that the state-of-the-art algorithms which are proficient for the additive white Gaussian noise cannot be applied. We first introduce an oracular non-local algorithm and prove its convergence with the optimal rate of convergence under a Hölder regularity assumption for the underlying image, when the search window size is suitably chosen. We also prove that the convergence remains valid when the oracle function is estimated within a prescribed error range. We then define a realisable filter by a statistical estimation of the similarity function which determines the oracle weight. The convergence of the realisable filter is justified by proving that the estimator of the similarity function lies in the prescribed error range with high probability. The experiments show that under low light conditions the proposed filter is competitive compared with the recent state-of-the-art algorithms. |
| Databáze: | OpenAIRE |
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