Nonlinear PDE-based models for photon-limited image restoration. (English) Zbl 07455322
Summary: An overview of the state of the art mathematical models for photon-limited image restoration is provided in this research article. The most important partial differential equation (PDE)-based Poisson denoising techniques are presented here. Thus, quantum noise filtering algorithms using Total Variation (TV) regularization – based models are described first. Then, some PDE variational filtering schemes for mixed Poisson – Gaussian noise removal are discussed. Our own contributions in this domain, representing a variational restoration approach and some non-variational anisotropic diffusion-based photon-limited image denoising solutions using nonlinear parabolic and hyperbolic PDE models, are also described in this paper and compared to the state of the art methods.
MSC:
| 68U10 | Computing methodologies for image processing |
| 94A08 | Image processing (compression, reconstruction, etc.) in information and communication theory |
| 93E11 | Filtering in stochastic control theory |
| 60G35 | Signal detection and filtering (aspects of stochastic processes) |
| 35A15 | Variational methods applied to PDEs |
| 35-XX | Partial differential equations |
| 35Kxx | Parabolic equations and parabolic systems |
| 35K10 | Second-order parabolic equations |
| 35K55 | Nonlinear parabolic equations |
| 35Lxx | Hyperbolic equations and hyperbolic systems |
| 35L70 | Second-order nonlinear hyperbolic equations |
Keywords:
photon-limited image; nonlinear PDE-based model; variational Poisson denoising scheme; mixed Poisson-Gaussian noise removal; non-variational anisotropic diffusion-based quantum denoisingSoftware:
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