Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Nonlinear total variation based noise removal algorithms
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
The use of the L-curve in the regularization of discrete ill-posed problems
SIAM Journal on Scientific Computing
Computational Methods for Inverse Problems
Computational Methods for Inverse Problems
Lanczos Algorithms for Large Symmetric Eigenvalue Computations, Vol. 1
Lanczos Algorithms for Large Symmetric Eigenvalue Computations, Vol. 1
Fundamentals of Digital Imaging
Fundamentals of Digital Imaging
A Variational Approach to Reconstructing Images Corrupted by Poisson Noise
Journal of Mathematical Imaging and Vision
Efficient computation for Whittaker-Henderson smoothing
Computational Statistics & Data Analysis
Robust smoothing of gridded data in one and higher dimensions with missing values
Computational Statistics & Data Analysis
A cross-validation framework for solving image restoration problems
Journal of Visual Communication and Image Representation
Image enhancement and denoising by complex diffusion processes
IEEE Transactions on Pattern Analysis and Machine Intelligence
Fourth-order partial differential equations for noise removal
IEEE Transactions on Image Processing
Speckle reducing anisotropic diffusion
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
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In this paper, the reconstruction of three nonlinear partial differential equation (PDE) based filters adapted to Poisson noise statistics have been proposed in a variational framework for restoration and enhancement of digital images corrupted with Poisson noise. The proposed and examined PDE based filters include total variation adapted to Poisson noise in L-1 framework; anisotropic diffusion; and complex diffusion based methods adapted to Poisson noise in L-2 framework. The resulting filters contain two terms namely data fidelity and regularization or smoothing function. The data fidelity term is Poisson likelihood term and the regularization functions are PDE based filters. Other choices for the regularization functions have also been presented. The two terms in the proposed filters are coupled with a regularization parameter lambda which makes a proper balance between the two terms during the filtering process. The choice of method for estimation of regularization parameter lambda plays an important role. In this study, the various regularization parameter estimation methods for Poisson noise have also been presented and their suitability has been examined. The resulting optimization problems are further investigated for efficient implementation for large scale problems. For estimating the regularization parameter, three choices are considered for Poisson noise case which are discrepancy principles, generalized cross validations (GCV), and unbiased predictive risk estimate (UPRE). GCV and UPRE functions are further other optimization problems in addition to main image reconstruction problem. For minimizing the GCV and UPRE functions, the methods of Conjugate Gradients (CG) is used. For digital implementations, all schemes have been discretized using finite difference scheme. The comparative analysis of the proposed methods are presented in terms of relative norm error, improvement in SNR, MSE, PSNR, CP and MSSIM for an adaptive value of regularization parameter calculated by every methods in consideration. Finally, from the obtained results it is observed that the anisotropic diffusion based method adapted to Poisson noise gives better results in comparison to other methods in consideration along with choice of GCV for regularization parameter selection.