A reweighted \(\ell^2\) method for image restoration with Poisson and mixed Poisson-Gaussian noise

DOI10.3934/ipi.2015.9.875zbMath1333.65067OpenAlexW2181619750MaRDI QIDQ256075

Zuowei Shen, Xiaoqun Zhang, Rujie Yin, Jia Li

Publication date: 9 March 2016

Published in: Inverse Problems and Imaging (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/ipi.2015.9.875

zbMATH Keywords

inverse problemregularizationframeletsPoisson noisePoisson-Gaussian mixed noisesplitting algorithm

Mathematics Subject Classification ID

Ill-posedness and regularization problems in numerical linear algebra (65F22) Numerical optimization and variational techniques (65K10) Numerical methods for wavelets (65T60) Image processing (compression, reconstruction, etc.) in information and communication theory (94A08)

Related Items

A variational method for Abel inversion tomography with mixed Poisson-Laplace-Gaussian noise, A combined first and fractional order regularization method for mixed Poisson-White spike noisy image restoration, A wavelet frame approach for removal of mixed Gaussian and impulse noise on surfaces, Bilinear constraint based ADMM for mixed Poisson-Gaussian noise removal

Cites Work

• Unnamed Item
• Unnamed Item
• Nonlinear total variation based noise removal algorithms
• Sparse inverse covariance estimation with the graphical lasso
• Primal and dual Bregman methods with application to optical nanoscopy
• A unified primal-dual algorithm framework based on Bregman iteration
• Why least squares and maximum entropy? An axiomatic approach to inference for linear inverse problems
• Affine systems in \(L_ 2(\mathbb{R}^d)\): The analysis of the analysis operator
• Framelets: MRA-based constructions of wavelet frames
• An efficient algorithm for \(\ell_{0}\) minimization in wavelet frame based image restoration
• Regularized estimation of large covariance matrices
• Linearized Bregman iterations for compressed sensing
• A discrepancy principle for Poisson data
• A General Framework for a Class of First Order Primal-Dual Algorithms for Convex Optimization in Imaging Science
• Analysis of an approximate model for Poisson data reconstruction and a related discrepancy principle
• The Split Bregman Method for L1-Regularized Problems
• Split Bregman Methods and Frame Based Image Restoration
• Image deblurring with Poisson data: from cells to galaxies
• Augmented Lagrangians and Applications of the Proximal Point Algorithm in Convex Programming
• Fast Alternating Direction Optimization Methods
• Image Restoration with Mixed or Unknown Noises
• Image restoration: Total variation, wavelet frames, and beyond
• Restoration of Poissonian Images Using Alternating Direction Optimization
• Image Denoising in Mixed Poisson–Gaussian Noise
• THE TRANSFORMATION OF POISSON, BINOMIAL AND NEGATIVE-BINOMIAL DATA
• Compressed sensing