# Poisson image reconstruction with total variation regularization

@article{Willett2010PoissonIR, title={Poisson image reconstruction with total variation regularization}, author={R. Willett and Z. Harmany and R. Marcia}, journal={2010 IEEE International Conference on Image Processing}, year={2010}, pages={4177-4180} }

This paper describes an optimization framework for reconstructing nonnegative image intensities from linear projections contaminated with Poisson noise. Such Poisson inverse problems arise in a variety of applications, ranging from medical imaging to astronomy. A total variation regularization term is used to counter the ill-posedness of the inverse problem and results in reconstructions that are piecewise smooth. The proposed algorithm sequentially approximates the objective function with a… Expand

#### 31 Citations

Total variation regularization for Poisson vector-valued image restoration with a spatially adaptive regularization parameter selection

- Computer Science, Mathematics
- 2011 7th International Symposium on Image and Signal Processing and Analysis (ISPA)
- 2011

We propose a flexible and computationally efficient method to solve the non-homogeneous Poisson (NHP) model for grayscale and color images within the TV framework. The NHP model is relevant to image… Expand

Non-negative Quadratic Programming Total Variation Regularization for Poisson Vector-Valued Image Restoration

- Mathematics
- 2011

We propose a flexible and computationally efficient method to solve the non-homogeneous Poisson (NHP) model for grayscale and color images within the TV framework. The NHP model is relevant to image… Expand

General convergent expectation maximization (EM)-type algorithms for image reconstruction

- Mathematics
- 2013

Obtaining high quality images is very important in many areas of applied sciences, such as medical imaging, optical microscopy, and astronomy. Image reconstruction can be considered as solving the… Expand

Deconvolution of poissonian images with the PURE-LET approach

- Mathematics, Computer Science
- 2016 IEEE International Conference on Image Processing (ICIP)
- 2016

Simulation experiments indicate that the proposed non-iterative image deconvolution algorithm outperforms current state-of-the-art techniques, in terms of both restoration quality and computational time. Expand

Total Variation Regularisation in Measurement and Image space for PET reconstruction

- Mathematics
- 2014

The aim of this paper is to test and analyze a novel technique for image reconstruction in positron emission tomography, which is based on (total variation) regularization on both the image space and… Expand

Logarithmic total variation regularization for cross-validation in photon-limited imaging

- Mathematics, Computer Science
- 2013 IEEE International Conference on Image Processing
- 2013

A new model is presented that solves for and regularizes the logarithm of the true scene, and focuses on the special case of total variation regularization. Expand

Proximal-Gradient methods for poisson image reconstruction with BM3D-Based regularization

- Computer Science
- 2017 IEEE 7th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP)
- 2017

This paper presents an alternative regularized maximum likelihood formulation of the reconstruction problem, and explains how it can be solved using a coarse-to-fine proximal gradient optimization algorithm. Expand

Total Variation Regularization Algorithms for Images Corrupted with Different Noise Models: A Review

- Mathematics, Computer Science
- J. Electr. Comput. Eng.
- 2013

This paper focuses on giving a summary of the most relevant TV numerical algorithms for solving the restoration problem for grayscale/color images corrupted with several noise models, that is, Gaussian, Salt & Pepper, Poisson, and Speckle (Gamma) noise models as well as for the mixed noise scenarios, such the mixed Gaussian and impulse model. Expand

Expectation maximization and total variation-based model for computed tomography reconstruction from undersampled data

- Computer Science, Engineering
- Medical Imaging
- 2011

This work proposes a method combining expectation maximization and total variation regularization, called EM+TV, which can reconstruct a better image using fewer views in the computed tomography setting, thus reducing the overall dose of radiation. Expand

Sampling-based uncertainty quantification in deconvolution of X-ray radiographs

- Mathematics, Computer Science
- J. Comput. Appl. Math.
- 2014

This work solves the deconvolution problem within a Bayesian framework for edge-enhancing reconstruction with uncertainty quantification and shows that this approach gives reconstructions as good as classical regularization methods, while mitigating many of their drawbacks. Expand

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