## Publications

Journal papers

• Anna Jezierska, Emilie Chouzenoux, Jean-Christophe Pesquet, and Hugues Talbot
A Convex Approach for Image Restoration with Exact Poisson-Gaussian Likelihood,
submitted to IEEE Transactions on Image Processing, 2013 [article]
• Anna Jezierska, Caroline Chaux, Jean-Christophe Pesquet,
Hugues Talbot and Gilbert Engler
An EM Approach for Time-Variant Poisson-Gaussian Model Parameter Estimation,
IEEE Transactions on Signal Processing,
vol 62, number 1, pages 17-30, 2014 [article] [bibtex]
• Emilie Chouzenoux, Anna Jezierska, Jean-Christophe Pesquet, and Hugues Talbot
A Majorize-Minimize Subspace Approach for l2-l0 Image Regularization,
SIAM Journal on Imaging Science, vol 6, pages 563-591, 2013 [article] [bibtex]
• Caroline Chaux, Anna Jezierska, Jean-Christophe Pesquet, and Hugues Talbot
A spatial regularization approach for vector quantization,
Journal of Mathematical Imaging and Vision,
vol 41, pages 23-38, 2011 [article] [bibtex]

Conference papers

• Mireille El Gheche, Anna Jezierska, Jean-Christophe Pesquet, and Joumana Farah
A Proximal Approach for Signal Recovery Based on Information Measures,
European Signal Processing Conference (EUSIPCO),
Marrakech, Marocco, 9-13 September, 2013 [article]
• Daniel Wesierski, Maher Mkhinini, Patrick Horain, and Anna Jezierska
Fast Recursive Ensemble Convolution of Haar-like Features,
Computer Vision and Pattern Recognition (CVPR),
Providence, Rhode Island, 18-20 June, 2012 [article] [poster] [bibtex]
• Anna Jezierska, Hugues Talbot, Caroline Chaux,
Jean-Christophe Pesquet, and Gilbert Engler
Poisson-Gaussian noise parameter estimation in fluorescence microscopy imaging,
International Symposium on Biomedical Imaging (ISBI),
Barcelona, 2-5 May, 2012 [article] [poster] [bibtex]
• Anna Jezierska, Emilie Chouzenoux, Jean-Christophe Pesquet, and Hugues Talbot
A primal-dual proximal splitting approach for restoring data corrupted with Poisson-Gaussian noise,
International Conference on Acoustics, Speech, and Signal Processing (ICASSP),
Kyoto, 25-30 March, 2012 . [article] [poster] [bibtex]
• Emilie Chouzenoux, Jean-Christophe Pesquet, Hugues Talbot, and Anna Jezierska
A memory gradient algorithm for l2 - l0 regularization with applications to image restoration,
International Conference on Image Processing (ICIP),
Brussels, 11-14 September 2011. [article] [poster] [bibtex]
• Anna Jezierska, Caroline Chaux, Jean-Christophe Pesquet, and Hugues Talbot
An EM approach for Poisson-Gaussian noise modeling,
European Signal Processing Conference (EUSIPCO),
Barcelona, 29 August - 2 September 2011. [article] [slides] [bibtex]
• Anna Jezierska, Hugues Talbot, Olga Veksler, and Daniel Wesierski
A fast solver for truncated-convex priors: quantized-convex split moves,
Energy Minimization Methods in Computer Vision and Pattern Recognition (EMMCVPR),
Saint Petersburg, 25-27 July 2011. [article] [poster] [bibtex]
• Anna Jezierska, Caroline Chaux, Hugues Talbot, and Jean-Christophe Pesquet
Image quantization under spatial smoothness constraints,
International Conference on Image Processing (ICIP),
Honk Kong, 26-29 September 2010. [article] [poster] [bibtex]

PhD

Image Restoration in the presence of Poisson-Gaussian noise [TEL]

The thesis deals with the restoration of images corrupted by blur and noise, with emphasis on confocal microscopy and macroscopy applications.

Due to low photon count and high detector noise, the Poisson-Gaussian model is well suited to this context. However, up to now it had not been widely utilized because of theoretical and practical difficulties. In view of this, we formulate the image restoration problem in the presence of Poisson-Gaussian noise in a variational framework, where we express and study the exact data fidelity term. The solution to the problem can also be interpreted as a Maximum A Posteriori (MAP) estimate. Using recent primal-dual convex optimization algorithms, we obtain results that outperform methods relying on a variety of approximations.

Turning our attention to the regularization term in the MAP framework, we study both discrete and continuous approximations of the $\ell_0$ pseudo-norm. This useful measure, well-known for promoting sparsity, is difficult to optimize due to its non-convexity and its non-smoothness. We propose an efficient graph-cut procedure for optimizing energies with truncated quadratic priors. Moreover, we develop a majorize-minimize memory gradient algorithm to optimize various smooth versions of the $\ell_2-\ell_0$ norm, with guaranteed convergence properties. In particular, good results are achieved on deconvolution problems.

One difficulty with variational formulations is the necessity to tune automatically the model hyperparameters. In this context, we propose to estimate the Poisson-Gaussian noise parameters based on two realistic scenarios: one from time series images, taking into account bleaching effects, and another from a single image. These estimations are grounded on the use of an Expectation-Maximization (EM) approach.

Overall, this thesis proposes and evaluates various methodologies for tackling difficult image noise and blur cases, which should be useful in various applicative contexts within and beyond microscopy.

Supervisors

Jury

## Université Paris-Est

Institut Gaspard Monge
Cité Descartes
5, Boulevard Descartes
Champs sur Marne
77454 Marne-la-Vallée Cedex 2
anna.jezierska@univ-paris-est.fr