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Space-Variant Hyperparameter Estimation in Image Deconvolution Problems by CNNs

6 December 2021

Catégorie : Stagiaire

Over the last decade, numerous advances in the modelling and in the numerical solution of several image microscopy inverse problems (deconvolution, super-resolution..) and in image classification and segmentation problems have been made, both in statistical and in variational contexts. For both cases, the resulting model is typically composed by a data attachment term and by another term encoding a priori assumptions on the solution where one or more hyperparameters appear. The estimation of these parameters is crucial for obtaining good reconstruction quality. Several approaches (heuristic or sophisticated) allow to estimate these parameters iteratively (see, e.g., Xing et al., 2017, Calatroni et al., 2019 for maximum likelihood approaches). However, in many cases, such estimation is performed globally, without taking into consideration the spatial variability of image contents. On the other hand, recent deep-learning-based approaches have been shown to be very effective for several image reconstruction and image analysis problems such as the estimation of classification classes or representative features associated to a set of data, Xing et al., 2017.

* X. Descombes, R.D. Morris, J. Zerubia, M. Berthod, Estimation of Markov Random Field Prior Parameters Using Markov Chain Monte Carlo Maximum Likelihood, IEEE Trans. on Image Processing, 8(7), 1999.

* L. Calatroni, A. Lanza, M. Pragliola, F. Sgallari, A Flexible Space-Variant Anisotropic Regularization for Image Restoration with Automated Parameter Selection, SIAM Journal on Imaging Sciences, 12(2), 2019.

* F. Xing, Y. Xie, H. Su, F. Liu, L. Yang, Deep Learning in Microscopy Image Analysis: A Survey, IEEE Transactions on Neural Networks and Learning Systems, 29(10), 2017.


The objective of this internship project is the development of a deep-learning-based approach for the estimation of locally varying hyperparameters following, for instance, the learning approaches detailed in Afkham et al. 2021. For this task, the training set will be constituted by patches extracted from natural images coupled with parameter values of the particular model at hand optimised in terms, e.g., of some standard quality measure, such as, e.g., the PSNR, the SSIM. For the numerical tests, hyperparameter maps will be estimated by the networks considered by considering different patches centred at each image pixels.

In a former M2 internship project, a well-performing CNN was conceived for the problem of image denoising, showing very good and robust performance for the exemplar Total Variation denoising model. Our preliminary tests on the use of a similar strategy for the problem of image deconvolution (with unknown PSF, that is a blind deconvolution problem) showed that some significant changes and a better insight on the architecture considered need to be done to deal with this more challenging task.

Different case studies on several simulated and real microscopy images will be tested in order to validate the approach proposed.

* B. Maboudi Afkham, J. Chung and M. Chung, Learning regularization parameters of inverse problems via deep neural networks, Inverse Problems 37(10), 2021.

Candidate profile:

Second year of Master degree in applied mathematics, data science and computer science with background in image processing, imaging inverse problems, deep learning and optimisation. Good coding skills for numerical simulation (Python, MATLAB, ...). A general interest in health and biology is welcome.


Please send your CV and a motivation letter to Xavier Descombes (, Luca Calatroni (