Space-Variant Hyperparameter Estimation in Image Microscopy
Inverse Problems by Deep Learning
M2 internship proposal for spring 2020 (Duration: 5/6 months)
Supervisors: Xavier Descombes (email@example.com), Luca Calatroni (firstname.lastname@example.org)
Host institution: MORPHEME research group (INRIA, CNRS, I3S, Sophia-Antipolis, France)
Over the last years, 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 assumption
on the solution where one or mor 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., [2, 1] 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 .
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, by means of U-NET  or the unrolling
strategy considered, e.g., in . For this task, the training set will be constituted by patches of reduced size
associated to optimal values of the parameters which will be created either by a simulation of the model
considered to which perturbations will be added or from samples extracted from real images on which the
parameters will be empirically adjusted. For the numerical tests, hyperparameter maps will be estimated by
the networks considered by considering different patches centred at each image pixels. We will compare the
results obtained with the ones computed by a direct deep-learning approach where no modelling is encoded.
Different case studies on several simulated and (possibly) real microscopy images will be tested in order
to validate the approach proposed.
Second year of Master degree in computer science, applied mathematics, data 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.
MORPHEME research team is a joint research group between INRIA Sophia Antipolis M´editerran´ee., I3S
Lab (Universit´e Cˆote d’Azur and CNRS).
Remuneration: internship gratification (approximately 550 euros/month) and possible discounts for nearby
accommodation facilities (CIV).
Please send your CV and a motivation letter to Xavier Descombes (email@example.com), Luca Calatroni
 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),
 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,
 G. Dardikman-Yoffe, Y. C. Eldar, Learned SPARCOM: unfolded deep super-resolution microscopy,
Optics Express, 28 (19), 2020.
 O. Ronneberger, P. Fischer, T. Brox, U-Net: Convolutional Networks for Biomedical Image Segmentation,
In: Navab N., Hornegger J., Wells W., Frangi A. (eds) Medical Image Computing and Computer-
Assisted Intervention – MICCAI 2015. MICCAI 2015. Lecture Notes in Computer Science, vol 9351.
Springer, Cham, 2015.
 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.
(c) GdR 720 ISIS - CNRS - 2011-2020.