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STUDENT PROJECTS

Proposals

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Conditions : The Bachelor Semester Projects and Master Semester Projects are only reserved for regular EPFL students or for students of enrolled in am official mobility program.

Project Proposals

All Project

Number of projects:13

Continuous-domain multicomponent image reconstruction with mixed regularization

Master Semester Project: Reserved

The problem of reconstructing biomedical images based on measurements from our acquisition system (microscopy, X-ray tomography, etc) is known as an inverse problem, which is typically formulated and solved as an optimization task. When one has some prior knowledge on the form of image (eg, sparsity in a transform domain or smoothness), one can enforce that the reconstructed image follow this prior by adding a suitable regularization term to the cost function. In this project, we consider a multicomponent image model, where each component follows different priors. More specifically, the first component is assumed to be piecewise-constant and is treated with total-variation regularization; the second is assumed to be smooth and is treated with a Laplacian-based regularizer. The reconstruction is done in the continuous domain by using a spline basis. The reconstruction algorithm will be implemented in Matlab using the GlobalBioIm library [1]. The student should be interested in biomedical imaging, optimization and functional analysis.
References:
[1] Soubies, E., Soulez, F., McCann, M. T., Pham, T. A., Donati, L., Debarre, T., ... & Unser, M. (2019). Pocket guide to solve inverse problems with GlobalBioIm. Inverse Problems, 35(10), 104006.

Supervision:

Differentiable Approximation of Hessian-Schatten Regularization for Image Reconstruction

Master Semester Project: Reserved

To reconstruct an image from given measurements, one usually solves a so-called inverse problem. The task is carried out by minimizing a cost function that consists of two terms: The first one is a data-fidelity term that ensures consistency with the measurements. The second one is a regularization term that imposes some prior knowledge about the image.
In [1], Lefkimmiatis et al. proposed the Hessian-Schatten seminorm (HS) as a novel regularizer for image reconstruction. Since it is not differentiable, proximal algorithms are the common way to solve the inverse problem. However, there are cases for which proximal algorithms are not applicable (e.g., deep image prior [2] combined with the HS).
In this project, the student will design differentiable approximations of the HS regularizer and implement them within the GlobalBioIm library (Matlab) [3]. The student will then apply the new regularizers on some common inverse problems (e.g., image deconvolution).

References
[1] S. Lefkimmiatis, J. P. Ward and M. Unser, "Hessian Schatten-Norm Regularization for Linear Inverse Problems," in IEEE Transactions on Image Processing, vol. 22, no. 5, pp. 1873-1888, May 2013, doi: 10.1109/TIP.2013.2237919.
[2] Ulyanov, D., Vedaldi, A., & Lempitsky, V. (2018). Deep image prior. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (pp. 9446-9454)
[3] Soubies, E., Soulez, F., McCann, M. T., Pham, T. A., Donati, L., Debarre, T., ... & Unser, M. (2019). Pocket guide to solve inverse problems with GlobalBioIm. Inverse Problems, 35(10), 104006.

Supervision:

Lightweight Deep Models for Dynamic MRI

Master Semester Project: Reserved

Dynamic MRI requires rapid data acquisition for the study of moving organs such as the heart. Existing reconstruction methods suffer from restrictions either in the model design or in the absence of ground-truth data, resulting in low image quality. Recently, we introduced a generalized version of the deep-image-prior approach, which optimizes the network weights to fit a sequence of sparsely acquired dynamic MRI measurements. Our method outperforms the existing state-of-the-art methods, but the model is very heavy and takes a long optimization time. These days, reducing the computations is one of the big issues in the deep learning community not only for an efficient application but for our environment. In this project, we aim to reduce the model size while retaining the performance as much as possible. The student should have solid programming skills, in particular being familiar with PyTorch and a general understanding of the main concepts of deep learning.

Supervision:

Effect of Simple Operations on the Linear Regions of Continuous Piecewise Linear Functions

Master Semester Project: Reserved

It is known that ReLU neural networks provide continuous and piecewise linear (CPWL) mappings. In other words, the input domain can be partitioned into regions on which the neural network is an affine function. The number of these so-called linear regions is therefore a metric for the complexity of the network. In this project, we want to understand how linear regions of CPWL functions are modified through simple operations (e.g. addition, composition, max, ...). In particular, we propose to analyse in-depth the statistics of the number of linear regions of the composition of CPWL functions in low dimensions. The project requires a good understanding on deep neural networks and solid programming skills.

Supervision:

Using regularization to reduce the number of projection angles in optical projection tomography

Master Semester Project: Reserved

Optical projection tomography (OPT) typically requires hundreds or thousands of projection angles in practice to acquire enough measurement data. This increases data acquisition time and light dose on the sample. By incorporating total-variation (TV) regularization, one can significantly reduce the number of projection angles without deteriorating the reconstruction quality. [1] In this project, the student will 1) use GlobalBioIm [2] library to construct a forward model equivalent to 3D Radon transform, 2) build an iterative reconstruction scheme with TV regularization, 3) evaluate the performance of this algorithm with/without regularization on a simulated 3D ground truth. The student should be good at image reconstruction and optimization algorithms, and experienced with Matlab. References: [1] Correia T, et al. Accelerated Optical Projection Tomography Applied to In Vivo Imaging of Zebrafish. PLoS One. 2015 Aug 26;10(8):e0136213. [2] E. Soubies, F. Soulez, M. T. McCann, T-A. Pham, L. Donati, T. Debarre, D. Sage, and M. Unser. Pocket Guide to Solve Inverse Problems with GlobalBioIm, Inverse Problems, 35-10, 2019.

Supervision:

Phase Retrieval in the GlobalBioIm library

Bachelor Semester Project or Master Semester Project: Reserved

GlobalBioIm is an open-source library to facilitate the implementation of models and algorithms in imaging, developed in the Biomedical Imaging Group. Its flexibility enables various applications such as fluorescence microscopy, magnetic resonance imaging (MRI), or X-ray tomography. In the past few years, recent advances in phase retrieval provide new algorithms to find x in the non-linear equation y = |Ax|^2. These new algorithms have only started to be applied in computational imaging. In this project, the student would implement and test these novel phase retrieval algorithms (spectral methods) in the GlobalBioIm library. This would help the student develop proficiency in MATLAB. This step would then enable a more exploratory study, with new applications in other imaging settings, thanks to the modularity of GlobalBioIm. Reference: Soubies, E., Soulez, F., Mccann, M. T., Pham, T. A., Donati, L., Debarre, T., ... & Unser, M. (2019). Pocket guide to solve inverse problems with GlobalBioIm. Inverse Problems, 35(10), 104006.

Supervision:

Deep learning for 3D particle field imaging

Master Semester Project: Reserved

Particle fields include a large range of samples of interest, such as bubbles, droplets, or biological cells. To obtain a three-dimensional (3D) volume of such fields, one popular method involves in-line digital holography (DH). In this imaging modality, the particle field is illuminated with an incident field (light) so that multiple scattering and diffraction occur. The resulting field is then holographically recorded. From a single two-dimensional (2D) DH image, computational methods are able to recover the particles within a 3D volume. When the density of particles and/or the depth of field are large, the reconstruction task becomes too difficult for conventional methods.
During this project, the student will implement and train a neural network to recover particles within a 3D volume from a 2D image. The programming language is Python (Pytorch). Based on an existing code in Matlab, the student will also implement the physical model which describes the wave propagation in Pytorch. The required skills are prior knowledge of deep learning, proficiency in coding in Pytorch. The student should be able to learn the basics of wave propagation and optics during the project.
During this project, the student will understand the physical model of an imaging modality, learn how to conduct a complete project with deep learning, and learn how to use a physical model combined with deep learning.
References Tahir, W., Kamilov, U. S., & Tian, L. (2019). Holographic particle localization under multiple scattering. Advanced Photonics, 1(3), 036003.

Supervision:

Sparse-View Computed Tomography Reconstruction using Generative Adversarial Networks

Master Diploma Project: Available

In computed tomography (CT), the goal is to reconstruct a 3D object from a set of its 2D projections. Typically, this reconstruction task is formulated as an optimization problem where one exploits certain properties of the signal of interest (e.g., sparsity in a transform domain). However, over the past decade, several learning-based methods have been shown to outperform the classical reconstruction methods. In this project, we consider a setting where relatively fewer projections are available and the idea is to use generative adversarial networks (GANs) for the reconstruction task. The student should be familiar with the PyTorch framework and should have a general understanding about basic deep learning concepts. Prior experience in inverse problems and/or optimization is a definite plus.

References: [1] H. Gupta, K.H. Jin, H.Q. Nguyen, M.T. McCann, M. Unser, "CNN-Based Projected Gradient Descent for Consistent CT Image Reconstruction" [2] A. Bora, A. Jalal, E. Price, A. G. Dimakis, "Compressed sensing using generative models"

Supervision:

High-resolution reconstruction in single-particle cryo-EM with a multiscale joint refinement scheme

Master Diploma Project: Reserved

Single-particle cryo-electron microscopy (cryo-EM) has revolutionised the field of structural biology over the last decade, culminating in 2017 by the awarding of the Nobel Prize in Chemistry to its three founders. Nowadays, single-particle cryo-EM permits the regular discovery of new biological structures at atomic resolution. Yet, the reconstruction task remains an enduring challenge due to the unknown orientations adopted by the 3D particles prior to imaging. The goal of this project is to further strengthen a recently-developed joint optimization scheme that efficiently alternates between the reconstruction and the estimation of the unknown orientations [1]. More precisely, the student will introduce a multiscale scheme [2] inside the iterative-refinement framework itself to benefit from the robustness gained by reconstructing volumes at coarser scales. The student should have a strong interest in image processing, and good Matlab skills are a prerequisite. An interest in inverse problems and/or optimization theory is a definite plus. References: [1] M. Zehni, L. Donati, E. Soubies, Z. Zhao, M. Unser, "Joint Angular Refinement and Reconstruction for Single-Particle Cryo-EM," IEEE Transactions on Image Processing, vol. 29, pp. 6151-6163, 2020. [2] L. Donati, M. Nilchian, C.Ó.S. Sorzano, M. Unser, "Fast Multiscale Reconstruction for Cryo-EM," Journal of Structural Biology, vol. 204, no. 3, pp. 543-554, December 2018.

Supervision:

High-speed imaging with any camera

Master Diploma Project: Available

High speed imaging can be achieved with any camera, as has recently been demonstrated with the Virtual Frame Technique. Using this method, any monotonic phenomenon that is imaged instantaneously with perfect contrast (such that the image is binary) can be recorded at high rates by increasing the exposure time of the camera. Thus, complex temporal dynamics can be recorded at high rates and high resolution, averting the traditional trade-off between size of the region of interest and imaging rate. In this project we explore the limits of this method, using a dual-approach of experimental demonstration and theoretical analysis. Project in collaboration with Engineering Mechanics of Soft Interfaces (EMSI) laboratory (https://www.epfl.ch/labs/emsi/).

Supervision:

Learning Piecewise-Constant Functions to Classify and Cluster

Master Diploma Project: Available

Classification and clustering are some of the most important objectives in supervised and unsupervised learning, respectively. Interestingly, in both scenarios, the learning scheme eventually produces a piecewise-constant function. This remarkable property allows one to analyze them jointly. The goal of this project is to develop a variational framework to estimate piecewise-constant functions and to derive an efficient learning algorithm, built as a module. One can then also use this module in deep neural networks and compare the performance with classical setups for various applications of classification and clustering.

Supervision:

Homotopy Methods for Regularized Inverse Problems

Master Semester Project: Reserved

In an inverse problem, the objective is to reconstruct a signal from a set of measurements. This is typically achieved by solving an optimization problem with a data-fidelity term that enforces the consistency between the reconstructed signal with the measured data. When the problem is ill-posed, a common technique is to add a regularization term that is based on our prior knowledge on the form of the signal. A regularization parameter then balances the weight between the data fidelity and the regularization terms. The choice of this parameter is crucial, and it is typically hard to tune. Hence, homotopy methods aim to solve the optimization problem for all possible values of the regularization parameter, so that the user can choose a suitable one. The goal of this project is to investigate such methods for some specific discrete inverse problems, starting with a literature review, and to implement an algorithm in practice. As the project is somewhat exploratory, the student should be able to take initiative and to work autonomously. He or she should also have strong mathematical interest, particularly in the field of optimization.

Supervision:

Image-based quantification of cell blebbing

Master Semester Project: Reserved

Blebbing is a very dynamic phenomenon that plays an important role during apoptosis, cell migration, or cell division. Using time-lapsed microscopy techniques, phase contrast and fluorescence, biologists can observe blebs which are spherical protrusions which appear and disappear on the membrane of the cell. The goal of the project is to design and to implement image-analysis algorithms based on active contour and curve optimization take into account the blebbing. It requires a automatic segmentation of the cell over the multichannel sequence of images and a local extraction of the bulges to quantify blebbing. The project will be implemented in Java as an ImageJ plugin with an user interface allowing a manual edition of the outlines of the blebs.

Supervision:

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