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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:10

Riesz Steerable Filters for Advanced Pattern Detection on 3D Images

Master Diploma Project: Available

Steerable filters provide a state-of-the art method based on a solid and beautiful mathematical theory to detect positions and orientations of patterns of interests on biomedical images. It can be incorporated as a tool to enable rotation invariance of convolutional neural networks. The complete detection pipeline is now well understood for 2D images. However, its extension to 3D reveals several stimulating challenges, where the possible directional patterns are much richer. In particular, the classical 3D setting based on spherical harmonics does not have a simple interpretation in terms of pattern characteristics. In this project, the goal is to revisit the 3D setting using Riesz filters for the design steerable detectors. The latter are all-pass filters that are intimately connected to directional derivatives, therefore highlighting the directional characteristics and higher-order transitions of the studied image. The project includes both the development of the adequate mathematical theory and the design of the corresponding detection algorithm. The importance of each part can be adapted to the studentís personal interests.


Statistical Model for Sparse Dictionary Learning

Master Diploma Project: Available

Dictionary learning aims at finding a transform domain on which the training data admits a sparse representation. Most approaches are based on deterministic regularization techniques (e.g., the minimization of L1 norm). We have recently developed a new statistical formulation to learn the dictionary, where the data are modeled as a random vector. The key novelty is to use probabilistic models in line with the sparsity paradigm called symmetric-alpha-stable. The goal of the project is to further extend the mathematics beyond this novel dictionary learning framework. In particular, we aim at formulating the dictionary learning as an optimization problem where the regularization corresponds to a mutual information estimator in the transform domain, under the symmetric-alpha-stable hypotheses. Several extensions shall be investigated in order to increase the applicability of the model on real data.


Poisson Sinogram Resampling

Master Diploma Project: Available

The X-ray transform of a signal measures its integral along all possible lines. It is the mathematical foundation of several tomographic imaging modalities including X-ray CT, PET, and single particle cryo-EM. Each measurement follows a Poisson distribution, the rate of which is given by a known measurement functional applied to the X-ray transform. The goal of the project is to study the resampling of the set of available measurements to obtain an approximation of unknown measurements, using statistics and sampling theory. The procedure will eventually be used as a preprocessing step to accelerate the recovery of the signal from its measurements. Thus, the resampling itself must not depend on recovering the full signal.


Signal Reconstruction Using Variational Methods Based on Lp Norms

Master Diploma Project: Available

Continuous-domain signals can be reconstructed from their discrete measurements using variational approaches. The reconstructed signal is then defined as a minimizer of a functional, which is composed of a convex combination of two terms, namely data-fidelity (quadratic) and regularization. This project aims at considering new regularizations characterized by the choice of the function norm (Lp norm) and the associated regularization operator. The classical L2 norm relies on the theory of reproducing kernel Hilbert space (RKHS), and we have recently obtained breakthrough results using L1 norm (total variation), yielding solutions that are sparse in the continuous-domain. Investigating the transition between p=1 and p=2 requires the development of new mathematical tools and will be at the heart of the project. The work also includes the design of new algorithms for signal reconstruction, with potential applications in machine learning and neural networks. The student should have strong mathematical interests and basic knowledge on optimization theory.


Two dimensional SIM reconstruction from 4 images

Master Semester Project: Available

Structured Illumination Microscopy (SIM) allows us to improve the resolution of classical wide-field imaging systems by moving high-frequency components into the observable microscope region. When dealing with 2D data, one generally requires 9 patterned images to reconstruct a super resolved image. Reducing this number of images is essential in order to improve temporal resolution of the system. The first part of this project will consist in showing properly that 4 patterned images are in fact sufficient to reconstruct a super resolved image (consistent system of equations). Based on this analysis, the second part of the project will be devoted to the development of a direct algorithm (non-iterative) requiring only 4 input images.


Benchmarking of numerical methods for solving inverse problems

Master Semester Project: Available

Inverse problems are at the heart of many microscopy and medical imaging modalities where one aims at recovering an unknown object from given measurements. Such a problem is generally addressed through the minimization of a given functional composed of a data-fidelity term plus a regularization term. Within the Biomedical Imaging Group, we are currently developing a Matlab library ( unifying the resolution of inverse problems. This library is based on several blocks (forward models, data-fidelity terms, regularizers, algorithms) that can be combined to solve any inverse problem. Given an imaging modality, one can thus easily compare methods that use different data terms, regularizers or algorithms. The goal of this project is to develop a Matlab code which, for a given modality, outputs in an elegant way different metrics showing the performances obtained using all the combinations of blocks (forward models, data-fidelity terms, regularizers, algorithms) that are available within the Library.


Shape analysis of C. elegans datasets using dictionary learning

Master Diploma Project: Reserved

Sparse dictionary learning is a powerful approach for revealing patterns in datasets. The idea of this project is to transpose the concept to the representation of parametric curves with, as a goal, the description of shape variability and motion types of C. elegans worms. The input data will consist of video sequences of swimming C. elegans worms, where the worm contours are outlined by spline curves in each individual image. The shape dictionnary will then be constructed considering this large collect of spline curves and some sparsity constraints. This should provide a new efficient way to describe the shape and motility of worms and help in the identification of particular phenotypes in a high-throughput screening context. Good notions on the theory of signal and image processing are strongly advised, and experience with Matlab/Mathematica is recommended.


Slowly Growing Poisson Processes

Master Semester Project: Available

Poisson processes are used to model sparse and piecewise-smooth signals. They are pure jump processes characterized by the law of the jumps and the average density of knots. The properties of the law of the jumps is intimately linked with the asymptotic behavior of the process. The goal of this project is to prove that a Poisson process is slowly growing (that is, bounded by a polynomial) if and only if the law of jumps has some finite moment. This result has been proven very recently with advanced technics, but we aim now at obtaining a short and relatively elementary proof. The student should have strong mathematical interests, with basic knowledge on probability theory and functional analysis.


Learning 3D Point-Spread Function (PSF) for Super-Resolution Microscopy

Master Semester Project: Available

In fluorescence microscopy, it is of utmost importance to get the 3D point-spread function (PSF) for several image-processing, like deconvolution, super-resolution reconstruction of images, or single-molecule localization microscopy. The PSF give the answer of the optical system to a point source, it characterizes the image formation model. To get a PSF, microscopists generally acquire a z-stack of a field of fluorescence small beads (eg. 100nm) and then pick up the good ones to average them. The drawback of this method is to create blurred PSF. In this project, we propose to design and to implement an image-processing method that jointly estimates the position of the beads and reconstructs a sharp PSF. In particular, the objective is to take into account in the method the size of the bead instead of considering it as a point source like in the traditional method.


Image-based quantification of cell blebbing

Master Semester Project: Available

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.


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