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STUDENT PROJECTS

Proposals

On-going Projects

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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:7

Dictionary Learning for Limited Angle Computed Tomography

Master Semester Project: Available

Computed tomography (CT) is a method for creating a 3D image of a sample. It proceeds by computationally combining many projection images (e.g., the X-ray image a doctor might take of a broken bone), taken from different angles. In some applications, a full 180į view of the object is not feasible. In the last decade, iterative procedures which exploit sparsity have been used for limited angle CT reconstructions. In this project, the student will apply a dictionary learning algorithm for limited angle CT to exploit redundancies in the measurements. Good Matlab skills are required for this project. For further details, donít hesitate to send a mail.

Supervision:

Sparse Signal Reconstruction using Variational Methods with Fractional Derivatives

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. We have recently proved that when using the L1 norm for the regularization, this reconstructed signal is sparse in the continuous-domain. The sparsity is enforced via a regularization operator: for example, the derivative leads to piecewise-constant solutions (total variation), while the second derivative yields piecewise-linear solutions. The goal of this project is to investigate novel regularization operators, namely fractional derivatives which allow us to vary continuously e.g. between the derivative and the second order derivative. The work would also include the design and implementation of an algorithm for signal reconstruction. The student should have strong mathematical interests (particularly in functional analysis), and basic knowledge of optimization theory.

Supervision:

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 (http://bigwww.epfl.ch/algorithms/globalbioim/) 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.

Supervision:

(Theoretical Project) Sparse Learning with Gaussian Kernels

Master Diploma Project: Available

The theory of reproducing kernel Hilbert spaces includes a large class of positive-definite kernels that can be used in different machine learning problems. Among the many choices, Gaussian kernels are the most popular and classical ones. Recently, we have developed a theory for continuous domain sparse learning using an adaptive kernel expansion. However, this theory is currently incompatible with Gaussian kernels. The goal of this project is to extend our theory to cover the Gaussian kernels. It requires a study beyond tempered distributions in order to consider Gaussian kernels as the Greenís function of some suitable operators. The student should have a solid understanding of functional analysis and distribution theory, and basic knowledge of convex optimization.

Supervision:

(Theoretical Project) Convergence Analysis of Grid-based Algorithms for Sparse Learning

Master Diploma Project: Available

Broadly speaking, machine learning algorithms aim to find an input-output relationship based on a (usually large) set of training examples. This is typically achieved by solving an optimization problem with a regularization term that reduces overfitting. In particular, sparsity-promoting regularizers lead to model simplifications and make the handling of large training datasets easier. We recently developed a theory for sparse learning that characterizes the form of the solution to this optimization problem in the continuous domain (i.e., the learned output is a parametric function). Based on these theoretical results, a grid-based discretization scheme has been proposed and implemented. The goal of this project is to study the convergence of these discretized problems in relation to the underlying continuous-domain problem in different setups. The ideal outcome would be to obtain bounds for the error rate as the grid goes finer. The student should have a solid understanding of functional analysis and convex optimization.

Supervision:

(Theoretical Project) Slowly Growing Poisson Processes

Master Diploma Project: Available

Poisson processes are used to model sparse 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 link the decay rate of its jumps probability with the (almost surely) inclusion of the process in the space of tempered distributions. This has recently been shown using advanced mathematical tools. Here, the aim is to find an elementary proof by studying the existence of moments of the law of jumps. The student should have a solid understanding of functional analysis and probability theory.

Supervision:

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.

Supervision:

2019 EPFL • webmaster.big@epfl.ch26.06.2019