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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:11

Resolution improvement by 3D multiview reconstruction in SPIM imaging

Master Semester Project: Available

Selective plane illumination microscopy (SPIM) is a fluorescence imaging technique that has gained great interest in the microscopy community in recent years. It improves resolution thanks to a perpendicular illumination of the sample with a light sheet, which enables to excite only a very narrow area of the sample and produce good optical sectioning. However, the shape of light sheet tends to deform itself when going through large samples, which causes visual artefacts and a loss of resolution. In this project, the student will develop reconstruction methods taking into account the spatial variability of the light sheet. The first step will be to model and estimate the variation of the point spread function in the sample. The second step will be the deconvolution of the sample using the spatially varying PSF. In a final step, the student will extend his work to reconstruction with mutliple views.

Supervision:

3D Steerable Filter Learning for Efficient Volumetric Image Analysis

Master Semester Project or Master Diploma Project: Available

The use of deep convolutional neural networks (CNN) for object recognition in computer vision has shown to provide excellent results in many applications. Deep CNNs learn multiple filters in each convolutional layer of a deep neural network architecture using backpropagation weight updates. A major drawback of the latter is the requirement of large amounts of training data and computational time to learn all pixel weights (i.e., free parameters) of the filters. Moreover, CNNs are not rotation-invariant and require extensive re-training with augmented data (e.g., rotated versions of the training images), which degrades the specificity of the learned filters. Steerable filters are used on image analysis as efficient and accurate rotation-invariant object detectors. They are excellent candidates to overcome these drawbacks. The 2D theory has been recently adapted to classification problems and applied to texture analysis. The goal of this project is to extend the framework to the 3D setting, where rotation-invariance is even more important. This presents both mathematical and implementation challenges.

Supervision:

Building a Theory for Hermite L-splines

Master Semester Project: Available

The theory of L-splines is a unifying representation of classical splines relying on differential operators. Recently, we focused on new spline models inspired from Hermite interpolation. Hermite splines differ from their classical counterpart by incorporating information about derivatives (possibly of various orders) at each control point location. We have been able to build several Hermite spline families, but are lacking a global theoretical framework that would comprise them all. The goal of this project is to build a general theory of Hermite L-splines, where L is a suitable differential operator. This implies studying the required properties of the operator, show that the existing Hermite spline families fit in the unifying representation, and derive new families. Strong mathematical interest is required, and knowledge on approximation theory and functional analysis is a plus.

Supervision:

Convergence of Discretized TV-Regularization Schemes to L-splines

Master Semester Project or Master Diploma Project: Available

We have recently shown that any generalized TV-regularization problem in continuous-domain is minimized by a non-uniform spline whose knot locations are not fixed a priori. This result was exploited to design new spline-based algorithms which are able to reconstruct spars e signal from their noisy measurements. The strategy we follow is to discretize the real axis into a uniform grid and to find the optimal spline with knots on the grid. We expect the procedure to converge to the optimal spline when the grid gets finer and finer. The goal of this project is to provide theoretical and/or experimental evidence of this convergence.

Supervision:

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.

Supervision:

Deep Learning for Image Inpainting

Master Semester Project or Master Diploma Project: Reserved

Image inpainting recovers missing information within images, for instance the data underlying blemishes from antique pictures. Another use is to counteract photo bombers by allowing for the erasure of unwanted elements. The most recent inpainting methods rely on various optimization methods, in particular, on iterative convex optimizers. However, this type of optimization methods are computationally demanding. Nowadays, convolutional neural network (CNN) are becoming a popular solver of various inverse problems in the framework of supervised deep learning. It is observed that the performance and speed of reconstruction of CNN are noticeably improved compared to conventional iterative optimization methods. However, until now, there is a lack of CNN approaches for image inpainting. The student's task will be to explore a CNN-based reconstruction method. The implementation will take advantage of the MatConvNet toolbox of MATLAB.

Supervision:

B-spline implementation to find the solution of continuous domain total-variation minimization problem

Master Semester Project: Reserved

In MRI and other real world applications, the measurements are generally obtained through a continuous-domain transformation of a continuous-domain signal (Fourier samples for MRI case). Yet, for computational feasibility, the inverse problem formulated to numerically reconstruct the signal from these measurements, are often formulated in discrete-domain. Continuous-domain formulation of inverse problems therefore can be advantageous in this sense, provided there is a way to tackle the computational complexity of the reconstruction task. Recently in [1], the solution for inverse problems in continuous domain with Total variation regularization is found out to be non-uniform spline. To perform the reconstruction we use Green's function of the operator used in regularization, as the dictionary basis. However, this often results in ill-conditioned system matrices leading to poor convergence rate. We propose a student project to use the corresponding B-splines as the dictionary basis for the TV-regularized solution. The resultant system matrix in this case is expected to be better conditioned and an appropriate algorithm can result in faster convergence to a solution. The task will be to effectively implement this formulation and contrast it with the results of the previous formulation. The student will have to understand the theoretical background of the problem and convex optimization techniques, and then implement the formulation in MATLAB. Prerequisites: Convex optimization [1] M. Unser, J. Fageot, and J. P. Ward, “Splines are universal solutions of linear inverse problems with generalized-TV regularization,” arXiv preprint arXiv:1603.01427, 2016.

Supervision:

Learning Approach for Image Restoration

Master Semester Project or Master Diploma Project: Reserved

l1-minimization has proved a powerful tool for image restoration. In this framework, the degraded image is iteratively deblurred in the space-domain and denoised with a soft thresholding in some transform-domain in which the original image is supposed to be sparse. In this project, we will adopt a learning approach to optimize the denoising step. Instead of using a soft thresholding, we learn a nonlinear shrinkage function from a collection of images and their synthetically degraded versions. The sparsifying transform can also be learned to improve the performance of the restoration. You are supposed to implement a learning algorithm for some reconstruction method such as total variation. Prerequisites: a good knowledge of image processing, linear algebra, a little vector calculus, and a little nonlinear optimization.

Supervision:

Building Experimental 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 pont 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 a image-processing module to select the "good" beads and to perform accurate localization first before to reconstruct a sharp PSF. The module should be enough flexible to handle various engineering PSF, like the astigmatism PSF or the double-helix PSF. The module will be a Java plugin of ImageJ or Icy.

Supervision:

Blind deconvolution for high resolution microscopy

Master Semester Project: Available

In the last decades, optical microscopy has made huge steps toward high spatial resolution reaching now few 10s nm scale. These super-resolution has been made possible by intensive research in optics and fluorochrome engineering, and there is still room for improvements by careful data processing. In this project, the student will extend the blind deconvolution algorithm we have previously developed for wide field microscopy to higher resolution modalities as confocal, two-photons and light-sheet microscopy. The code will be developed in JAVA to be used as a plugin in the Icy software.
Check the demonstration on You tube.

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:

2017 EPFL • webmaster.big@epfl.ch17.03.2017