Biomedical Imaging Group

Student Projects

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STUDENT PROJECTS

Proposals On going Completed Conditions:The projects are reserved for EPFL students or students of mobility program.

Project Proposals

All Project

Number of projects:25

Extracting high-speed insect behavior at micrometer precision

Master
project: Reserved

Insects exhibit robust terrestrial locomotion while relying on a relatively small and simple controller, the nervous system. This makes it an ideal source of bio-inspiration for robust legged walking robots. However, owing to the tiny size and rapid kinematics of most insect behavior we cannot model this behavior precisely without advanced computer vision approaches.

The main objective of this project is to develop an algorithm for extracting the leg positions of freely walking flies in high-speed, high-resolution movies. Ultimately, the goal is to perform a quantitative analysis of the means by which flies use dynamic gaits to achieve optimal avoidance of other flies during collective behavior. This new knowledge will provide inspiration for efficient and robust robotic locomotion as well as a substrate for further studies into neural control of gait in animals.

A preliminary breakdown of the project follows:

1. Propose a suitable active-contour model. In particular, a) search the literature for mathematical models of leg joints in insects and b) investigate whether these can be used to constrain active contours for better fitting results.
2. Build upon existing code developed at the Biomedical Imaging Group to fit the model to fruit flies in still images.
3. Incorporate the procedure into a complete tracking framework for processing video sequences.
4. Extract biologically relevant data and, if possible, publish the results.

The project will primarily be supervised at the Biomedical Imaging Group (EPFL), in close interaction with the Laboratory of Intelligent Systems (EPFL) and in collaboration with the Benton Lab (UNIL).

Image super-resolution from interpolated edges in the Riesz-wavelet domain

Master
project: Available

In a recent work, we have demonstrated that one can obtain accurate image reconstruction from Riesz-wavelet coefficients located on edges. This shows that these coefficients contain the essential information of the natural images and the biomedical images that we have tested. The goal of this project is to use this finding to build super-resolutive images. We propose to extrapolate edges at finer wavelet scales using the Riesz-wavelet coefficients located at edges in the coarser bands. This would involve defining a method for edges extrapolation at different scales that uses the Riesz-wavelet coefficients from upper scales, and reconstructing the images with custom optimization tools.

Variational formulation of MMSE-type estimators for sparse processes

Master
project: Available

In recent work, we have introduced a broad class of sparse processes whose statistical distribution can be determined analytically. We have also shown how to specify MAP estimators for such processes that are compatible with the popular algorithms for sparse signal recovery (e.g. TV regularization). A basic limitation, however, is that the standard MAP criterion does not offer any guarantee of optimality with respect to mean square error (MSE), except in the Gaussian case. The purpose of this project is to develop a methodology for specifying pseudo-MAP estimators—that is, estimators that minimize a modified energy functional—in order to achieve better MSE performance. A test bed for developing such estimators is the family of Lévy processes for which an extensive toolkit is available in the laboratory (generation of processes, implementation of a variety of MAP estimators, as well as the MMSE solution which can serve as gold standard).
Relevant paper: M. Unser, P.D. Tafti, Stochastic Models for Sparse and Piecewise-Smooth Signals IEEE Transactions on Signal Processing, vol. 59, no. 3, pp. 989-1006, March 2011.

Biological Particles with Levy Motility

Semester
project: Reserved

We have a movie (which is a sequence of frames) of the motion of a particle. This particle could be any moving biological particles, as fluorescent particles, bacteria or etc. Because of the imperfections of the measurement equipment, the detected location for the particle is corrupted by noise. Now, using this movie, we would like to estimate the real path of the particle. The goal is to implement a MATLAB code that takes the noisy movie and gives the denoised version.
We assume that the motion of the particle is a Levy process (as a special case, a Brownian motion). Also, the measurement noise is assumed to be Additive White Gaussian Noise.
As an extra step, we can suppose situations in which there are more than 1 particle in the movie and try to track them.

Characterization of G protein coupled receptors by image analysis

Semester
project: Reserved

G protein coupled receptors (GPCRs) are transmembrane proteins responsible for signal transmission between cells or between a cell and its environment. They are involved in vision, olfaction and audition as well as in growth, memory or sleep regulation for example. Due to their central role in cellular signalling, GPCRs are targeted by 50% of modern medicines. We have developed a bioanalytical platform enabling the study of GPCRs in their native membrane transferred inside-out from live cells to beads. We now use this bioanalytical platform to study the activation of adenosine receptors upon fluorescent ligand binding. This receptor is involved in sleep regulation and reacts upon caffeine intake.
The goal of the project is design image-analysis algorithms: 1) to track the fluorescent receptors in noisy images 2) to extract the intensity profile over time and 3) to identify these intensity signatures based on a priori simple models.
The program will be implemented as Java plugin for ImageJ.
Collaboration: Sophie Roizard, Laboratory of Physical Chemistry of Polymers and Membranes, EPFL
Prerequisites: a course on image processing

GPU accelerated 3D deconvolution

Semester
project: Available

In this project our aim is to accelerate a 3D deconvolution algorithm using a Graphical Processing Unit (GPU). In a first part, the student will implement the critical modules of the algorithm in the GPU. After completing this part, the whole deconvolution algorithm will be transferred to the GPU. The student is expected to have good programming skills in C/C++, and motivation to learn about GPU libraries (CUDA or OpenCL depending on available hardware).

Variational decomposition of images

Semester | Master
project: Available

Traditional variational denoising seeks to separate measurement noise from data by way of imposing different penalties (regularity criteria) on each.  Specifically, this is achieved by formulating denoising as the problem of minimising a cost function

J(u) = J1(y-u) + J2(u)

where y denotes the noisy measurements, u is the reconstructed (i.e. denoised) data, and the difference y-u is attributed to noise. In this formulation, J1 measures the discrepancy between the noisy measurements and the reconstruction, and is often referred to as the data fidelity term, while J2 imposes our prior assumptions or information on the data by way of promoting solutions that are more `regular' in some specific and appropriate sense.

The aim of this project is to study extensions of this idea where the original measurements are decomposed into a superposition of `multiple' components (as opposed to the two above) with different distributional characteristics. The intention is to come up with more informative ways of representing and understanding the measurements, which could be useful in restoration as well as analysis of images and other kinds of biomedical data.

Prerequisites: Familiarity with MATLAB; solid understanding of linear algebra

Optical Flow Estimation under Sparsity Constraints

Semester | Master
project: Available

The aim of this project is to formulate the problem of optical flow estimation in the framework of non-quadratic optimisation using sparsity-inducing penalties that impose or enhance certain types of vectorial behaviour while being invariant or quasi-invariant to a variety of geometrical transformations. Prerequisites: Proficiency in MATLAB programming; solid understanding of linear algebra; some familiarity with convex optimisation would be helpful but is not strictly necessary.

Radially-symmetric compactly-supported image modeling

Semester | Master
project: Reserved

The Shannon sampling theorem tells us that 2-D band-limited signals can be reconstructed from their values on a scaled integer lattice, and it provides a reconstruction formula in terms of the sinc function. In practice, one can not compute an infinite amount of data, so Shannon's formula must be truncated. The apodized sinc function has poor decay and it generalizes to 2-D in a separable manner. These properties yield, in turn, unsatisfactory image modeling and interpolation results.
As an alternative, one can define a reconstruction algorithm by using 2-D functions that are non-separable and have fast decay, for example the collection of Wendland functions. These functions have the following properties: 1)They are defined radially, taking a single value along circles about the origin; 2) Along a radial line, they are defined by piecewise polynomials; 3)They have compact support.
The goals of this project are to implement an image interpolation algorithm that utilizes the Wendland functions, to demonstrate their approximation properties, and to compare it with the separable polynomial B-spline model.
Prerequisites: a course on image processing, some coding experience in Matlab or ImageJ

Reconstruction of Signals from Sign Measurements

Semester | Master
project: Available

Recent investigations have shown that it is possible to reconstruct substantial information about signals from mere sign measurements. In particular, good results have been obtained for signals that are well represented in some transform domain (e.g. Wavelets). In this project, the goal is to extend the previous works to a more general measurement model in order to further improve the performance. Prerequisites: Notions of Signal Processing, MATLAB programming, interest in algorithms.

Solving Inverse Problems with Sparsifying Transforms

Semester
project: Reserved

Many naturally occurring signals can be accurately represented by a small number of coefficients in some transform domain (e.g. Fourier, Wavelet). In this work, the objective is to study image estimation by using some transforms potentially beyond traditional ones. We will mostly concentrate on image denoising, i.e. cleaning up a bad quality image. Prerequisites: Basic notions in Image Processing, MATLAB (or Java with ImageJ) programming.

Phase Wrapping in X-ray Differential Phase-Contrast Tomography

Semester
project: Reserved

Many materials in biological samples produce indicative phase shift in the transmitted beam while showing insignificant absorption contrast. Differential phase contrast imaging (DPCI) uses the phase information to retrieve the real part of the refractive index distribution of the object. The mathematical model of DPCI is based on the first derivative of the Radon Transform. One challenge in DPCI is phase wrapping in the measured data. In this project, we aim at presenting a method to diminish the efect of phase wrapping on the reconstructed image.

• Study on DPCI, phase wrapping and iterative reconstruction methods.
• presenting a method to solve the problem (we suggest to find an appropriate regularization term) and implementing in Java
• applying the proposed method on the real data.

Collaboration: Paul Scherrer Institut (PSI).

When the iPhone Meets Fourier

Semester
project: Reserved

Conveying to students the interest of representing an image in the Fourier domain is often a lost cause. One fundamental reason is that human beings are such that their eyes and brain enjoy an inherently spatial perception of the visual world. Thus, interpreting an image in the Fourier domain always will remain an acquired taste. But there is a second obstacle: not only are humans used to a visual perception that is spatial, they are also accustomed to view scenes change through time.

To help overcome this second obstacle, in this project we propose to build a real-time iPhone application that captures images and restitutes them simultaneously as a pair of displays, one depicting each frame as acquired spatially (i.e., a traditional image), and the other one depicting its 2D Fourier transform. By pointing the camera of the iPhone towards various scenes of interest, the Fourier display will change accordingly. This interactive nature of the application should provide for a more memorable experience of Fourier relations with the space domain.

The project will be conducted partly in Java on ImageJ, where issues like the most attractive display of the phase and amplitude of the spectrum of an image will be investigated, along with questions regarding the handling of the colors found in the input image. The bulk of the project will then take place in ObjectiveC on an iPhone, where the real-time aspects of the processing will become crucial.

Requirements: to be following or to have followed the course on image processing taught by Michael Unser.

Object classification with Kinect

project: Available

The recently released Kinect (TM) controller from Microsoft presents an interesting framework for computer vision and image analysis. The aim of this project is to develop a tool for object recognition and classification. The first goal would be to calibrate the device in order to obtain a optimal depth computation. Ultimately, the final software should be able to recognize standard ISO paper sheets and inform the user of their format (A0, A1…). Programming experience (preferably in Java) required.

3D point-spread function of a microscope -- from measured data to realistic optical modeling

Semester
project: Available

The properties of a linear optical system are described by its point-spread function (PSF). This function corresponds to the 3D pattern that originates from a single point-source and it is used in many applications, among which are denoising, deblurring, depth estimation and super-resolution particle localization. It is common practice to obtain the measured PSF a z-stack data of fixed point-sources. Such data, however, suffers from contrast and background noise limitations. It also relies on relatively large point-sources, around 100[nm] in diameter, which makes it less useful for fluorescence super-resolution applications. Voxel interpolation is yet another limitation of the measured PSF. The goal of this project is to fit a theoretical PSF model to such measured data by taking all of theses factors into account. The main stages of the project are: obtain measured PSF data with the collaboration of the bio-imaging and optics platform (PTBIOP) at the EPFL, fit the acquired data with the Gibson and Lanni PSF model, conduct sensitivity analysis to the optical parameters of the model. Prerequisites: a course in image processing, some experience in Matlab or ImageJ coding. Knowledge on optical models of microscopes is a plus.

Image inpainting with second-order diffusion

Semester
project: Reserved

Image inpainting consists in recovering lost or deteriorated parts of an image. For this task, successful numerical methods include diffusion-based schemes. More specifically, this type of algorithm can apply an anisotropic partial differential equation (PDE) to fill in the gaps of the incomplete image. The quality of the restored image depends on the choice of the PDE. The most common approaches employ the gradient or other first-order differential operators. In this project, our goal is to investigate whether the use of higher-order differential operators can restore more details in the solution. In particular, we aim at generalizing current first-order-based PDEs to also include second-order operators based on the Hessian matrix.

Identification of biomarkers in defocussed images

Semester
project: Reserved

Biocartis engages in the development of novel diagnostics technology platforms for multiplex detection of biomarkers. The detection technology is based on encoded micro-particles, which are bio-functionalized and arrayed in a micro-fluidic cartridge for rapid and quantitative capture of target analytes in patient’s sample. Image analysis is used to localize and identify the micro-particles, as well as for fluorescence quantification. In this context, new algorithms of image analysis have to be evaluated and optimized in order to improve the performance of the image analysis system and to define the minimal requirements (focus quality, resolution) of the image acquisition.
The project aims for designing and implementing (Java/ImageJ) dedicated filters to enable image analysis on defocused images. The proposed algorithms will be validated and evaluated on real data.
This work will be done in collaboration with, Biocartis S.A., Quartier de l'Innovation, EPFL, under the supervision of Mathieu Gaillard

Self-Similar Image Doubling by Hallucinating the Lazy Wavelet

Semester
project: Available

Image reduction and magnification are two faces of the same coin. If one masters the operation M that magnifies a small image f to obtain a large image F = M(f), then the reduction of an image G can be stated as the search for the image g that satisfies G = M(g). These processes are well understood in a linear framework. For instance, magnifying (or reducing) a discrete image f using discrete Fourier techniques can be achieved by padding (or cropping) the discrete Fourier transform of f. In this case obviously, the question arises as to how one should pad the Fourier domain when performing a magnification. Clearly, any arbitrary choice is acceptable, not only the constant value zero, but also any sort of nontrivial and non-constant Fourier padding. However, even if the mathematics dictate that every one of these choices is acceptable, some will work perceptually better than others when applied to images.

In this project, the student is going to explore two approaches to double the linear dimensions of an image while introducing a controlled component belonging to the null space of the reduction operator. In the first case (upper system of the figure), a lazy wavelet transform will be sandwiched between a lowpass analysis filter G and a finite-support synthesis filter H that are the inverse of one another. Since each branch of the global system acts as an independent antialiasing/sampling system, it is possible to learn (large green box), by reducing an image, how best to actually magnify it. In the second case (lower system of the figure), the residue of a nonlinear edge-enhancing operation (small green box) will be added to the signal to populate the null-space of the reduction operator.

Type of work: mathematical filter design and Java programming with ImageJ
Prerequisites: to follow or to have followed the course on image processing taught by M. Unser

Cell Lineage Phantom Generator

Semester
project: Available

Due to the dynamic nature of biological systems, it is highly desirable to quantify their temporal evolution. Large-scale time-lapse imaging of cells is nowadays performed routinely, but it is not possible to analyze such data manually, thus the research community have created a large variety of algorithms to perform the analysis automatically. However, it is often difficult to compare the performance of the algorithms due to the lack of reliable datasets that can be used as ground truth.

The goal of this project is to implement an ImageJ plugin that generates time-lapse sequences of migrating cells for different imaging modalities and different motion models. Then, using this ground truth, the student should propose some performance metrics to evaluate existing algorithms.

Accurate approximations for L1 image denoising

Semester
project: Reserved

Removing noise in images is an important issue that arises in several fields, e.g., in photography or biomedical applications. The denoising methods that we consider in this project are expressed in a variational framework, as the minimization of two summed terms. The first term is a data part that enforces relative closeness between the noisy measurements at each pixel position and the denoised solution. The second term acts as a regularizer. It enforces image regularity, seeking to minimize the Lp-norm of some linear differential operator in (e.g., gradient) applied to the whole image. In all cases, the important issue is how to properly evaluate this continuous differential operator, given the available image pixels that are discrete. To do so we consider an underlying continuous-image model that interpolates the pixel values, using B-spline basis functions with appropriate continuity. The differential operator can then be evaluated as a discrete filter applied to the corresponding B-spline coefficient sequence. Linear denoting fits into the case p = 2. Within the B-spline framework, such a regularizer applied on the continuous image can be used in its exact form, yielding the so-called smoothing-spline solution. However, L2 regularization smoothes out certain image details. For this reason, recent methods consider L1 regularization using similar differential operators (i.e.,TV denoising). However, in order for the problem to be solvable, the continuous L1 term must be approximated. So far, this has always been done by evaluating these operators at a finite number of positions that correspond to the number of image pixels. It has been observed that this approximation can substantially affect the final results, depending on how it is defined. In this project, we thus want to investigate whether finer approximations of the continuous L1 term can further improve the denoising result.

Artifact reduction in phase-contrast X-ray imaging

Semester
project: Reserved

Grating interferometry is a phase-contrast X-ray imaging method that is extraordinarily sensitive to density variations in the sample. The method is especially suited for imaging of biomedical samples and will play an indispensable role in future X-ray imaging applications. However, the high sensitivity to variations in the sample is accompanied by a high sensitivity to intensity fluctuations (horizontal streaks) during image acquisition. The latter lead to artifacts in the 3D reconstructions, which in turn constitute a major obstacle for 3D data visualization and analysis.
The goal of the project is to design and test out image processing algorithms to reduce these artifacts. The potential impact of such work could be quite significant; in case of success, it would be immediately incorporated in the data processing pipeline of the TOMCAT beamline at the Swiss Light Source (Paul Scherrer Institute).

Penalized-likelihood method for 3-D fluorescence deconvolution microscopy

Master
project: Available

Our team has developed one the first practical wavelet-regularized deconvolution algorithm for 3-D fluorescence microscopy. The primary goal of this project is to improve the method by: 1) introducing a non-quadratic data term that is matched to the Poisson statistics of the noise (penalized likelihood criterion), and 2) fine tuning the regularization to the specificities of fluorescence micrographs. The secondary goal is to make the algorithm fast enough to be used in practice; specifically, one needs to investigate acceleration techniques to make the scheme competitive with commercial deconvolution software.
The work is in close collaboration with the bio-microscopy center of the EPFL.
Relevant papers:
http://bigwww.epfl.ch/publications/vonesch0901.pdf
http://bigwww.epfl.ch/publications/vonesch0601.pdf

Dictionary and sparsity-based methods for the design of signal-adapted steerable wavelets

Master
project: Available

In recent work, we have proposed a general framework for the specification of tight steerable wavelet frames (in 2-D and 3-D). These wavelets are unique in the sense that they can be rotated locally to best match the features of the image. We also introduced a general construction where the wavelets are parameterized by a series of unitary shaping matrices that can be freely specified by the user.
The goal of this project to to develop learning techniques to optimize the wavelets for specific image tasks, including feature detection, texture classification and denoising. Ideally, we would like to find the wavelets that yield the "sparsest" decomposition for a given class of images.
Relevant paper: http://bigwww.epfl.ch/preprints/unser1001p.pdf

Estimation of the 3D structure in super-resolution fluorescence microscopy (PALM)

Semester
project: Reserved

The goal of this project is to extract the 3D structure of a biological sample that has been acquired by the bi-plane PALM (Photo-Activated localization Microscopy) method. At first, a theoretical model of the PSF (Point Spread Function) will be compared with experimental data of single beads. The experimental data will then be used for calibrating the two focal planes. The third stage would consist of deriving a 3D reconstruction algorithm that will be implemented in Matlab or in Java. The algorithm will be verified by both simulated and real data.
Collaboration: Prof Suliana Manley, LEB, EPFL

Two-Sided Laminography

Master | Doctoral School
project: Available

The Konrad Witz' masterpiece "La Pêche miraculeuse" ("The miraculous Catch", which is the link panel of Saint-Peter's reredos that was realized in 1444 for Saint-Peter cathedral in Geneva), is amongst the very first european paintings to represent a true landscape: Lake of Geneva in the foreground and Mont Blanc's glaciers in the background, rather than an idealized or imagined scene.
Methods like radiography take advantage of the radio-opacity of certain pigments to highlight the painter's technique: mannerism, hesitations, corrections, or even changes in compositional intentions are clearly brought to the front by this method. This painting however, like many others, is technically challenging when one desires to understand its genesis: the radiography sees through the whole work, including the medium—except when the latter is made of lead or copper. Now, the panel of interest at the left of the reredos, like its counterpart on the right, is printed on two sides. Thus, the radiological plates (30 x 40cm) record every details of the two sides of the painting, one being mirrored. With the aid of mirrors or stereo glasses, our visual system is able to disentangle the two superposed images, so long that we have at our disposal a pair of radiographs acquired with different projection angles. But how to record these mental representations?
The goal of this project is to take advantage of signal-processing methods to independently recover the radio-opaque elements of each side. Unfortunately, although the number of images to recover matches the available input, it is possible to show that the linear solution to this problem is ill-posed. At first, the student will make the problem well-posed thanks to regularization methods that encourage the solution to be piecewise smooth. Then, the geometry will be considered to be nonideal, and not only images will be reconstructed, but also the departure from planarity of the painting.
In collaboration with "Laboratoire des Musées d'art et d'histoire de Genève".

2012 EPFL • webmaster.big@epfl.ch • 01.02.2012