Number of projects:4
In generative adversarial networks, it has been shown that controlling the Lipschitz regularity of a network largely improves the generative performance. For example, Wasserstein GAN (WGAN) and Spectral Normalization GAN (SNGAN) achieve this by restricting the discriminative function to be 1-Lipschitz. Recently, we developed a framework for learning activations of deep neural networks with the motivation of controlling the global Lipschitz constant of the input-output relation.
The goal of this project is 1) to investigate the effect of our framework in the generative adversarial networks and 2) to develop a better Lipschitz regularization method for training generative models. We have already seen some promising results on several toy datasets such as a mixture of Gaussians, Swiss roll, and (partially) MNIST. We aim to extend this to more complicated datasets such as human faces (CelebA dataset). The student must be familiar with PyTorch and a general understanding of the main concepts of deep learning. (+ it would be nice if one has some experience in generative adversarial networks)
References Aziznejad, S., Gupta, H., Campos, J., & Unser, M. (2020). Deep neural networks with trainable activations and controlled Lipschitz constant. arXiv preprint arXiv:2001.06263.
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:  H. Gupta, K.H. Jin, H.Q. Nguyen, M.T. McCann, M. Unser, "CNN-Based Projected Gradient Descent for Consistent CT Image Reconstruction"  A. Bora, A. Jalal, E. Price, A. G. Dimakis, "Compressed sensing using generative models"
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/).
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.