09:00 to 09:40 Registration 09:40 to 09:50 Welcome from Christie Marr (INI Deputy Director) 09:50 to 10:40 James Nagy (Emory University)Spectral Computed Tomography Co-authors: Martin Andersen (Technical University of Denmark), Yunyi Hu (Emory University)An active area of interest in tomographic imaging is the goal of quantitative imaging, where in addition to producing an image, information about the material composition of the object is recovered. In order to obtain material composition information, it is necessary to better model of the image formation (i.e., forward) problem and/or to collect additional independent measurements. In x-ray computed tomography (CT), better modeling of the physics can be done by using the more accurate polyenergetic representation of source x-ray beams, which requires solving a challenging nonlinear ill-posed inverse problem. In this talk we explore the mathematical and computational problem of polyenergetic CT when it is used in combination with new energy-windowed spectral CT detectors. We formulate this as a regularized nonlinear least squares problem, which we solve by a Gauss-Newton scheme. Because the approximate Hessian system in the Gauss-Newton scheme is very ill-conditioned, we propose a preconditioner that effectively clusters eigenvalues and, therefore, accelerates convergence when the conjugate gradient method is used to solve the linear subsystems. Numerical experiments illustrate the convergence, effectiveness, and significance of the proposed method. INI 1 10:40 to 11:10 Morning Coffee 11:10 to 12:00 Eldad Haber (University of British Columbia)tba INI 1 12:00 to 12:50 Christoph Brune (Universiteit Twente)tba INI 1 12:50 to 14:00 Lunch @ Wolfson Court 14:00 to 14:50 Lars Ruthotto (Emory University)PDE-based Algorithms for Convolution Neural Network This talk presents a new framework for image classification that exploits the relationship between the training of deep Convolution Neural Networks (CNNs) to the problem of optimally controlling a system of nonlinear partial differential equations (PDEs). This new interpretation leads to a variational model for CNNs, which provides new theoretical insight into CNNs and new approaches for designing learning algorithms. We exemplify the myriad benefits of the continuous network in three ways. First, we show how to scale deep CNNs across image resolutions using multigrid methods. Second, we show how to scale the depth of deep CNNS in a shallow-to-deep manner to gradually increase the flexibility of the classifier. Third, we analyze the stability of CNNs and present stable variants that are also reversible (i.e., information can be propagated from input to output layer and vice versa), which in combination allows training arbitrarily deep networks with limited computational resources. This is joint work with Eldad Haber (UBC), Lili Meng (UBC), Bo Chang (UBC), Seong-Hwan Jun (UBC), Elliot Holtham (Xtract Technologies) INI 1 14:50 to 15:40 Gitta Kutyniok (Technische Universität Berlin)Optimal Approximation with Sparsely Connected Deep Neural Networks Despite the outstanding success of deep neural networks in real-world applications, most of the related research is empirically driven and a mathematical foundation is almost completely missing. One central task of a neural network is to approximate a function, which for instance encodes a classification task. In this talk, we will be concerned with the question, how well a function can be approximated by a neural network with sparse connectivity. Using methods from approximation theory and applied harmonic analysis, we will derive a fundamental lower bound on the sparsity of a neural network. By explicitly constructing neural networks based on certain representation systems, so-called $\alpha$-shearlets, we will then demonstrate that this lower bound can in fact be attained. Finally, we present numerical experiments, which surprisingly show that already the standard backpropagation algorithm generates deep neural networks obeying those optimal approximation rates. This is joint work with H. Bölcskei (ETH Zurich), P. Grohs (Uni Vienna), and P. Petersen (TU Berlin). INI 1 15:40 to 16:00 Eva-Maria Brinkmann (Westfalische Wilhelms-Universitat Munster); (Westfalische Wilhelms-Universitat Munster)Enhancing fMRI Reconstruction by Means of the ICBTV-Regularisation Combined with Suitable Subsampling Strategies and Temporal Smoothing Based on the magnetic resonance imaging (MRI) technology, fMRI is a noninvasive functional neuroimaging method, which provides maps of the brain at different time steps, thus depicting brain activity by detecting changes in the blood flow and hence constituting an important tool in brain research. An fMRI screening typically consists of three stages: At first, there is a short low-resolution prescan to ensure the proper positioning of the proband or patient. Secondly, an anatomical high resolution MRI scan is executed and finally the actual fMRI scan is taking place, where a series of data is acquired via fast MRI scans at consecutive time steps thus illustrating the brain activity after a stimulus. In order to achieve an adequate temporal resolution in the fMRI data series, usually only a specific portion of the entire k-space is sampled. Based on the assumption that the full high-resolution MR image and the fast acquired actual fMRI frames share a similar edge set (and hence the sparsity pattern with respect to the gradient), we propose to use the Infimal Convolution of Bregman Distances of the TV functional (ICBTV), first introduced in \cite{Moeller_et_al}, to enhance the quality of the reconstructed fMRI data by using the full high-resolution MRI scan as a prior. Since in fMRI the hemodynamic response is commonly modelled by a smooth function, we moreover discuss the effect of suitable subsampling strategies in combination with temporal regularisation. This is joint work with Julian Rasch, Martin Burger (both WWU Münster) and with Ville Kolehmainen (University of Eastern Finland). [1] {Moeller_et_al} M. Moeller, E.-M. Brinkmann, M. Burger, and T. Seybold: Color Bregman TV. SIAM J. Imag. Sci. 7(4) (2014), pp. 2771-2806. INI 1 16:00 to 16:30 Afternoon Tea 16:30 to 17:20 Joan Bruna (New York University); (University of California, Berkeley)tba INI 1 17:20 to 18:10 Justin Romberg (Georgia Institute of Technology)tba INI 1 18:10 to 19:10 Poster Session & Welcome Wine Reception at INI