FPGA Implementation of Convolutional Neural Networks with Fixed-Point Calculations

Neural network-based methods for image processing are becoming widely used in practical applications. Modern neural networks are computationally expensive and require specialized hardware, such as graphics processing units. Since such hardware is not always available in real life applications, there is a compelling need for the design of neural networks for mobile devices. Mobile neural networks typically have reduced number of parameters and require a relatively small number of arithmetic operations. However, they usually still are executed at the software level and use floating-point calculations. The use of mobile networks without further optimization may not provide sufficient performance when high processing speed is required, for example, in real-time video processing (30 frames per second). In this study, we suggest optimizations to speed up computations in order to efficiently use already trained neural networks on a mobile device. Specifically, we propose an approach for speeding up neural networks by moving computation from software to hardware and by using fixed-point calculations instead of floating-point. We propose a number of methods for neural network architecture design to improve the performance with fixed-point calculations. We also show an example of how existing datasets can be modified and adapted for the recognition task in hand. Finally, we present the design and the implementation of a floating-point gate array-based device to solve the practical problem of real-time handwritten digit classification from mobile camera video feed

Markovian integral equations and path-dependent partial differential equations

This thesis provides a construction of solutions to Markovian integral equations. By introducing path-dependent diffusion processes, this yields a general existence and uniqueness result for mild solutions to semilinear parabolic path-dependent partial differential equations (PPDEs). In this connection, we verify that mild solutions are also solutions in a viscosity sense

Solving the Inverse Problem of Electrocardiography on the Endocardium Using a Single Layer Source

The inverse problem of electrocardiography consists in reconstructing cardiac electrical activity from given body surface electrocardiographic measurements. Despite tremendous progress in the field over the last decades, the solution of this problem in terms of electrical potentials on both epi- and the endocardial heart surfaces with acceptable accuracy remains challenging. This paper presents a novel numerical approach aimed at improving the solution quality on the endocardium. Our method exploits the solution representation in the form of electrical single layer densities on the myocardial surface. We demonstrate that this representation brings twofold benefits: first, the inverse problem can be solved for the physiologically meaningful single layer densities. Secondly, a conventional transfer matrix for electrical potentials can be split into two parts, one of which turned out to posess regularizing properties leading to improved endocardial reconstructions. The method was tested in-silico for ventricular pacings utilizing realistic CT-based heart and torso geometries. The proposed approach provided more accurate solution on the ventricular endocardium compared to the conventional potential-based solutions with Tikhonov regularization of the 0th, 1st, and 2nd orders. Furthermore, we show a uniform spatio-temporal behavior of the single layer densities over the heart surface, which could be conveniently employed in the regularization procedure

Angiodysplasia Detection and Localization Using Deep Convolutional Neural Networks

Accurate detection and localization for angiodysplasia lesions is an important problem in early stage diagnostics of gastrointestinal bleeding and anemia. Gold-standard for angiodysplasia detection and localization is performed using wireless capsule endoscopy. This pill-like device is able to produce thousand of high enough resolution images during one passage through gastrointestinal tract. In this paper we present our winning solution for MICCAI 2017 Endoscopic Vision SubChallenge: Angiodysplasia Detection and Localization its further improvements over the state-of-the-art results using several novel deep neural network architectures. It address the binary segmentation problem, where every pixel in an image is labeled as an angiodysplasia lesions or background. Then, we analyze connected component of each predicted mask. Based on the analysis we developed a classifier that predict angiodysplasia lesions (binary variable) and a detector for their localization (center of a component). In this setting, our approach outperforms other methods in every task subcategory for angiodysplasia detection and localization thereby providing state-of-the-art results for these problems. The source code for our solution is made publicly available at https://github.com/ternaus/angiodysplasia-segmentatioComment: 12 pages, 6 figure