Acceleration of 3D ECT image reconstruction in heterogeneous, multi-GPU, multi-node distributed system Michal Majchrowicz * , Pawel Kapusta † , Lidia Jackowska-Strumillo ‡ and Dominik Sankowski § Lodz University of Technology Institute of Applied Computer Science ul. Stefanowskiego 18/22, Lód´ z, Poland * Email: mmajchr@iis.p.lodz.pl † Email: pawel.kapusta@p.lodz.pl ‡ Email: lidia_js@iis.p.lodz.pl § Email: dsan@iis.p.lodz.pl Abstract—Electrical Capacitance Tomography (ECT) is an effective and non-invasive visualization technique, which is used in many industrial applications. Unfortunately, image reconstruc- tion in 3D ECT is a complex computational task requiring operations on large size matrices. In this paper, a new approach to 3D ECT image reconstruction is proposed. A new heterogeneous, multi-GPU, multi-node distributed system has been developed, with a framework for parallel computing and a special plug-in dedicated to ECT. I. I NTRODUCTION E LECTRICAL Capacitance Tomography (ECT) is a mea- surement technique that can be used for non-invasive monitoring of industrial processes in 2D [7], 3D [1] and even 4D dynamic mode. ECT is performing the task of imaging of materials with a contrast in dielectric permittivity by measuring capacitance from a set of electrodes placed around the investigated object. In order to achieve a high quality of 3D image, complex re- construction algorithms performing many matrix calculations have to be applied. Therefore different solutions accelerat- ing these calculation have been reported in the past by the Authors[8][14], especially these dealing with sparse matrices and Finite Elements Method [9] as well as neural networks approach [5][6] and even fuzzy logic [21]. In this work we propose a novel heterogeneous, multi-GPU (Graphics Processing Unit), multi-node distributed system, with a framework for parallel computing and a special plug-in dedicated to ECT. The system features and its efficiency have been compared to the previously developed distributed system based on the Xgrid platform. A. Image reconstruction in ECT The scheme of image synthesis in Electrical Capacitance Tomography is called image reconstruction. It is based on solving the so called inverse problem, in which the spatial distribution of electric permittivity from the measured values of capacitance C is approximated [1] [16]. Image reconstruction using deterministic methods requires execution of a large number of basic operations of linear algebra, such as transposition, multiplication, addition and subtraction [10][15]. Matrix calculations for a large number of elements is characterized by a high computational load. Matrix multiplication is a key operation in ECT imaging and therefore many researchers decided even to build a custom hardware for this purpose. The LBP algorithm is one the most used reconstruction algorithms, even though it is characterized by low spatial resolution. Nevertheless it is not as computationally complex as other solutions. Moreover there is still active research on improving it’s characteristics [17]. It is based on the following equation [3]: ε = SC m (1) where: ε - electric permittivity vector (output image), S - sensitivity matrix, C m - capacitance measurements vector. The Landweber algorithm is based on the following iterative equation: ε k+1 = ε k − αS T (Sε k − C m ) (2) where: ε k+1 - image obtained in current iteration, ε k - image from the previous iteration, α - convergence factor (scalar), S T - sensitivity matrix, transposed, S - sensitivity matrix, C m - capacitance measurements vector. In the case of the Landweber algorithm each iteration improves the overall quality of the output image. As a result acceleration of image reconstruction process is a very impor- tant issue. Nevertheless, due to its nature it is necessary to exchange the data (ε k+1 ) in every iteration. II. DESIGN ASSUMPTIONS As a result of the earlier performed studies [8][13] the Authors have developed a new distributed system dedicated to ECT computations. It is specially designed to accelerate matrix computations that are a crucial part of reconstruction Proceedings of the Federated Conference on Computer Science and Information Systems pp. 347–350 DOI: 10.15439/2018F60 ISSN 2300-5963 ACSIS, Vol. 15 IEEE Catalog Number: CFP1885N-ART c 2018, PTI 347