Oliveros-Oliveros, J.J.; Conde-Sánchez, J.R.; Hernández-Gracidas, C.A.; Morín-Castillo, M.M.; Conde-Mones, J.J. FPGA-Based Hardware Implementation of a Stable Inverse Source Problem Algorithm in a Non-Homogeneous Circular Region. Appl. Sci.2024, 14, 1388.
Oliveros-Oliveros, J.J.; Conde-Sánchez, J.R.; Hernández-Gracidas, C.A.; Morín-Castillo, M.M.; Conde-Mones, J.J. FPGA-Based Hardware Implementation of a Stable Inverse Source Problem Algorithm in a Non-Homogeneous Circular Region. Appl. Sci. 2024, 14, 1388.
Oliveros-Oliveros, J.J.; Conde-Sánchez, J.R.; Hernández-Gracidas, C.A.; Morín-Castillo, M.M.; Conde-Mones, J.J. FPGA-Based Hardware Implementation of a Stable Inverse Source Problem Algorithm in a Non-Homogeneous Circular Region. Appl. Sci.2024, 14, 1388.
Oliveros-Oliveros, J.J.; Conde-Sánchez, J.R.; Hernández-Gracidas, C.A.; Morín-Castillo, M.M.; Conde-Mones, J.J. FPGA-Based Hardware Implementation of a Stable Inverse Source Problem Algorithm in a Non-Homogeneous Circular Region. Appl. Sci. 2024, 14, 1388.
Abstract
This work implements a stable algorithm in Field-Programmable Gate Arrays (FPGAs) for which two architectures (unrolling the loop) were developed and analyzed. The algorithm recovers sources located at the boundary separating two homogeneous media that make up a two-dimensional non-homogeneous region from measurements on the boundary of such region. The problem of recovering these sources is an ill-posed inverse problem as small errors in the measurement can produce important changes in the source location. Inverse source problems have many applications in different areas, such as engineering and medicine, making the proposed implementation important. The first architecture (mode one) allows considering different operating speeds, which is an advantage depending on whether we work with fast or slow signals. The second one (mode two) reduces resource consumption by exploiting the characteristics of the source identification algorithm, which is an advantage for multichannel problems such as inverse electrocardiography or electroencephalography. The architectures were tested on four FPGAs of the 7 Series of Xilinx: Spartan-7 xc7s100fgga484, Virtex-7 xc7v585tffg1157, Kintex-7 xc7k70tfbg484, and Artix-7 xc7a35tcpg236. The two FPGA implementations of the algorithm were validated using synthetic examples implemented in MATLAB. The results presented here can be extended to concentric spheres and complex geometries.
Computer Science and Mathematics, Applied Mathematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
