Electrical Tomography Hardware Systems for Real-Time Applications: a Review

This paper presents a review of two-dimensional (2D) and three-dimensional (3D) electrical tomography (ET) hardware accelerators for real-time applications. While many recent review papers have discussed various algorithms for image reconstruction or acquisition systems, none of them has considered state-of-the-art hardware implementations of the associated image reconstruction algorithms to achieve real-time performance, especially for 3D ET where the computation requirement is excessively high. A 3D ET is useful in various applications such as robotics, autonomous vehicles, and process control, but it is computationally very expensive with respect to its 2D counterpart. Most implementations are based on single or multi-core CPUs and, to a lesser extent, on either graphics processing units (GPUs) or field programmable gate arrays (FPGAs). However, there is a clear gap between the currently available processors, whose computation power exceeds hundreds of teraflops per second (TOPS) at a reasonable low power consumption, and the ones recently used in ET systems. This gives great potential for next-generation ET systems to achieve real-time 2D and 3D ET reconstruction within a small form factor. The paper summarizes the most recent ET hardware systems with respect to their performance in terms of quality and processing frame rate, reconstruction methods, along with optimization and future directions.

reconstruction. Figure 1 shows the methodology adapted 88 for the article search. At first, the keywords were identi-89 fied, which can help in finding the most relevant articles. 90 The keywords included ''Electrical Tomography'', ''EIT'', 91 ''ECT'', ''ERT'', ''Hardware'', ''Embedded'', ''Portable'', 92 ''Real Time'', ''FPGA'', ''GPU'', and ''SOC'' in different 93 combinations in article title and topic/meta-data search along 94 with their plurals or derivative forms such as ''FPGAs'', 95 ''GPUs'', ''Real-time'', ''Field programmable gate array'', 96 ''System on chip'', etc. The search was conducted using the 97 three major databases, i.e., WoS, GS, and IEEE. The most 98 recent articles from 2017 onward were considered. While 99 the title-based search is a good method to quickly find the 100 relevant articles, given the limited amount of work done in the 101 hardware systems for ET image reconstruction, we adopted 102 a title and title + topic/metadata based search to collect a 103 larger number of papers initially. For instance, a title-based 104 search with the selected keywords yielded 80 articles in 105 the WoS database, while a title+topic-based search yielded 106 371 articles. Similarly, for the IEEE database, the title-based 107 search resulted in 33 articles, while the title+metadata-based 108 search resulted in 228 articles. While all the articles from the 109 title-based search results were considered for further analy-110 sis, only the top 100 results from title+topic/metadata-based 111 search results from both the databases were used. In the next 112 step, the common articles were filtered and the results were 113 a general acquisition system. The electrodes are interfaced 143 with the data acquisition system through multiplexers and 144 demultiplexers. A high speed 12 to 16 bit analog to digital 145 (ADC) is usually required to provide the digitized voltage 146 reading of the output voltage of the selected pair of electrodes 147 to the processing unit for the image reconstruction. A current 148 or voltage source for an ECT or EIT system is connected 149 to the multiplexer/demultiplexer together with the voltage 150 reading unit. The measured data of a frame is then transferred 151 to the data processing unit to reconstruct the corresponding 152 2D or 3D image. Figures 4 (a) and (b) show typical electrodes 153 placement around the boundary of a region for 2D and 3D 154 ET systems, respectively. In a 2D ET system, the electrodes 155 are generally placed uniformly to cover a 2D cross section 156 and the associated finite element model (FEM) is planar, 157 whereas, in a 3D ET system, the electrodes are generally 158 placed to cover a volume and, accordingly, the FEM is pre-159 pared for volumetric computation [31]. The reconstruction 160 of the image is carried out using the measured signal and a 161 forward model. As the number of boundary measurements 162 is going to be much smaller than the number of conductiv-163 ities/permeabilities to be solved, the problem is ill-posed. 164 Transforming it into a well-posed problem requires some 165 prior information using a regularization technique. 166

A. FORWARD MODEL
167 This is a model that can estimate the spatial electric field and 168 obtain voltage measurements at boundaries by stimulating 169 a current/voltage in a known conductivity/permeability dis-170 tribution space [32]. The final image is obtained by repeat-171 edly running this forward model with an inverse solver 172 100 kHz is applied, depending on the application requirement 210 where high frequency usually provides more details but at 211 the expense of penetration depth. Multifrequency excitation 212 is also suggested in some ET systems in order to reduce the 213 data acquisition time [38], [39]. 214 Thus, the choice of the measurement pattern is application 215 dependent and defines the total number of measurements 216 per frame, which in turn determines the size of the Jacobian 217 matrix. High computation latency caused by the high dimen-218 sion of the Jacobian matrix and the number of measurements 219 to be performed for each single frame requires dedicated 220 hardware to achieve real-time performance for an embedded 221 and portable system.

223
The placement of the electrodes is important in ET systems 224 as it defines the sensitivity distribution in the region which 225 determines the quality of the reconstructed image. For 2D 226 ET systems, the electrodes are generally placed uniformly 227 around the boundary of the region to be imaged. But, in some 228 applications were more sensitivity is required within a known 229 sub-region of the region, non-uniform placement can be 230 observed with more electrodes placed closer to the region 231 of interest [40]. Similarly, for 3D ET systems, the electrodes 232 are usually uniformly distributed around the region/volume 233 of interest. For instance, in [41], a special ECT sensor with 234 a double helical electrode arrangement in a co-axial pipe for 235 3D volume imaging of two-phase annular flow was designed 236 and assessed. It consisted of four electrodes placed on the 237 inner pipe and eight electrodes placed on the surface of 238 the outer pipe. It was observed that the reconstruction qual-239 ity was better than the conventional ring placement. But, 240 these types of custom sensors are only suitable for limited 241 applications where it is possible to install them. Therefore, 242 authors in [31], suggested different electrode placements for 243 multi-phase flow through a single pipe in a non-invasive way 244 for 3D ET. This includes double concave, multiple concave, 245 double helix, staggered concave, multiple helix, two semi-246 cylinders, and a ring. It was concluded that while one type 247 93936 VOLUME 10, 2022  The inverse problem is to determine the conductiv-252 ity/permeability distribution in the region by using the mea-253 sured data. This is an ill-conditioned problem where any 254 small variation in the measured data can cause a huge vari-255 ation in the reconstructed image. Many linear or non-linear 256 methods have been introduced in the literature to solve this 257 non-linear problem, which can be either single or multiple 258 iteration-based. In general, it is observed that the iterative 259 methods tend to yield better image quality with an increasing 260 number of iterations. Figure 5 shows the process of image 261 reconstruction using iterative methods.

262
The solution of the inverse problem in its simplest form can 263 be given as follows: It is worth noting that since the number of measurements is The reconstruction is simple and fast as it removes the 274 requirement for inverse matrix calculation. However, the 275 reconstructed image quality is poor and might be suitable 276 only for applications where a low resolution image at a high 277 frame rate is acceptable [42]. This image is also sometimes 278 used by many iterative methods as an initial solution.

279
Another way to solve the inverse problem is to modify 280 equation (1) as: so that, if the inverse of S T S exists then, Mostly, the inverse does not exist because N M . There-285 fore, a regularization term is added to S T S so that, where, λ is a scalar hyperparameter and I is the iden-288 tity matrix. This is also known as Tikhonov regularization 289 method. Another similar method which is widely used is 290 one-step Gauss Newton (GN) for difference imaging and is 291 given as: where, W is the inverse of the measurement covariance, and 294 considering the measurements to be independent, it is a sparse 295 diagonal matrix of dimension M xM . R is the sparse regular-296 ization matrix with dimension of N xN , and Y is the difference 297 of measured potential with a reference signal. Equations (6) 298 and (7) show the requirements of matrix inversion and several 299 matrix multiplications, which are rather time-consuming and 300 thus require dedicated hardware accelerators.

301
If we include the eventual errors, e, which may occur 302 during the measurements, then the equation (1) can be written 303 as: Thus, the approach to find the solution can be modified as a 306 minimization problem, where σ is the conductivity/dielectric distribution for which 309 the error is minimum. The solution in this form is generally 310 done iteratively. One of most widely used method is Landwe-311 ber method which is given by, where α is a relaxation factor, which determines the rate 314 of convergence, (Sσ k − V i ) is the voltage difference in the 315 measured and the estimated value from the forward model 316 during the k th iteration. Another approach is the iterative 317 Tikhonov which is formulated as follows: Several other methods have been developed in the recent 320 past to improve the image quality while achieving real-321 time performance, which is challenging and requires careful 322 hardware-software co-design methodology.  access for data fetching or writing is also slower in the case 363 of GPUs. Therefore, the computations that have to be carried 364 out on a GPU need to be optimized for parallel execution by 365 minimizing the frequent memory accesses.

366
FPGAs are other hardware platforms that can be poten-367 tially used for parallel computing. They have the advantage 368 of offering a flexible hardware structure that can be pro-369 grammed. FPGAs typically comprise reconfigurable control 370 logic blocks (CLBs), digital signal processor (DSP) blocks, 371 and re-programmable interconnects, which can be used to 372 build customized hardware. An FPGA based system may 373 not suffer from frequent data read/write because the memory 374 units can be designed to be very close to the data process-375 ing unit. However, the number of CLBs and DSP blocks is 376 relatively limited, which hinders their usage to host complex 377 hardware algorithms. Due to the complex hardware structure 378 to support their reprogrammability, the overall system clock 379 speed is usually slower than the one available for the GPU 380 and CPU processors [47].

381
While any of the multi-core CPU, GPU, or FPGA based 382 platforms can be utilized to develop efficient ET accelerator 383 hardware systems, multi-CPU cores using personal com-384 puters (PCs) have been the most frequently used without 385 actually exploring the hyper-threading feature. FPGA based 386 ET systems have been extensively explored in the recent past, 387 but mainly ifor implementing the sequencer of the data acqui-388 sition module and capturing the measurement data into local 389 memory rather than accelerating the image reconstruction 390 algorithm. In the next section, we will discuss some of the 391 recent works which were done for the design of real-time 392 portable and embedded 2D/3D ET hardware accelerators.  It is used to measure the correlation between the actual con-403 ductivity/dielectric values and the reconstructed values, it is 404 given as: where, is the ground truth distribution and σ is the final 407 calculated distribution values obtained after reconstruction.

408
A value close to 0 shows no correlation and a value close to 409 1 shows a high correlation. Naturally, a value close to 1 is 410 desirable for good reconstruction quality. given as: a value close to 0 is desirable for high quality reconstruction.

419
It is used to measure the mean squared error between the 420 actual conductivity/dielectric values and the reconstructed 421 values and is given as: 423 a value closer to 0 represent better quality of reconstruction.

429
AR value close to 1 represents better reconstruction. 430

431
It measures the reconstruction accuracy with respect to target 432 position and is calculated as: where p t is the target position in the ground truth image and p r 435 is the estimated target position from the reconstructed image. 436 The smaller the value of PE higher is the positional accuracy. 437

439
Developing accurate, high-speed, and portable 2D ET sys-440 tems has been an active area of research. In this section we 441 review some of the latest works which were conducted in this 442 area since year 2017. As was mentioned in the introduction 443 section, we used the WoS and GS databases to find all the 444 relevant articles. In [48], a 2D PC-based 16 electrode ECT based airflow injec-448 tion system for industrial process control was presented. The 449 ECT system consists of one upstream and one downstream 450 ring to capture the 2D particle distribution inside the pipe. The 451 upstream electrodes, along with the airflow injection system, 452 were used to control the downstream particle distribution in 453 real-time. The acquisition rate of the system was up to 100 fps 454 and the ECT reconstruction throughput was 67 fps for an 455 image size of 64 × 64 pixels with 835 outer pixels in the cross 456 section using the LBP algorithm.

457
Authors in [49], designed a real-time compact EIT 458 system with a PCI platform (cPCIS-2501) using FPGA 459 (XC6SLX100) based board for data acquisition and CPU 460 (Intel core i7, 4GB, @2.2GHz) for image reconstruction as 461 shown in Fig. 9. The acquisition system supported a frame 462 rate of 120 and the complete reconstruction was carried out 463 @32 fps with 1024 mesh elements. The system used Split 464 augmented Lagrangian shrinkage algorithm (SALSA), which 465 transforms an unconstrained optimization EIT inverse prob-466 lem into an equivalent constrained optimization problem. The 467 algorithm was implemented using EIDORS library and was 468 compared with two-step iterative Shrinkage/Thresholding 469 (TwIST), sparse reconstruction by separable approximation 470 algorithm (SpaRSA) and one-step GN. For a mesh count of 471 6400 elements, the time required by SALSA was 0.1782s 472 which was only 10.3% of SpaRSA, 3.8% of TwIST and 2.3% 473 of GN. The experiments showed that SALSA significantly 474 improves the computation time compared to other methods 475 but is still dependent on the number of mesh elements and 476 achieves a throughput of 5 fps for 6400 pixels/frame. This is 477 still not suitable for real-time applications where larger mesh 478 size with higher frame rate are much needed. 479 Researchers in [50], designed a portable 8-electrodes EIT 480 system with a client server architecture. The server consists 481 of a Red Pitaya board (Fig. 10), which comprises a Xilinx's 482 VOLUME 10, 2022 FIGURE 9. Block diagram of PCI platform based EIT system [49]. 8.07% with ICC of 0.65 when the electrode size was 10 mm 494 (diameter), and was 1.49% with ICC of 0.75 when the size 495 was 30 mm (diameter). Increasing the number of electrodes 496 or optimizing the size of the electrodes may be required to 497 further improve the image quality. Also, an equivalent frame 498 rate with much higher number of mesh elements is generally 499 required for many applications. In [53] a wearable and portable 16-electrode belt was 501 designed. Similar to [50], the processing was done using 502 a general-purpose IBM-compatible PC while the data was 503 acquired using an Avnet Zedboard with Zynq 7000 (SOC 504 module) at a rate of up to 30 fps. Another wearable EIT-belt 505 was designed in [54]. But, in this implementation, the cap-506 tured data was continuously sent to the Azure cloud through 507 a secure shell (SSH) for 2D image reconstruction. The cloud 508 compute engine consisted of NV24s series virtual machines 509 with 24 cores hyper-threading processor and 224GB of RAM. 510 A parallel cluster based method was employed for Jaco-511 bian matrix computation of the flexible belt boundary. The 512 hyper-threading technique allowed the OS to address two 513 virtual cores per physical core. A significant speed-up of 514 20.17 times was obtained using the parallel approach com-515 pared to the sequential method. The optimum performance 516 (op) defined as: where, sp is the speed-up and sp ref is the speed-up reference 519 based on Amdahl's law [55] and is given as: with ''spatial sensitivity aware mean-squared error'' 582 (SSA-MSE) as the loss function for image reconstruction. 583 The voltage measurements were the input to the model, and 584 the mesh conductivities were imposed as model output. The 585 training of the model was conducted using a GPU (NVIDIA, 586 Titan X, 11 GB), but the image reconstruction task was 587 carried out using a general-purpose PC. The authors claim 588 that the EIT-NN with SSA-MSE showed a better quality 589 reconstruction compared to the conventional one-step GN, 590 iterative GN, primal-dual interior-point method (PDIPM) and 591 SA-SBL with a computation time of 0.0640 seconds. The 592 achieved frame rate of around 15 fps may be suitable for 593 many applications, but the image size of only 576 pixels is 594 considered low for many of them. A Deep D-bar method for 595 real-time image reconstruction was also suggested in [66]. 596 The regularized D-bar method, which uses a non-linear 597 Fourier transform, tailor-made for the EIT problem, suffers 598 from blurring due to low-pass filtering of scattering data [67]. 599 This was improved by using an additional Convolutional 600 Neural Network(CNN) to remove the blur and to identify 601 sharp boundaries. The model was trained without using any 602 experimental data but with simulated data only, yet it was able 603 to enhance the image contrast. Methods like this one, where 604 the dependency on experimental training data is not required, 605 deserve to be explored further.

606
A GPU-based parallel computation method for 2D EIT 607 absolute image reconstruction with 32 electrodes was dis-608 cussed in [61]. It used a simulated annealing (SA) approach 609 to solve the inverse problem in which a conjugate gradi-610 ent (CG) algorithm was used for the forward problem [68], 611 with 32 instances corresponding to 32 independent current 612 injections. The solution utilized CPU and GPU data pro-613 cessing with workload distribution as shown in Fig. 13. 614 The authors showed that an efficient GPU based hardware 615 algorithm does not exhibits divergence and that it allows 616 to avoid random memory access. A contiguous access of 617 memory in a sequence is preferred for faster execution. 618 In their parallel hardware implementation, the colored padded 619 jagged diagonal storage (pJDS) matrix format was consid-620 ered for the entire parallel implementation of the conjugate 621 gradient (CG) algorithm. The computation involved matrix-622 vector multiplication, the inner product of two vectors, and 623 a triangular solver, which was implemented using a parallel 624 approach with the pJDS matrix format. Whereas the serial 625 implementation of the same suffered from the increasing 626 size of the matrix, the parallel implementation showed sig-627 nificant speedups with increasing size, even including the 628 data transfer time. For instance, matrix-vector multiplica-629 tion for the size of 1046 mesh elements required 23.3 ms 630 using the serial approach but only 14.9 ms using the parallel 631 approach. For the size of 9500 mesh elements, 211.4 ms and 632 43.6 ms were needed for the serial and parallel approaches, 633 respectively. The GPU-based parallel implementation exhib-634 ited higher processing time gains with the increasing size of 635 the matrix, but this gain is limited by the number of cores and 636 VOLUME 10, 2022 where V t i and σ t are the measured voltage and foreground where S r and σ r are the smaller sub-matrices corresponding 675 to the small region of change. This helped to significantly 676 reduce the processing time as there were lesser pixels to 677 compute and update every frame in the continuous flow. The 678 reconstruction was performed by modifying equation (6) as: 679 Furthermore, a parallel pipelined architecture was designed 681 on the FPGA for carrying out this computation. Matrix multi-682 plication and inversion using QR decomposition were imple-683 mented. A frame rate of 560 frames/second was achieved 684 for an average of 520 mesh elements to be updated each 685 iteration out of a total of 4096 mesh elements. A hardware 686 accelerator consisting of 797K LE and 456 M20K memory 687 blocks for IEEE 754 floating point multiplications was used, 688 which led to a maximum power consumption of 32.6 W, 689 which remains excessively high for embedded ET systems. 690 Another limitation of this design is that the initial distribution 691 is supposed to be known. In the event of a sudden change in 692 the flow, a full image reconstruction may be required.

693
In [64], a complete standalone 2D ECT system 694 (16×16 frame size) using FPGA (Cyclone-V) was suggested. 695 The system, which hosts the LBP algorithm, was designed for 696 imaging lost foam coating process. It used six wireless capac-697 itive sensors, with each sensor being a pair of electrodes. The 698 electrodes were placed around the rectangular foam pattern in 699 the compressed sand. A reconfigurable, segmented, parallel 700 inner product architecture for parallel matrix multiplication 701 was implemented in the aforementioned FPGA platform, 702 which doubled the processing throughput compared to the 703 sequential PC-based implementation. The system utilized 704 only 11% of logic gates and 15% of memory, which may 705 make it adequate to host other more complex ET algorithms 706 with a larger number of image pixels. In a similar extension 707 of this work in [65], the complete image reconstruction was 708 implemented on an FPGA (Cyclone-V) SoC platform, and the 709 measurement data was acquired wirelessly. The iterative LBP 710 method was used for reconstruction, and a segment-based 711 matrix-vector architecture was proposed, where the large 712 matrix multiplications were carried out in smaller parallel 713 segments. MATLAB's model-based design platform was 714 used to design the system where the segment length worked 715 as an input to the design flow and could be configured as 716 per the requirements. A higher segment length enables faster 717 computation, but at the cost of more resources. The authors 718 claimed to have achieved a frame rate of over 12000 fps for 719 a 16 × 16 image size with eight electrodes. While the frame 720 rate is sufficient for several applications, the image resolution 721 is very low. The performance of this approach for a higher 722 number of electrodes and much higher resolution needs to be 723 evaluated.

725
It can be observed from Table 2, which summarizes the 726 most recent 2D ET hardware accelerators, that the hardware 727 computing platforms used for real-time 2D ET systems are 728 VOLUME 10, 2022 are relatively limited because of the heavy computation time 766 they require. For instance, while mesh elements for 2D ET 767 systems are typically in the 100-1000 range (refer to Table 2), 768 they easily exceed 10,000 for a 3D ET system. Processing this 769 much data in real-time is a challenging problem and needs 770 continuous hardware and software research. To the best of 771 our findings, the most recent and relevant real-time 3D ET 772 systems present in the literature are summarized in Table 3. 773 Authors in [69] used a twin plane electrode arrangement 774 for 3D imaging and velocity measurement in a two-phase 775 flow through pipes. The ECT system uses a total of 24 elec-776 trodes, with 12 in each plane. The 3D images were recon-777 structed using 21 × 21 × 29 mesh elements. A dedicated 778 data acquisition system was used with an acquisition rate 779 of 241 fps for 276 independent measurements per frame. 780 The reconstruction was carried out using LBP, Landweber, 781 Tikhonov, and iterative Tikhonov on a PC. The reconstruction 782 time using the Tikhonov method was 2.5 ms i.e., 400 fps, 783 which is promising, but the image resolution, which consists 784 of 12,789 pixels per frame was relatively low for several real-785 life 3D ET applications.

786
In [70], authors designed a 3D wireless ERT system 787 (WERT) for determining in real-time the two-phase particles' 788 distribution of glass beads-Nacl solution within a rotating 789 vessel. A total of 40 invasive electrodes were placed around 790 a PVC cylindrical vessel in 5 layers, with 8 electrodes in 791 each layer. The measurements were conducted using the 792 adjacent method, yielding 40 measurements for each plane. 793 The acquisition system was designed using an Arduino Uno 794 microcontroller with a 10-bit ADC that supported a frame rate 795 of 2 fps. The acquired data was transmitted to the host PC 796 wirelessly through Bluetooth with a maximum transmission 797 speed of about 921 kbits/s, which satisfied the requirements 798 of the designed WERT system. As the vessel was rotating, 799 the actual measurement data was collected and time-averaged 800 over 5 seconds to allow the rotating field to stabilize. A single-801 step GN algorithm was used for image reconstruction using 802 EIDORS on an IBM-compatible PC, and the reconstructed 803 image was binarized as there were only two phases (liquid 804 and solid particles). The actual measured and the numeri-805 cally simulated analysis showed a deviation of only 7.21%. 806 While 3D reconstruction provided encouraging results, the 807 reconstruction was implemented using only sequential data 808 processing. A dedicated hardware accelerator could have 809 substantially increased the system throughput.

810
In another implementation, authors in [71], developed a 811 wearable 3D real-time lung ventilation monitoring system. 812 A total of 48 electrodes were placed in 3 planes, with 16 in 813 each plane. A 48-channel active electrode SoC was placed 814 on the belt using a flexible printed circuit board. Another 815 Hub-SoC was used for data gathering and communication 816 via Bluetooth @10 fps to a PC, which executes the iterative 817 GN image reconstruction algorithm for an image size of 818 150,000 pixels. The reconstruction quality was compared 819 with a 2D model using only one plane data and a 2.5D model 820 using three planes of data without information exchange 821  only 2.5ms. This shows that a parallel and optimized imple-844 mentation of the algorithm on a high-performance computing 845 platform is much needed to improve the frame rate of the 846 system.

847
Recently, a 3D Micro EIT dedicated system for cell 848 imaging was designed and accessed in [73]. A cylindrical 849 container of 10 mm in height and 12 mm in diameter was 850 prepared with 17 electrodes placed at the bottom of the plane 851 as shown in Fig. 14. One reference electrode was placed at 852 the center of the bottom plane. The other electrodes were 853 placed in the form of two concentric circular rings, consisting 854 of eight electrodes each. The FEM analysis was conducted 855 using 235,000 mesh elements, which spanned the complete 856 cylindrical volume to be imaged. Measurements were con-857 ducted using the multi-frequency EIT system [77], with a 858 frame rate of 546 fps under serial mode and 1014 fps under 859 semi-parallel mode. The basis pursuit denoising method was 860 used for reconstruction using a Xeon X5650 CPU, 2 cores 861 and 24 GB RAM as a compute platform. It took 5 seconds to 862 complete the reconstruction of a single frame, which remains 863 excessively high for efficient real-time applications.  multiple GPUs was able to achieve a frame rate of up to 8 fps 910 with 50 iterations. The largest image size which was tested 911 corresponded to 672 KB, for which a throughput of 1 fps 912 using 400 iterations could be achieved.

914
It can be seen that the research work conducted so far for the 915 design of a real-time 3D ET system is very limited compared 916 to its 2D counterpart. The higher electrode count leads to 917 more measurements, which increases the acquisition time. 918 Furthermore, the larger mesh count exponentially increases 919 the computation time, which is required for 3D image recon-920 struction. As discussed in section III some embedded 2D ET 921 systems have used FPGA and GPU-based compute platforms, 922 but their use for 3D ET systems remains very limited. Thus, 923 most 3D ET image reconstruction tasks are carried out using 924 high-end CPUs with a large amount of RAM. A distributed 925 on-premise or cloud-based architecture can be a very useful 926 approach for very large size matrices. However, dedicated 927 parallel architecture on modern compute-intense embedded 928 platforms is much needed for portal real-time ET systems. The major challenge in the computation of the ET image 932 reconstruction arises due to the increasing size of matrices 933 that are necessary for capturing accurate volume informa-934 tion. A high quality image can be obtained if large-sized 935 matrices are supported by the appropriate computing plat-936 form. As observed from sections III and IV, most of the 937 research works which were conducted on ET systems mainly 938 used Matlab/Octave on IBM-compatible computers. Table 4 939 shows various compute platforms which were discussed in 940 this paper. Matlab/Octave uses mostly sequential computa-941 tion processes using a general-purpose PC. The size of the 942 matrix in this case is limited by the amount of the RAM 943 capacity and its utilization. The lack of fine-grained par-944 allel hardware implementation on PCs has consistently led 945 to excessively high computation time to no match real-time 946 constraint. Some works that have used FPGA platforms as 947 hardware accelerators for ET reconstruction algorithms could 948 show attractive results to handle in real-time even large matrix 949 sizes. In addition, since many recent data acquisition systems 950 are already using FPGA for implementing the sequencer of 951 the data acquisition module [28], [57], [77], using them for 952 image reconstruction as well seems to be a preferable choice 953 ally, synthetic data is generated and used, [80] has presented a 989 standard database for training various ECT systems. [66] pro-990 posed DNN based deep D-bar reconstruction which showed 991 some improvements over the basic D-bar method. An addi-992 tional CNN was added to the D-bar method to improve the 993 final reconstructed image. While continuous efforts in this 994 direction can lead to higher accuracy, modern GPU proces-995 sors, which were specifically designed for AI and machine 996 learning algorithms, can be valuable to meet the real-time 997 constraints of ET systems such as: Gesture recognition [75], 998 where full image reconstruction is not required. Nevertheless, 999 while implementing ML, special attention needs to be paid to 1000 the data precision of the underlined hardware platform. It was 1001 revealed in the literature that a ML/DNN based method may 1002 not require a full double-precision calculations and the use of 1003 even half-precision may not significantly reduce the accuracy 1004 of the system [81]. Many recent compute platforms and edge 1005 devices are now optimized for half-precision calculations, 1006 and this can significantly enhance the processing throughput 1007 of 2D and 3D ET systems.

1008
Another advantage of the use of ML-based reconstruction 1009 methods is that there are some software tools available to eas-1010 ily optimize the implementations to some extent, especially 1011 on GPUs. For example, Python-based model quantization 1012 libraries are available in TensorFlow, which can be used 1013 to develop quantized models with lower bit precision and 1014 faster execution on the target hardware [82]. The supported 1015 target hardware includes multi-core CPUs, GPUs, or Tensor 1016 Core Units (TPUs). While this is a good starting point for 1017 and R. Ramos, ''Electrical conductivity effect on the performance eval-1147 uation of EIT systems: A review,'' Measurement, vol. 178, Jun. 2021,