Improving SNR and Sensitivity for Low-Coupling EMT Sensors

Electromagnetic tomography (EMT), also known as magnetic inductance tomography (MIT) is a tomographic modality widely employed in process industry and biomedical applications. In particular, this technique plays an important role in imaging metallic objects since it can produce conductivity and permeability distributions in the region of interest. An EMT system consists of a coil array, a data acquisition system, and an imaging reconstruction computer. Coils are used to generate electromagnetic field which interacts with the objects under investigation and measure the induced voltages. Conventionally, coils with sufficient inductance coupling (considerable number of turns or dimensions) are used to achieve high sensitivity and good SNR performance. However, this poses limitations for some applications, such as high-temperature applications and small-scale facilities. In high-temperature applications such as in steel or copper production processes, coils of the large number of turns are more likely to be damaged due to the breakdown of insulating materials between the turns, resulting in measuring errors. Besides, EMT applied in small-scale facility requires sensors with reduced dimensions, which results in weak magnetic coupling and lower SNR. In order to address these issues, this article proposes a method to transform the impedance and hence increase the sensor signal level through designing boosting transformers. Simulation and experimental results suggest that this increases the system SNR and image stability.


I. INTRODUCTION
O VER the past decades, a diverse range of tomographic systems have been developed and investigated for their potential applications. Electrical tomography (ET) has gathered significant interest. This technology relies on the electromagnetic properties of the measured materials and encompasses three distinct methods: 1) electrical capacitance tomography (ECT); 2) electrical resistance tomography (ERT); and 3) electromagnetic tomography (EMT).
EMT, also known as magnetic induction tomography (MIT), is a relatively new and emerging technology in the field of ET. In recent decades, EMT has gained attention as a promising imaging technique for its noncontact, high imaging speed, and noninvasion properties. This imaging technique applies electromagnetic fields to generate 2-D or 3-D images based on measuring boundary voltages on the coils surrounding the circumference of the imaging area. Altering current in the excitation coils generates a magnetic field known as the primary field that can be detected by one or more detection coils. Eddy current occurs when the conductive sample is placed in the cross section area and generates an induced magnetic field which is known as a secondary field. Both the primary field and secondary field induce voltage on the detection coils, this voltage varies with the location, the size, and the electromagnetic properties of the object under test. Therefore, EMT can image electrically conductive, ferromagnetic metals, or living organisms and has been widely used in biomedical applications [1], [2], nondestructive evaluations [3], and industrial inspections [4], e.g., inspecting cracks for airplane wings and for pipeline [5], [6]. Research on EMT has been focused on the analysis of the magnetic field, the design and optimization of the system [7], the design of excitation and measuring method [5], the optimization of image reconstruction algorithms, and multiflow monitoring [8], [9]. Most of them focus on the large-scale EMT applications. There is still a lack of small-sized or small-turns EMT systems which is capable for some industry applications, such as inspection of small bearing balls and molten metal monitoring in metal production of the continuous casting process. The implementation of the EMT system in monitoring molten metal has several physical obstacles. For instance, high temperature caused by the molten steel flow may damage the insulating material of sensors and therefore result in malfunction of the EMT sensor array. Normally, the temperature of liquid steel can reach up to 1500 • C. The EMT with a large number of coil turns requires longer thin wires to be wound tightly to a coil. More turns and intimate contact results in poor heat dissipation in high-temperature applications, and the coil will be easily damaged due to the breakdown of the insulating materials between the turns and will result in measuring errors. General solutions are applying high-temperature resistance insulation for the winding wires, utilizing sensor shielding, and employing large-scale EMT to avoid close contact. These solutions can introduce outstanding expense and low mobility of the EMT equipment [4], [10], [12], [13]. Sensor array with a small number of turns can mitigate these issues. Smaller turns of coil have better heat dissipation and less stringent wire radius requirements, which can minimize the possibility of coil damage and alleviate the requirement of the extensive thermal resistance material in the shielding. Besides, reducing the number of turns of the sensor array is also in need for small-scale applications, for example, in detecting defects on small bearing balls with small radius of 4 mm or less. Although promoting image stability, large number of turns will introduce a thicker detection coil and introduce relative lift-off which results in uncertainties in measurement [14], [15]. The implementation of small number of turns has some barriers, such as low received signal value due to low coupling. Transformers are primarily used to transfer electrical energy from one circuit to another through electromagnetic induction and may benefit in the enhancement of coupling and received signal value [16]. In some cases, transformer can be used to increase the voltage or current amplitude, depending on the turning ratio of the transformer. Transformer can transfer impedance based on the turning ratio and may exhibit an apparent increase in relative impedance due to impedance matching of the primary side and secondary side [17].
In this article, a novel method was proposed by implementing transformer on the coil side to solve the low coupling in EMT. The EMT sensor arrays with small number of turns (no more than 3) of coil have been studied. The objectives of this study are twofold: first, to amplify the signal amplitude and improve the SNR of the received signal; second, to enhance the image stability of the EMT system. First, coils of different sizes with different distances are analyzed to determine the influence of sensor size on received signal SNR. Second, coils with varying number of turns are analyzed to determine the relationship between coil turns and received signal SNR. Third, transformers of different ratios (1:20 and 1:80) are employed to amplify the impedance of the reduced turns coil in the EMT system under different frequencies. A novel EMT sensing system has been implemented to accommodate three turns detection coils with transformers. Different ratios of transformers are applied on the detection coil side and both the excitation and detection sides of the EMT sensor array. The improvement of the amplitude of the received signal and SNR is observed. When the 1:80 transformer is applied on the detection side, 17-dB increment in the SNR can be achieved. When the 1:80 transformer is applied on both sides of the EMT sensor array, the increment of SNR can reach 18 dB. The stability of the reconstructed image is evaluated by using a novel convergency analysis method. The 1:80 transformer performs the best when being applied on the detection side and both sides of the EMT sensor array; the cases when 1:20 and 1:80 transformers are applied on both sides perform better compared to the cases when they are applied on detection side only.

II. METHODOLOGY
The aim of this research is to amplify the received signal amplitude and improve SNR of the reduced-turn coils. The received induced voltage at the detection coils decreases when the number of coil turns decreases, which results in lower amplitude of the received signal. The relationship between received voltage V received and coil turns is depicted by where λ is the flux linkage to the detection coil, ϕ is the magnetic flux, and S A is the surface bounded by each turn. To amplify the mutual inductance of the reduced-turn coils, two transformers are employed in this research, whose turning ratios are 1:20 and 1:80, respectively. They are commercial CST2010 series transformers produced by Coilcraft. Fig. 1(a) depicted the implementation of the transformers in the EMT sensor array, which are applied on both the excitation and detection coils. A photography of the EMT sensor array with transformers on is shown in Fig. 1(b). The induced voltage is then measured on the secondary side of the transformer in series with the detection coil of the EMT sensor array. The primary side of the applied transformer is connected to the coils in the EMT sensor array, in this case, the excitation current will increase by N times and the induced primary magnetic field will be enhanced. At the secondary side of the transformer, the induced voltage at the detection coils will be amplified by N times, which will be fed into the front-end circuit of the EM instrument. With the transformer, the detectability of the EMT system can be improved.
The electromagnetic response of a conductive object is typically frequency-dependent and the field is governed by (2) in terms of magnetic vector potential A [18] 1 μ where μ and σ are permeability and conductivity, respectively; ω is the angular frequency; − → A is the magnetic vector potential; and J is the current density.
On the other hand, the penetration depth of the eddy current into the object under test is inversely proportional to the square root of the excitation frequency as shown in (2). Therefore, high-frequency measurement reveals EM properties near the surface while low-frequency measurement provides information deeper inside the test object. The electromagnetic skin depth δ is given by where f is the excitation frequency, and μ is the permeability of air. Hence, the operating frequency will also be carefully considered in this research. In Section IV, experiments are carried out at different excitation frequencies to verify the performance of the proposed method with respect to SNR.

III. THEORETICAL ANALYSIS AND SIMULATION A. EQUIVALENT CIRCUIT
In this section, theoretical analysis and simulations have been carried out to verify the performance of the EMT sensor array in terms of the signal amplitude, when embedded with transformers. First, the equivalent circuit of the EMT sensor and the test piece was proposed, which is shown in Fig. 2. In free space, mutual inductance can be derived from 12 (4) where V det represents the detected voltage, I exc represents the excitation current, and M 12 is the mutual inductance between excitation and detection coil pair.
When a conductive object is placed between the coil pair, the relationship between the induced voltage V det and excitation current I exc can be obtained by where M 32 is the mutual inductance between device under test and detection coil; R 1 + jωL 3 is the impedance of device under test, and I ind is the induced eddy current. The presence of the conductive object between the excitation coil and detection coil contributes to changes in the mutual inductance between the coil pair. Therefore, the electromagnetic properties of the object are reflected in the effective mutual inductance change between the excitation and detection coil pair.

B. SIMULATION
Mutual inductances under three different transformer configurations are simulated: one transformer on the excitation coils side, one transformer on the detection coils side, and transformers on both sides. Results are compared with simulations without transformers. The simulation is performed in LTSPICE, which is a high-performance circuit simulation program from Analog Devices. The schematics are demonstrated in Fig. 3. Fig. 3(a) demonstrates the simulation without the transformer, Fig. 3(b) shows the simulation with the transformer on the excitation coil side, Fig. 3(c) shows the simulation with the transformer on the detection coil side, and Fig. 3(d) shows the simulation with transformers on both sides.
As aforementioned, this research intends to employ coils with small number of turns. Three-turn hand wound coils were constructed for this purpose. In order to observe the performance of the coil with different number of turns, parameters, such as the self-impedance of the coils, are obtained by a commercial impedance analyzer Zurich instrument (MFIA) ahead of the simulation. During the experiment, the impedance analyzer performed frequencyswept measurements from 1 to 510 kHz to observe the  frequency response of the coils. The resistance and inductance of measured impedances are depicted in Fig. 4. The disordered inductances at lower frequencies result from the poor performance of the instrument when measuring small inductance at lower frequencies.
From the results, it can be observed that no resonance occurred in the frequency range of interest and the resistance and inductance were maintained at similar level from 50 to 100 kHz. Therefore, the resistance and inductance at 50 kHz are selected as simulation parameters.
From the measurement, the inductance of 3, 2, and 1 turn(s) coil is 1.7, 0.9, and 0.5 μH, respectively. In this case, 3 turns coil is applied in the simulation. The perturbation of the conductive sample is represented by the changes in the coupling coefficient k 2 in Fig. 3. The mutual impedance, including their real parts and imaginary parts of four different situations, is depicted in Fig. 5, in which the mutual inductance of the transformer on the excitation side is the same as that of the transformer on the detection side.
The impedance of the simulated transformer is derived from the datasheet of the 1:20 transformer from Coilcraft, which is 850 nH at the primary side and 1.7 μH at the secondary side.
It can be seen from the figures that the mutual inductance increases significantly when the transformer is applied on both the excitation and detection sides of the coil pair. To be specific, at 50 kHz, the mutual inductance increases by 18.16 times compared to the situation without the transformer; when the 1:20 transformer is applied to one side of the coil, the inductance increased by 5.13 times compared to the case without the transformer.

A. EM INSTRUMENT
Typically, the EMT system consists of three key elements: 1) a host PC; 2) the conditioning electronics; and 3) the EMT sensor array. In this research, a 16-channel EMT data acquisition system is utilized, which is based on a Zynq-7020 FPGA system-on-a-chip (SoC). The SoC consists of a processing system based on an ARM dual Cortex-9 processor and a Xilinx 7-series FPGA which is also called programmable logic. The architecture of the EMT instrument is shown in Fig. 6. The FPGA is responsible for generating excitation signal, I/Q demodulation for receiving signals, digital filters implementation, and data communication with the host PC. The front-end circuit of the instrument contains AD/DA modules, power amplification modules, multiplexing modules, and analog filters. The instrument contains 4 four-channel analog multiplexers for excitation coils and 4 four-channel analog multiplexers for detection coils. Each of the switch can be selected in a LabVIEW-based user interface on the host PC. Therefore, the coil pair, the excitation, and the sensing sequence can be configurated flexibly during the experiments. For exciting the coil, one of the 16 switches at the multiplexers is closed, and an AC excitation current is fed into the excitation coil. Then, the multiplexer handles the received voltage from the detection coils sequentially controlled by the FPGA via the host PC. Due to the fast  integrated processing of the presented EMT system, the maximum data speed can reach up to 10 000 samples/s which is equivalent to 178 frames/s. In addition, a typical SNR of 80-90 dB can be obtained under a loopback configuration, which can satisfy the requirements for the most of industrial applications. When equipped with coils with small number of turns, the SNR is degraded significantly. However, it is due to the fact that coils with small number of turns have much smaller inductance which results in much lower detectable signal level.

B. SENSOR COIL CONFIGURATION
Though the EMT instrument can support up to 16-coil sensor array, this research mainly focuses on 8-coil EMT sensor arrays. Therefore, there are typically 56 coil pairs in a single EMT frame. During the measurement, a completed measuring sequence is explained as follows. The coils were excited in turn and the signals were received from the rest of the coils individually. For example, when coil 1 is selected to be an excitation coil and the mutual inductance between coil 1 and other coils, represented as coil pairs as coil 1,2 , coil 1,3 , . . . , and coil 1,8 are measured sequentially. Then, coil 2 is selected to be the next excitation coil and the mutual inductances between coil 2 and other coils are measured, in this case represented by coil pairs coil 2,1 , coil 2,3 , . . . , and coil 2,8 . This process will continue until coil 8 is selected to be the excitation coil and the last mutual inductance of coil 8 and coil 7 is measured. A total number of measured inductances in this EMT is obtained from where N is the number of coils in EMT. For this case, N = 8 and M = 56. Preliminary experiments were carried out with only one coil pair to verify the ability of the proposed method to amplify signal levels, before the implementation of the transformer on the 8-coil EMT sensor array. In the experiment, each coil is placed on the opposite side facing to each other, which can be regarded as coil pair coil 1,5 in the 8-coil EMT sensor array. Four different types of coil pair with different sizes and different turns are evaluated in these experiments. The SNR of received signal is obtained by SNR = 20 log 10  where n represents the number of measured values, V rec,i represents the measured received voltage, and V rec represents the average of the received voltage. The experimental setup is depicted in Fig. 7. A 1:20 transformer is applied at the detection coil only, at the exciting coil only and both at excitation and detection coils. The actual size of the EMT sensor array highly depends on the application. Based on previous applications [7], [9], [12], [13], [18], a typical diameter of the EMT sensor array is between 6 and 11 cm. Thus, the experiments were carried out under similar configurations. Coil of Different Shapes: A pair of 3 turns circular coils and a pair of 3 turns elliptical coils, as shown in Table 1, are employed to determine the relationship between the signal SNR and the coil shape. The SNR of round coils without transformer is under 20 dB when the applied frequency is below 50 kHz, which is not acceptable in EMT measurement. Therefore, the applied frequencies are chosen to be 50 and 70 kHz. Three set-ups of the 1:20 transformer are implemented: 1) transformer applied on the excitation side; 2) transformer applied on the detection side; and 3) transformers applied on both sides. Fig. 8 shows the free space SNR of received signals at 50 and 70 kHz for an elliptical commercial coil pair (c) and a circular coil pair (r) with different transformer configurations.
As shown in Fig. 9, the performance of elliptical coils is better than that of round coils in all cases. Larger surface area results in larger received signal value. The surface area of the elliptical coil is larger than that of the circular coil. Therefore, the elliptical coil received larger signal compared to the circular coil, which can be obtained by (1). For the same measuring system, a coil with higher inductance/received voltage contributes to a better performance. Transformer applied on both sides performs the best in terms of the SNR in most cases. Specifically, with the 1:20 transformer applied on both sides of the coil at 11 cm, the SNR of the elliptical coil pair at 50 kHz is 44.8 dB, while the SNRs of the circular coil are 39.3 dB under the same conditions. For the same distance and frequency, when the 1:20 transformer is applied on the detection side of the coils, the SNRs of the elliptical and round coils are 44.3 and 32.5 dB, respectively. And for the same case when the transformer is applied on excitation coil side, the SNRs of elliptical and round coil are 31.8 and 20.7 dB, which only slightly increase. When the transformer is applied on both sides of the elliptical coil pair, average improvements of SNR are 16.5 dB at 50 kHz and 13.8 dB at 70 kHz. When the transformer is only applied on the detection side of elliptical coil, increments of SNR for elliptical coils are 17.2 dB at 50 kHz and 14.8 dB at 70 kHz. This indicates that transformer benefits on the SNR increment of smaller size of coil. The transformer applied to the detection side improves the SNR of the received signal of the opposite coil pair better than the transformer applied to both sides. When the transformer is only applied on the excitation side, no significant enhancement in SNR is achieved. For elliptical coils, the average SNR increments are 2.2 dB at 50 kHz and 0.5 dB at 70 kHz. Therefore, it can be concluded that the signal SNR can be improved when transformers are introduced at the detection coil side and at both sides. There are few improvements when the transformer is applied at the excitation side, so this configuration is not considered in the following experiments.
Number of Turns: This section intends to investigate the impact of coil turns on the signal SNR performances of coil pairs. SNR is evaluated at 1 turn, 2 turns, and 3 turns. The experimental setup remains the same as in section coil of different shapes. As aforementioned, only the cases when the transformer is placed on the detection side and both sides of the coil are considered, and elliptical shape is used for better SNR performance. Fig. 9 shows the SNR for three coil pairs with two different transformer configurations at different distances at 50 and 70 kHz. The SNR performance has been significantly improved when the transformers are applied on both sides of the coil pairs for 2 turns and 1 turn coil. For the 3 turns coil, the performance with the transformer on both sides is similar to that with the transformer on the detection side. The SNR increments of the two transformer configurations can reach up to 5.5 and 7.4 dB at 50 kHz for 2 turns coil and 1 turn coil at 11 cm, respectively. The average SNR increments for transformer applied on the detection side and both sides of 3 turns coil at the same distance and frequency are 16.8 and 16.5 dB, respectively, which indicates that the SNR increment values of two transformer configurations are similar when 3 turns coils are used.

Transformer on One Side (Detection Side):
This section investigates the potential of applying transformer to an 8-coil   sensor array with an outer diameter of 10.5 cm. Transformers of different ratios (1:20 and 1:80) are adapted on the detection coil side of the EMT sensor array. A cylindrical copper bar represents the perturbation in the cross section area. The tested copper slag is placed at the middle of the image cross section. Typically, the received signal will increase as the perturbation approaches the coils. A photograph of the setup is shown in Fig. 10.
For each coil pair, the received voltage increases with the approach of the coils and decreases with the separation of the two coils. This constructs to a "U" shape depicted in Fig. 11. A typical "U" shape can be observed from the received data, which indicates that the EM instrument is capable of carrying out EMT measurements.   detection side, the amplitudes of the received signal increase by 1.016 and 3.673 times on average compared to the case without the transformer, respectively. The small amplification of the signal amplitude compared to impedance analyzer is due to the loading effect of the resistors in the input stage of the op-amp. Table 2 demonstrates the SNR of I, Q, and M value when the excitation coil is coil 1 and the detection coil is coil 2 , and when transformers of different ratios are applied on the detection side of the coils at different frequencies. When placing the 1:20 and 1:80 transformers, the SNR increments of the magnitude of the received signal at 30 kHz are 9.4 and 17.3 dB, respectively. At 50 kHz, the increments are 2.8 and 19.3 dB; and at 70 kHz, these values are 17.3 and 22.1 dB. Overall, amplitude and SNR performances are the best when the 1:80 transformer is placed on the detection side of the sensor array. The frequency sweeper plot of 3 turns coil is shown in Fig. 4, which also demonstrates the frequency dependence of the EMT coil. It shows that the coil operates smoothly from 500 Hz to 500 kHz. The received signal amplitude and SNR increment are smaller when the operating frequency is set to be 30 kHz. For 70 kHz, it has larger received signal and SNR increment, but it has less penetrate depth compared to 50 kHz. In many industrial applications, in particular for metal inspection, high frequency can only inspect surface due to skin depth effect. Therefore, 50 kHz is the most reasonable operation frequency, since it has large enough received signal as well as SNR and contains more information than 70 kHz.
Transformer on Both Sides: In this section, transformers with different ratios are applied on both the excitation coil and the detection coil. The real part and imaginary parts of the received voltage under 50 kHz are depicted in Fig. 13. The cases when 1:20 and 1:80 transformers placed on both EMT coil sides increase the signal amplitude by 4 and 15 times, respectively, relative to the receiving voltage without transformer. Table 3   the detection sides and both detection sides and excitation sides of the EMT sensor array at 50 kHz, respectively. From Fig. 14, an average increment of 15.97 dB in SNR is observed when the 1:80 transformer is applied on the detection sides compared to the SNR without transformer; this average SNR increment is 21.17 dB when the 1:80 transformer is placed on both sides, it also indicates that the case when the 1:80 transformer on both sides has significant effect on coils with weaker coupling.

D. IMAGE STANDARD DEVIATION ANALYSIS
Time-based standard deviation analysis indicates the mean value of the standard deviations of pixel values at different locations in the imaging area of interest in the time domain and helps to provide a better view of the stability of the reconstructed image [13]. The imaging area consists of a circle with 100 pixels in both the x-axis and y-axis. To assess the image stability, reconstructed pixels (colored dots) were selected at different radius with equal spacing, including R = 50, R = 25, R = 10, and at the center, as depicted in Fig. 15(a). When there is no transformer, the pixel values of these selected dots are depicted in Fig. 15(b). Fig. 15(c) shows the standard deviation analysis, lower standard deviation indicates more stable reconstructed image.
The accessed pixels are measured under 50 kHz on two transformer configurations. Each experiment took about 2 min, the copper bar is placed in the middle of the cross section area after 1 min. When introducing the copper bar into the imaging area, signal-level change should be observed. The level of change depends on the location and the stability of the system. For example, when placing the copper bar at the center of the imaging area, pixel value at R = 0 should give the largest change. A system with better stability or SNR should have pixel value maintained at similar level when there is no presence of any sample. With the presence of the sample, a detectable pixel value change should be observed for a stable system. The convergence results based on the pixel location for different transformer configurations in the time domain are shown in Fig. 16. Fig. 15(c) shows the average of the standard deviation values of pixels at different radius without transformer on, indicating the reconstructed pixel values have lower standard deviation in the more central part. Fig. 17 indicates the average of the standard deviation values of pixels at different radius under different transformer configurations, illustrating the effect of the transformers. The reconstructed image values are more stable when transformers of higher ratios are implemented on both the excitation and detection sides. The 1:80 transformer placed on both sides performs the best, with an average standard deviation of 8 × 10 −4 for all the selected pixels.

V. CONCLUSION
In this article, a real-time EMT system with small number of turns of coil has been presented. Simulations of three transformer configurations, where the transformer is applied on the excitation coil side, the detection coil side, and both the excitation and detection coil sides, are analyzed. When the 1:20 transformers are placed on both sides, the amplitude of the received signal increases by up to 18.16 times compared to the case without transformers. The amplitude increases by up to 5.13 times for configurations with singleside transformer. Then, a single pair of coils with different sizes and different turns are measured under these three transformer configurations. Three turns commercial ellipse-sized coil pair provides better SNR performance than the round coil pair. The 1:20 transformer placed on the detection coil side and both sides of the ellipse-sized coil pair can provide SNR increment of 17.2 and 16.5 dB at 50 kHz, respectively, compared to the case without transformer. Finally, transformers of different ratios are placed on the ellipse-size 8-coil EMT sensor array, on the detection side and on both sides of the EMT sensor array. The performance of magnitude, SNR, and a time-domain standard deviation analysis shows the 1:80 transformer placed on both sides of the EMT sensor array performs the best, with the smallest standard deviation of 8×10 −4 for the selected pixels of the reconstructed image. Compared to the case without transformer, the case when the 1:80 transformer is placed on both sides increases the magnitude of the received signal by 15 times and improves the signal SNR from 47.4 to 70.1 dB for the adjacent coil pair. Eight-coil EMT system with 100 turns coil has an SNR range between 46.7 and 60 dB [19], and another 8-coil EMT system with 448 turns coil claimed having an average SNR of 48 dB [20]. The SNR depends on the size of the sensor array and the number of coil turns. The proposed EMT system with 1:80 transformer on both sides has an SNR range from 44.3 to 70.1 dB. The proposed EMT system has good performance in the upper SNR limit compared to the EMT system with large number of coil turns, which can provide more reliable measurements on the intended applications. However, the lower limit of the SNR range of the proposed EMT system is smaller than that of the EMT system with larger number of coil turns. The lower limit of the SNR can be improved by applying transformer with higher turns ratio on both sides of the coils.
In conclusion, the number of turns can be reduced to as low as 3-turn for an EMT sensor according to this research, which is believed to be the first quantification of an EMT sensor array of this kind. When applying 1:80 transformers on both excitation and detection coils, an average improvement of 21.17 dB in SNR has been achieved. According to the standard deviation analysis, under this transformer configuration, the stability of the system has been enhanced as reflected in the reconstructed images.