## 4 Results and Analysis
### Deblur of Experiment Results  
We built an imaging system in a microwave darkroom and performed imaging experiments on three horizontally-placed, double-ridged horn antennas (3-6 GHz, 10 dBm), as shown in Figure 9. The results are shown in Figure 10.  
Figure 8: Row above: (**a**) Blur image; (**b**) after log-polar transformation; (**c**) results of the L-R method; (**d**) final result; row below, from left to right: results of (**e**) the direct L-R method; (**f**) polar transformation with the L-R method; (**g**) log-polar transformation with the L-R method (the same as (**d**)); (**h**) segmentation with the L-R method.  
Figure 7: (**a**) Simulation of 10 dipole sources (4 GHz,1 V/m); (**b**) resulting image.  
The row above in Figure 10 is the step result of the log-polar transformation algorithm, and the row below shows the results of the other algorithms. It can be seen that the direct SR and segmentation SR algorithms still generate noise and interfere, which will cause mistakes in the judgment and localization of the electromagnetic leakage. The log-polar algorithm can effectively suppress this problem. Figure 11 below shows the results of the imaging (upper) and resolution recovery (lower) results of radiation sources of different frequencies. So, as we can see, the algorithm can be applied to a wide-range spectrum if we can get the PSF.  
In theory, the recovered image should have the same resolution and position as the target signal. The resolution can be measured by the beamwidth of the recovered signal. So, we evaluated the results in Figure 11 by the consistency of position and beamwidth of the three signals.  
Figure 10: (**a**) blur image; (**b**) after log-polar transformation; (**c**) result of L-R method; (**d**) final result; (**e**) result of direct L-R method; (**f**) polar transformation with L-R method; (**g**) log-polar transformation with L-R method; (**h**) segmentation with L-R method.  
Figure 9: The off-axis parabolic reflector antenna with optical-electronic sensors (**a**) and horn antennas on the object plane (**b**).  
In the evaluation, the positions of different antennae were determined by the \(x\) and \(y\)-axes (unit: pixel) of the maximum value of their beams. The beamwidth used in this evaluation was introduced from the antenna area and was set at a beamwidth of \(-6\) dB, which means the area (unit: pixel) of the value that is \(6\) dB less than the peak of the beam. In this paper, it was calculated by the following:  
* Step 1 Convert the \(z\)-axis of the image matrix into a dB area by log operation.
* Step 2 Mark the pixel as 1 if its value is larger than the peak subtracted by \(6\) dB and \(0\) if not.
* Step 3 Calculate the number of 1 in the whole image as the \(-6\) dB beamwidth.  
The results are as follows. In Tables 1 and 2, left means the left signal on the recovered image, and similarly with the center and right. The units of both tables are pixels. Table 1 shows that the positions of the three signals were almost the same and met up with the real antenna. Table 2 shows that the recovery signals had good consistency in beamwidth with each other at different frequencies. The position and beamwidth prove that the method is suitable for wide-frequencies.  
The transformation is not complex and the size of image is also not too big, so the time that the algorithm consumes (on the laptop with MatLAB R2014b, Windows 7, Intel I5) is within 1 s. The number of iterations in the L-R iteration method is set to 300 for regularization.