# A Space-Variant Deblur Method for Focal-Plane Microwave Imaging

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## Abstract

**:**

## 1. Introduction

## 2. Space-Variant PSF of OAP System

#### 2.1. Space-Variance Correction in the Angular Direction

#### 2.2. Space Variance Correction in the Radial Direction

## 3. Methods

#### 3.1. Log-Polar Transformation

- Step 1 Obtain the image data $f(x,y)$ of M*N by photoelectric sensors and the point spread function $PSF(x,y)$ of M*N by simulation of the ideal point source in FEKO.
- Step 2 Transform the image data $f(x,y)$ and $PSF(x,y)$ coordinate into the polar-coordinate to get the new image $g(r,\theta )$ and the new $PSF(r,\theta )$ Equation (8), and interpolate the new image using the bicubic interpolation method.$$r=log(\sqrt{{x}^{2}+{y}^{2}})\phantom{\rule{2.em}{0ex}}\theta =arctan(y/x)$$
- Step 3 Use the Lucy–Richardson algorithm with $g(r,\theta )$ and $PSF(r,\theta )$ to reconstruct the high-resolution image ${g}^{\prime}(r,\theta )$.
- Step 4 Inverse transform ${g}^{\prime}(r,\theta )$ into the Cartesian coordinate system and interpolate it by the bicubic method to obtain the final result with resolution recovery.

#### 3.2. Lucy–Richardson Iterative Algorithm

## 4. Results and Analysis

#### 4.1. PSF Used for the Results

#### 4.2. Deblur of Simulation Results

#### 4.3. Deblur of Experiment Results

- 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.

## 5. Conclusions

## Author Contributions

## Funding

## References

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**Figure 3.**(

**a**): y-z plane of the blur image with three points located at (x, y) = (0, 0.5 m), (0, 1 m), and (0, 2 m); (

**b**): the result of log-polar transformation of the left one.The unit of x-axis is pixel.

**Figure 6.**The 3 GHz PSFs of different methods: (

**a**) the PSF of direct deconvolution algorithm; (

**b**) the polar transformation’s PSF; (

**c**) the PSF of our method; and (

**d**) the PSF of the segmentation method.

**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 9.**The off-axis parabolic reflector antenna with optical-electronic sensors (

**a**) and horn antennas on the object plane (

**b**).

**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 11.**Blur image of the radiation antenna at frequencies of (

**a**) 3 GHz; (

**b**) 4 GHz; (

**c**) 5 GHz; (

**d**) 6 GHz; restoration result by log-polar transformation at (

**e**) 3 GHz; (

**f**) 4 GHz; (

**g**) 5 GHz; and (

**h**) 6 GHz frequency.

3 GHz | 4 GHz | 5 GHz | 6 GHz | |
---|---|---|---|---|

Left | (36,28) | (32,28) | (32,28) | (34,25) |

Center | (33,50) | (33,50) | (33,50) | (33,50) |

Right | (33,73) | (33,73) | (30,71) | (33,73) |

3 GHz | 4 GHz | 5 GHz | 6 GHz | |
---|---|---|---|---|

Left | 2 | 2 | 2 | 3 |

Center | 6 | 6 | 6 | 6 |

Right | 7 | 7 | 8 | 10 |

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## Share and Cite

**MDPI and ACS Style**

Luan, S.; Xie, S.; Wang, T.; Hao, X.; Yang, M.; Li, Y.
A Space-Variant Deblur Method for Focal-Plane Microwave Imaging. *Appl. Sci.* **2018**, *8*, 2166.
https://doi.org/10.3390/app8112166

**AMA Style**

Luan S, Xie S, Wang T, Hao X, Yang M, Li Y.
A Space-Variant Deblur Method for Focal-Plane Microwave Imaging. *Applied Sciences*. 2018; 8(11):2166.
https://doi.org/10.3390/app8112166

**Chicago/Turabian Style**

Luan, Shenshen, Shuguo Xie, Tianheng Wang, Xuchun Hao, Meiling Yang, and Yuanyuan Li.
2018. "A Space-Variant Deblur Method for Focal-Plane Microwave Imaging" *Applied Sciences* 8, no. 11: 2166.
https://doi.org/10.3390/app8112166