# A Fuzzy Inference System for Unsupervised Deblurring of Motion Blur in Electron Beam Calibration

## Abstract

**:**

## 1. Introduction

## 2. Modeling and Implementation

#### 2.1. PSF Length Deviation

#### 2.2. Null Frequency Magnitude

#### 2.3. Deconvolution Artifact Residues

#### 2.4. Deconvolution Grade

## 3. Practical Result

#### Membership Function Parameters

## 4. Conclusions and Discussion

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Normalized power spectrum of $G$ exhibits ${\omega}_{1}$ and ${\omega}_{2}$ at 0.12 and 0.165 MHz frequencies with their harmonics at higher frequencies.

**Figure 2.**Deconvolution of the degraded pulse in Figure 1, using two different point spread function (PSF) lengths and demonstration of their deconvolution residues.

**Figure 3.**Process diagram, ${\widehat{L}}_{i}$ connections to the fuzzy inference system (FIS) are optional.

**Figure 5.**Null frequencies in the spectrum of the degraded pulse. Result of restoration with detected null frequencies, expected PSF length of $1$ mm on the left and $0.2$ mm on the right.

**Figure 6.**Null frequencies in the spectrum of the degraded pulse. Result of restoration with detected null frequencies, expected PSF length of $0.4$ mm.

Antecedent | Consequence | Rule Weight | ||
---|---|---|---|---|

PSF Dev | Attenuation | Residue | Restoration Quality | |

${\mu}_{m}$ | ${\mu}_{o}$ | ${\mu}_{r}$ | ${\mu}_{g}$ | 1 |

${\mu}_{m}$ | ${\mu}_{o}$ | ${\mu}_{r}^{\prime}$ | ${\mu}_{g}$ | 0.66 |

${\mu}_{m}$ | ${\mu}_{o}^{\prime}$ | ${\mu}_{r}$ | ${\mu}_{g}$ | 0.66 |

${\mu}_{m}$ | ${\mu}_{o}^{\prime}$ | ${\mu}_{r}^{\prime}$ | ${\mu}_{b}$ | 0.66 |

${\mu}_{m}^{\prime}$ | ${\mu}_{o}$ | ${\mu}_{r}$ | ${\mu}_{g}$ | 0.66 |

${\mu}_{m}^{\prime}$ | ${\mu}_{o}$ | ${\mu}_{r}^{\prime}$ | ${\mu}_{b}$ | 0.66 |

${\mu}_{m}^{\prime}$ | ${\mu}_{o}^{\prime}$ | ${\mu}_{r}$ | ${\mu}_{b}$ | 0.66 |

${\mu}_{m}^{\prime}$ | ${\mu}_{o}^{\prime}$ | ${\mu}_{r}^{\prime}$ | ${\mu}_{b}$ | 1 |

PSF Deviation | Attenuation | Residue | Restoration Quality | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

${\mu}_{m}$ | ${\mu}_{m}^{\prime}$ | ${\mu}_{o}$ | ${\mu}_{o}^{\prime}$ | ${\mu}_{r}$ | ${\mu}_{r}^{\prime}$ | ${\mu}_{q}$ | ${\mu}_{q}^{\prime}$ | ||||||||

${a}_{m}$ | ${c}_{m}$ | ${a}_{m}$ | ${c}_{m}$ | ${a}_{o}$ | ${c}_{o}$ | ${a}_{o}$ | ${c}_{o}$ | ${a}_{r}$ | ${c}_{r}$ | ${a}_{r}$ | ${c}_{r}$ | ${a}_{q}$ | ${c}_{q}$ | ${a}_{q}$ | ${c}_{q}$ |

0.02 | 1 | 0.04 | 1 | 0.02 | 0.3 | 0.05 | 0.3 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 |

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**MDPI and ACS Style**

Hosseinzadeh, S.
A Fuzzy Inference System for Unsupervised Deblurring of Motion Blur in Electron Beam Calibration. *Appl. Syst. Innov.* **2018**, *1*, 48.
https://doi.org/10.3390/asi1040048

**AMA Style**

Hosseinzadeh S.
A Fuzzy Inference System for Unsupervised Deblurring of Motion Blur in Electron Beam Calibration. *Applied System Innovation*. 2018; 1(4):48.
https://doi.org/10.3390/asi1040048

**Chicago/Turabian Style**

Hosseinzadeh, Salaheddin.
2018. "A Fuzzy Inference System for Unsupervised Deblurring of Motion Blur in Electron Beam Calibration" *Applied System Innovation* 1, no. 4: 48.
https://doi.org/10.3390/asi1040048