# A POCS Algorithm Based on Text Features for the Reconstruction of Document Images at Super-Resolution

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Classical Image Super-Resolution Reconstruction Algorithm

#### 2.1.1. Establishment of Degraded Model

#### 2.1.2. Image Registration Based on SIFT Algorithm

- Construct a scale space
- Detect extreme points in the scale space
- Locate the extreme points accurately
- Determine the main direction of key points
- Find the descriptors of key points

#### 2.1.3. Image Reconstruction Based on the POCS Algorithm

_{1}, m

_{2}, and frame l. $f({n}_{1},{n}_{2})$ is a pixel of the HR image. $n({m}_{1},{m}_{2},l)$ is the noise carried by the frame $l$ of LR image, which is generally considered additive noise. The corresponding point of $({m}_{1},{m}_{2})$ in reference frame is $({m}_{1}^{\prime},{m}_{2}^{\prime})$. $H({n}_{1},{n}_{2};{m}_{1}^{\prime},{m}_{2}^{\prime},l)$ is the point spread function of the observation image at point $({m}_{1}^{\prime},{m}_{2}^{\prime})$. Formula (3) can be expressed as follows:

#### 2.2. A POCS Algorithm Based on Text Feature

#### 2.2.1. Features of Document Images

#### 2.2.2. Text Features Based on the POCS Algorithm

- Formula (8) is added to the constraint conditions as an a priori function. The initial estimation is repeatedly revised based on it until the results meet the reconstruction conditions.
- In the original POCS algorithm, the image reduction formula is as follows:$$g({m}_{1},{m}_{2},l)={\displaystyle \sum _{{n}_{1},{n}_{2}}\stackrel{\wedge}{H}({n}_{1},{n}_{2};{m}_{1}^{\prime},{m}_{2}^{\prime},l)f({n}_{1},{n}_{2})+n({m}_{1},{m}_{2},l)}$$

#### 2.2.3. Algorithm Implementation

- Read an LR image and make a bilinear interpolation of it. The interpolation multiplier is a multiple of the desired improved resolution, then this interpolated image was selected as a reference frame. Let the initial estimate be ${f}_{0}$ and the threshold value be ${\delta}_{0}$.
- Read the remaining LR frames to register with the reference frame after bilinear interpolation, and estimate the motion between each frame and the reference frame to produce the registration mapping parameters.
- Define the convex set C of the sequences and calculate the residual r values to correct the reference frame.
- According to the data consistency constraint, the operator P was calculated, and the relationship between r and ${\delta}_{0}$ was assessed to correct $f$.
- The cycle end condition was set to $\frac{\Vert {f}^{(t+1)}-{f}^{(t)}\Vert}{{f}^{(t)}}\le \epsilon $. If the conditions are met, then $\stackrel{\wedge}{{f}^{(t)}}={f}^{(t)}$, and the loop ends. Otherwise, let $t=t+1$, and return to the step 3 until ${f}^{(t+1)}$ meets the convergence conditions. Then $\stackrel{\wedge}{{f}^{(t)}}$ is the eligible solution of the algorithm.

## 3. Analysis of Experimental Results

#### 3.1. Registration with the Optimized SIFT Operator

#### 3.2. Reconstructed Results and Analysis

#### 3.2.1. The Reconstructed Result of an LR Image Which Is Generated by Simulation

#### 3.2.2. Reconstruction of Ancient Books and Ancient Inscriptions Taken by Camera

#### 3.2.3. Reconstruction Quality Evaluation

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 5.**Effective feature point matching results of the original scale invariant feature transform (SIFT) algorithm.

**Figure 7.**(

**a**) Original high-resolution (HR) image; (

**b**) low-resolution (LR) image sequences; (

**c**) reference image after registration using the improved SIFT; (

**d**) reconstruction of the original projection onto convex sets (POCS); (

**e**) reconstruction using the method in [11]; (

**f**) reconstruction using the method in [12]; (

**g**) reconstruction of the improved POCS.

Algorithm Types | Characteristic Points | Matching Points | Matching Points | Time Spent on Matching (s) | The Correct Matching Rate (%) | |
---|---|---|---|---|---|---|

n_{1} | n_{2} | |||||

Original algorithm | 220 | 227 | 184 | 7 | 1.795 | 96 |

Improved algorithm | 220 | 227 | 180 | 1 | 1.763 | 99 |

Algorithm Types | PSNR/dB | MOS | The Execution Time/s | The Memory Occupation/KB |
---|---|---|---|---|

Original POCS | 23.29 | 3.302 | 7.319 | 2464.00 |

the method in [11] | 23.57 | 3.534 | 7.434 | 2934.00 |

the method in [12] | 24.31 | 3.708 | 7.327 | 2585.00 |

Improved POCS | 24.68 | 4.149 | 7.323 | 2324.00 |

Algorithm Types | PSNR/dB | MOS | The Execution Time/s | The Memory Occupation/KB |
---|---|---|---|---|

Original POCS | 36.97 | 3.452 | 10.371 | 3173.00 |

the method in [11] | 37.34 | 3.598 | 11.453 | 3528.00 |

the method in [12] | 38.16 | 3.974 | 11.185 | 3259.00 |

Improved POCS | 38.23 | 4.079 | 10.548 | 3194.00 |

Algorithm Types | PSNR/dB | MOS | The Execution Time/s | The Memory Occupation/KB |
---|---|---|---|---|

Original POCS | 37.98 | 3.548 | 11.079 | 3279.00 |

the method in [11] | 38.03 | 3.746 | 11.855 | 3371.00 |

the method in [12] | 38.74 | 4.032 | 11.273 | 3284.00 |

Improved POCS | 38.82 | 4.214 | 11.143 | 3281.00 |

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**MDPI and ACS Style**

Liang, F.; Xu, Y.; Zhang, M.; Zhang, L.
A POCS Algorithm Based on Text Features for the Reconstruction of Document Images at Super-Resolution. *Symmetry* **2016**, *8*, 102.
https://doi.org/10.3390/sym8100102

**AMA Style**

Liang F, Xu Y, Zhang M, Zhang L.
A POCS Algorithm Based on Text Features for the Reconstruction of Document Images at Super-Resolution. *Symmetry*. 2016; 8(10):102.
https://doi.org/10.3390/sym8100102

**Chicago/Turabian Style**

Liang, Fengmei, Yajun Xu, Mengxia Zhang, and Liyuan Zhang.
2016. "A POCS Algorithm Based on Text Features for the Reconstruction of Document Images at Super-Resolution" *Symmetry* 8, no. 10: 102.
https://doi.org/10.3390/sym8100102