## Improving image quality of x-ray in-line phase contrast imaging using an image restoration method |

Optics Express, Vol. 19, Issue 23, pp. 23460-23468 (2011)

http://dx.doi.org/10.1364/OE.19.023460

Acrobat PDF (2548 KB)

### Abstract

For practical application of x-ray in-line phase contrast imaging, a high-quality image is essential for object perceptibility and quantitative imaging. The existing approach to improve image quality is limited by high cost and physical limitations of the acquisition hardware. A useful image restoration algorithm based on fast wavelet transform is proposed. It takes advantage of degradation model and extends the modulation transform function (MTF) compensation algorithm from Fourier domain to wavelet domain. The modified algorithm is evaluated through comparison with the conventional MTF compensation algorithm. Its deblurring property is also characterized with the evaluation parameters of image quality. The results demonstrate that the modified algorithm is fast and robust, and it can effectively restore both the lost detail and edge information while ringing artifacts are reduced.

© 2011 OSA

## 1. Introduction

1. B. Zoofan, J. Y. Kim, S. I. Rokhlin, and G. S. Frankel, “Phase-contrast x-ray imaging for nondestructive evaluation of materials,” J. Appl. Phys. **100**(1), 014502 (2006). [CrossRef]

4. Y. S. Kashyap, P. S. Yadav, T. Roy, P. S. Sarkar, M. Shukla, and A. Sinha, “Laboratory-based X-ray phase-contrast imaging technique for material and medical science applications,” Appl. Radiat. Isot. **66**(8), 1083–1090 (2008). [CrossRef] [PubMed]

5. S. Wilkins, T. Gureyev, D. Gao, A. Pogany, and A. Stevenson, “Phase contrast imaging using polychromatic hard x-ray,” Nature **384**(6607), 335–338 (1996). [CrossRef]

6. X. Wu and H. Liu, “X-Ray cone-beam phase tomography formulas based on phase-attenuation duality,” Opt. Express **13**(16), 6000–6014 (2005). [CrossRef] [PubMed]

## 2. Degradation model of x-ray in-line phase contrast image and MTF compensation

3. X. Wu and H. Liu, “Clinical implementation of x-ray phase-contrast imaging: theoretical foundations and design considerations,” Med. Phys. **30**(8), 2169–2179 (2003). [CrossRef] [PubMed]

*R*

_{1}and

*R*

_{2}are the distance between the source and sample, and the sample-to-detector distance,

*I*

_{0};

*M*= (

*R*

_{1}+

*R*

_{2})/

*R*

_{1}and

*u*and

*v*are spatial frequencies.

25. E. Samei, M. J. Flynn, and D. A. Reimann, “A method for measuring the presampled MTF of digital radiographic systems using an edge test device,” Med. Phys. **25**(1), 102–113 (1998). [CrossRef] [PubMed]

*k*and the asterisk denote the normalization factor and convolution, respectively. All noises in the system are classified as either nonstochastic or stochastic noises. The image of additive nonstochastic noise is the average of the dark current images. The image of multiplicative nonstochastic noise is obtained by

26. D. Donoho, “De-noising by soft thresholding,” IEEE Trans. Inf. Theory **41**(3), 613–627 (1995). [CrossRef]

27. Z. Wang, Z. Geng, Y. Zhang, and X. Sui, “The MTF measurement of remote sensors and image restoration based on wavelet transform,” in *Proceedings of International Conference on Wavelet Analysis and Pattern Recognition* (Institute of Electrical and Electronics Engineers, Beijing, 2007), pp. 1921 −1924.

## 3. Wavelet transform theory and the modified algorithm

### 3.1 Wavelet transform based on FFT

28. S. G. Mallat, “A theory for multiresolution signal decomposition: the wavelet representation,” IEEE Trans. Pattern Anal. Mach. Intell. **11**(7), 674–693 (1989). [CrossRef]

22. M. R. Banham, N. P. Galatsanos, H. L. Gonzalez, and A. K. Katsaggelos, “Multichannel restoration of single channel images using a wavelet-based subband decomposition,” IEEE Trans. Image Process. **3**(6), 821–833 (1994). [CrossRef] [PubMed]

*J*th level image has a size of

*J*= 1, 2, 3... is the level of the decomposition and

*h*(

*n*),

*g*(

*n*) are real coefficients with same length, corresponding to L and H filters for

*n*= 1, 2, …

*n*× 1 matrix. The Fourier transform (FT) of Eq. (4) is expressed aswhere

*h*(

*N*) and

*g*(

*N*) are corresponding to

*h*(

*n*) and

*g*(

*n*) for

*N*= 1, 2, …

*x*(

*N*) is given byLetwhere

*C*

_{0}(

*u*,

*v*) denotes the FT of the finest scaling coefficients for

*u*,

*v*= 1, 2,…

### 3.2 The modified algorithm for image restoration

27. Z. Wang, Z. Geng, Y. Zhang, and X. Sui, “The MTF measurement of remote sensors and image restoration based on wavelet transform,” in *Proceedings of International Conference on Wavelet Analysis and Pattern Recognition* (Institute of Electrical and Electronics Engineers, Beijing, 2007), pp. 1921 −1924.

22. M. R. Banham, N. P. Galatsanos, H. L. Gonzalez, and A. K. Katsaggelos, “Multichannel restoration of single channel images using a wavelet-based subband decomposition,” IEEE Trans. Image Process. **3**(6), 821–833 (1994). [CrossRef] [PubMed]

## 4. Experiment and image quality assessment

*M*was 2, and the exposure time was 30 s. The experiment was conducted with tube currents of 50 μA and tube voltage of 80 kV. Figure 4(a) illustrates the x-ray image of an edge device (1384 × 1032) made of lead, and Fig. 4(b) shows the wavelet transform of the image whose approximation subimage is adopted to compute the MTF curve. The results of the edge spread function and MTF are given in Fig. 5 .

*i*and

*j*are the values of gray level. The contrast of restored image increases 2.17 times (from 0.06 to 0.19) compared with that of denoised image, which implies that the visibility of the image is enhanced remarkably. The energy describes the uniformity of gray level distribution within the image and is expressed as

*x*and

*y*are the spatial coordinates. The variation of local energy from 0.12 to 1.11 suggests that the detail information has been recovered with our modified algorithm. The edge energy of an image represents the rich degree and clarity of edge. It is defined as

## 5. Conclusions

## Acknowledgments

## References and links

1. | B. Zoofan, J. Y. Kim, S. I. Rokhlin, and G. S. Frankel, “Phase-contrast x-ray imaging for nondestructive evaluation of materials,” J. Appl. Phys. |

2. | R. A. Lewis, “Medical phase contrast x-ray imaging: current status and future prospects,” Phys. Med. Biol. |

3. | X. Wu and H. Liu, “Clinical implementation of x-ray phase-contrast imaging: theoretical foundations and design considerations,” Med. Phys. |

4. | Y. S. Kashyap, P. S. Yadav, T. Roy, P. S. Sarkar, M. Shukla, and A. Sinha, “Laboratory-based X-ray phase-contrast imaging technique for material and medical science applications,” Appl. Radiat. Isot. |

5. | S. Wilkins, T. Gureyev, D. Gao, A. Pogany, and A. Stevenson, “Phase contrast imaging using polychromatic hard x-ray,” Nature |

6. | X. Wu and H. Liu, “X-Ray cone-beam phase tomography formulas based on phase-attenuation duality,” Opt. Express |

7. | R. Toth, J. C. Kieffer, S. Fourmaux, T. Ozaki, and A. Krol, “In-line phase-contrast imaging with a laser-based hard x-ray source,” Rev. Sci. Instrum. |

8. | L. Chen, L. Zheng, Y. Ai-Min, and L. Cheng-Quan, “Influence of tube voltage and current on in-line phase contrast imaging using a microfocus x-ray source,” Chin. Phys. |

9. | Y. I. Nesterets, S. W. Wilkins, T. E. Gureyev, A. Pogany, and A. W. Stevenson, “On the optimization of experimental parameters for x-ray in-line phase-contrast imaging,” Rev. Sci. Instrum. |

10. | X. Wu, H. Liu, and A. Yan, “Optimization of X-ray phase-contrast imaging based on in-line holography,” Nucl. Instrum. Meth. B |

11. | W. Clem Karl, “Regularization in image restoration and reconstruction,” in |

12. | Y. T. Zhou, R. Chellappa, A. Vaid, and B. K. Jenkins, “Image restoration using a neural network,” IEEE Trans. Acoust. Speech Signal Process. |

13. | J. K. Paik and A. K. Katsaggelos, “Image restoration using a modified Hopfield network,” IEEE Trans. Image Process. |

14. | L. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithm,” Physica D |

15. | T. Chan, S. Esedoglu, F. Park, and A. Yip, “Recent development of total variation image restoration,” in |

16. | A. Chambolle and P. Lions, “Image recovery via total variation minimization and related problems,” Numer. Math. |

17. | S. Kim, “PDE-based image restoration: a hybrid model and color image denoising,” IEEE Trans. Image Process. |

18. | W. Wu and A. Kundu, “Image estimation using fast modified reduced update Kalman filter,” IEEE Trans. Signal Process. |

19. | V. Caselles, J. M. Morel, A. Tannenbaum, and G. Sapiro, “Introduction to the special issue on partial differential equations and geometry-driven diffusion in image processing and analysis,” IEEE Trans. Image Process. |

20. | W. Chen, M. Chen, and J. Zhou, “Adaptively regularized constrained total least-square image restoration,” IEEE Trans. Image Process. |

21. | H. Lee and J. Paik, “Space-frequency adaptive image restoration based on wavelet decomposition,” in |

22. | M. R. Banham, N. P. Galatsanos, H. L. Gonzalez, and A. K. Katsaggelos, “Multichannel restoration of single channel images using a wavelet-based subband decomposition,” IEEE Trans. Image Process. |

23. | R. Neelamani, H. Choi, and R. Baraniuk, “ForWaRD: Fourier-wavelet regularized deconvolution for ill-conditioned systems,” IEEE Trans. Image Process. |

24. | L. Sendur and L. Selesnick, “Bivariate shrinkage functions for wavelet-based denoising exploiting interscale dependency,” IEEE Trans. Signal Process. |

25. | E. Samei, M. J. Flynn, and D. A. Reimann, “A method for measuring the presampled MTF of digital radiographic systems using an edge test device,” Med. Phys. |

26. | D. Donoho, “De-noising by soft thresholding,” IEEE Trans. Inf. Theory |

27. | Z. Wang, Z. Geng, Y. Zhang, and X. Sui, “The MTF measurement of remote sensors and image restoration based on wavelet transform,” in |

28. | S. G. Mallat, “A theory for multiresolution signal decomposition: the wavelet representation,” IEEE Trans. Pattern Anal. Mach. Intell. |

29. | C. H. Chen, L. F. Pau, and P. S. P. Wang, |

30. | J. Wang, X. Qi, and X. Li, “Edge and local energy NSCT based remote sensing image fusion,” J. Graduate School Chin. Acad. Sci. |

**OCIS Codes**

(100.1830) Image processing : Deconvolution

(100.3020) Image processing : Image reconstruction-restoration

(100.7410) Image processing : Wavelets

(110.7440) Imaging systems : X-ray imaging

**ToC Category:**

Image Processing

**History**

Original Manuscript: May 25, 2011

Revised Manuscript: August 13, 2011

Manuscript Accepted: October 20, 2011

Published: November 2, 2011

**Citation**

Xue-jun Guo, Xiao-lin Liu, Chen Ni, Bo Liu, Shi-ming Huang, and Mu Gu, "Improving image quality of x-ray in-line phase contrast imaging using an image restoration method," Opt. Express **19**, 23460-23468 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-23-23460

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### References

- B. Zoofan, J. Y. Kim, S. I. Rokhlin, and G. S. Frankel, “Phase-contrast x-ray imaging for nondestructive evaluation of materials,” J. Appl. Phys.100(1), 014502 (2006). [CrossRef]
- R. A. Lewis, “Medical phase contrast x-ray imaging: current status and future prospects,” Phys. Med. Biol.49(16), 3573–3583 (2004). [CrossRef] [PubMed]
- X. Wu and H. Liu, “Clinical implementation of x-ray phase-contrast imaging: theoretical foundations and design considerations,” Med. Phys.30(8), 2169–2179 (2003). [CrossRef] [PubMed]
- Y. S. Kashyap, P. S. Yadav, T. Roy, P. S. Sarkar, M. Shukla, and A. Sinha, “Laboratory-based X-ray phase-contrast imaging technique for material and medical science applications,” Appl. Radiat. Isot.66(8), 1083–1090 (2008). [CrossRef] [PubMed]
- S. Wilkins, T. Gureyev, D. Gao, A. Pogany, and A. Stevenson, “Phase contrast imaging using polychromatic hard x-ray,” Nature384(6607), 335–338 (1996). [CrossRef]
- X. Wu and H. Liu, “X-Ray cone-beam phase tomography formulas based on phase-attenuation duality,” Opt. Express13(16), 6000–6014 (2005). [CrossRef] [PubMed]
- R. Toth, J. C. Kieffer, S. Fourmaux, T. Ozaki, and A. Krol, “In-line phase-contrast imaging with a laser-based hard x-ray source,” Rev. Sci. Instrum.76(8), 083701 (2005). [CrossRef]
- L. Chen, L. Zheng, Y. Ai-Min, and L. Cheng-Quan, “Influence of tube voltage and current on in-line phase contrast imaging using a microfocus x-ray source,” Chin. Phys.16(8), 2319–2324 (2007). [CrossRef]
- Y. I. Nesterets, S. W. Wilkins, T. E. Gureyev, A. Pogany, and A. W. Stevenson, “On the optimization of experimental parameters for x-ray in-line phase-contrast imaging,” Rev. Sci. Instrum.76(9), 093706 (2005). [CrossRef]
- X. Wu, H. Liu, and A. Yan, “Optimization of X-ray phase-contrast imaging based on in-line holography,” Nucl. Instrum. Meth. B234(4), 563–572 (2005). [CrossRef]
- W. Clem Karl, “Regularization in image restoration and reconstruction,” in Handbook of Image and Video Processing, Second Edition, (Elsevier, 2005).
- Y. T. Zhou, R. Chellappa, A. Vaid, and B. K. Jenkins, “Image restoration using a neural network,” IEEE Trans. Acoust. Speech Signal Process.36(7), 1141–1151 (1988). [CrossRef]
- J. K. Paik and A. K. Katsaggelos, “Image restoration using a modified Hopfield network,” IEEE Trans. Image Process.1(1), 49–63 (1992). [CrossRef] [PubMed]
- L. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithm,” Physica D60(1-4), 259–268 (1992). [CrossRef]
- T. Chan, S. Esedoglu, F. Park, and A. Yip, “Recent development of total variation image restoration,” in Handbook of Mathematical Models of Computer Vision (Springer Verlag, 2005), pp. 17–32.
- A. Chambolle and P. Lions, “Image recovery via total variation minimization and related problems,” Numer. Math.76(2), 167–188 (1997). [CrossRef]
- S. Kim, “PDE-based image restoration: a hybrid model and color image denoising,” IEEE Trans. Image Process.15(5), 1163–1170 (2006). [CrossRef] [PubMed]
- W. Wu and A. Kundu, “Image estimation using fast modified reduced update Kalman filter,” IEEE Trans. Signal Process.40(4), 915–926 (1992). [CrossRef]
- V. Caselles, J. M. Morel, A. Tannenbaum, and G. Sapiro, “Introduction to the special issue on partial differential equations and geometry-driven diffusion in image processing and analysis,” IEEE Trans. Image Process.7(3), 269–273 (1998). [CrossRef] [PubMed]
- W. Chen, M. Chen, and J. Zhou, “Adaptively regularized constrained total least-square image restoration,” IEEE Trans. Image Process.9(4), 589–596 (2000).
- H. Lee and J. Paik, “Space-frequency adaptive image restoration based on wavelet decomposition,” in Proceedings of IEEE Asia Pacific Conference on Circuits and Systems (Institute of Electrical and Electronics Engineers, Seoul, 1996).
- M. R. Banham, N. P. Galatsanos, H. L. Gonzalez, and A. K. Katsaggelos, “Multichannel restoration of single channel images using a wavelet-based subband decomposition,” IEEE Trans. Image Process.3(6), 821–833 (1994). [CrossRef] [PubMed]
- R. Neelamani, H. Choi, and R. Baraniuk, “ForWaRD: Fourier-wavelet regularized deconvolution for ill-conditioned systems,” IEEE Trans. Image Process.52(2), 418–433 (2004).
- L. Sendur and L. Selesnick, “Bivariate shrinkage functions for wavelet-based denoising exploiting interscale dependency,” IEEE Trans. Signal Process.50(11), 2744–2756 (2002). [CrossRef]
- E. Samei, M. J. Flynn, and D. A. Reimann, “A method for measuring the presampled MTF of digital radiographic systems using an edge test device,” Med. Phys.25(1), 102–113 (1998). [CrossRef] [PubMed]
- D. Donoho, “De-noising by soft thresholding,” IEEE Trans. Inf. Theory41(3), 613–627 (1995). [CrossRef]
- Z. Wang, Z. Geng, Y. Zhang, and X. Sui, “The MTF measurement of remote sensors and image restoration based on wavelet transform,” in Proceedings of International Conference on Wavelet Analysis and Pattern Recognition (Institute of Electrical and Electronics Engineers, Beijing, 2007), pp. 1921 −1924.
- S. G. Mallat, “A theory for multiresolution signal decomposition: the wavelet representation,” IEEE Trans. Pattern Anal. Mach. Intell.11(7), 674–693 (1989). [CrossRef]
- C. H. Chen, L. F. Pau, and P. S. P. Wang, Handbook of Pattern Recognition and Computer Vision (World Science Publishing Co. Pte. Ltd, 1993), Chap 2.
- J. Wang, X. Qi, and X. Li, “Edge and local energy NSCT based remote sensing image fusion,” J. Graduate School Chin. Acad. Sci.26(5), 657–662 (2009) (in Chinese).

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