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

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2009

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).

2008

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]

2007

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]

2006

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]

S. Kim, “PDE-based image restoration: a hybrid model and color image denoising,” IEEE Trans. Image Process. 15(5), 1163–1170 (2006).
[CrossRef] [PubMed]

2005

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]

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]

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. B 234(4), 563–572 (2005).
[CrossRef]

2004

R. A. Lewis, “Medical phase contrast x-ray imaging: current status and future prospects,” Phys. Med. Biol. 49(16), 3573–3583 (2004).
[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).

2003

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]

2002

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]

2000

W. Chen, M. Chen, and J. Zhou, “Adaptively regularized constrained total least-square image restoration,” IEEE Trans. Image Process. 9(4), 589–596 (2000).

1998

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]

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]

1997

A. Chambolle and P. Lions, “Image recovery via total variation minimization and related problems,” Numer. Math. 76(2), 167–188 (1997).
[CrossRef]

1996

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]

1995

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

1994

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]

1992

W. Wu and A. Kundu, “Image estimation using fast modified reduced update Kalman filter,” IEEE Trans. Signal Process. 40(4), 915–926 (1992).
[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 D 60(1-4), 259–268 (1992).
[CrossRef]

1989

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

1988

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]

Ai-Min, Y.

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]

Banham, M. R.

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]

Baraniuk, R.

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).

Caselles, V.

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]

Chambolle, A.

A. Chambolle and P. Lions, “Image recovery via total variation minimization and related problems,” Numer. Math. 76(2), 167–188 (1997).
[CrossRef]

Chellappa, R.

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]

Chen, L.

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]

Chen, M.

W. Chen, M. Chen, and J. Zhou, “Adaptively regularized constrained total least-square image restoration,” IEEE Trans. Image Process. 9(4), 589–596 (2000).

Chen, W.

W. Chen, M. Chen, and J. Zhou, “Adaptively regularized constrained total least-square image restoration,” IEEE Trans. Image Process. 9(4), 589–596 (2000).

Cheng-Quan, L.

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]

Choi, H.

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).

Donoho, D.

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

Fatemi, E.

L. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithm,” Physica D 60(1-4), 259–268 (1992).
[CrossRef]

Flynn, M. J.

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]

Fourmaux, S.

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]

Frankel, G. S.

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]

Galatsanos, N. P.

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]

Gao, D.

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]

Gonzalez, H. L.

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]

Gureyev, T.

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]

Gureyev, T. E.

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]

Jenkins, B. K.

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]

Kashyap, Y. S.

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]

Katsaggelos, A. K.

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. K. Paik and A. K. Katsaggelos, “Image restoration using a modified Hopfield network,” IEEE Trans. Image Process. 1(1), 49–63 (1992).
[CrossRef] [PubMed]

Kieffer, J. C.

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]

Kim, J. Y.

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]

Kim, S.

S. Kim, “PDE-based image restoration: a hybrid model and color image denoising,” IEEE Trans. Image Process. 15(5), 1163–1170 (2006).
[CrossRef] [PubMed]

Krol, A.

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]

Kundu, A.

W. Wu and A. Kundu, “Image estimation using fast modified reduced update Kalman filter,” IEEE Trans. Signal Process. 40(4), 915–926 (1992).
[CrossRef]

Lewis, R. A.

R. A. Lewis, “Medical phase contrast x-ray imaging: current status and future prospects,” Phys. Med. Biol. 49(16), 3573–3583 (2004).
[CrossRef] [PubMed]

Li, X.

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).

Lions, P.

A. Chambolle and P. Lions, “Image recovery via total variation minimization and related problems,” Numer. Math. 76(2), 167–188 (1997).
[CrossRef]

Liu, H.

X. Wu, H. Liu, and A. Yan, “Optimization of X-ray phase-contrast imaging based on in-line holography,” Nucl. Instrum. Meth. B 234(4), 563–572 (2005).
[CrossRef]

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]

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]

Mallat, S. G.

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

Morel, J. M.

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]

Neelamani, R.

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).

Nesterets, Y. I.

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]

Osher, S.

L. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithm,” Physica D 60(1-4), 259–268 (1992).
[CrossRef]

Ozaki, T.

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]

Paik, J. K.

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]

Pogany, A.

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]

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]

Qi, X.

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).

Reimann, D. A.

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]

Rokhlin, S. I.

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]

Roy, T.

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]

Rudin, L.

L. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithm,” Physica D 60(1-4), 259–268 (1992).
[CrossRef]

Samei, E.

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]

Sapiro, G.

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]

Sarkar, P. S.

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]

Selesnick, L.

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]

Sendur, L.

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]

Shukla, M.

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]

Sinha, A.

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]

Stevenson, A.

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]

Stevenson, A. W.

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]

Tannenbaum, A.

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]

Toth, R.

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]

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Figures (6)

Fig. 1
Fig. 1

Schematic of the in-line phase contrast imaging system includes an x-ray source, sample, and a detector. The profile of intensity distribution is also shown.

Fig. 2
Fig. 2

(a) Cameraman decomposed in seven subbands and (b) the configuration of subbands.

Fig. 3
Fig. 3

Flowchart of the modified MTF compensation algorithm. FWT denotes the fast wavelet transform based on FT, MTFC represents the MTF compensation algorithm, and IFWT denotes the inverse transform of FWT.

Fig. 4
Fig. 4

(a) X-ray image of an edge device and (b) its wavelet transform image.

Fig. 5
Fig. 5

Plots of the (a) edge spread function and (b) the MTF of the system.

Fig. 6
Fig. 6

The results of a cockroach’s leg image: (a) original, (b) denoising, (c) conventional MTF compensation algorithm, (d) modified MTF compensation algorithm.

Tables (1)

Tables Icon

Table 1 Comparison of the Quality between Denoised and Restored Images

Equations (13)

Equations on this page are rendered with MathJax. Learn more.

F( u,v )= I 0 R 2 1 { 1sin[ πλ R 1 R 2 R 1 + R 2 ( u 2 + v 2 ) ]Φ( u M , v M ) },
G(u,v)=kF(u,v)MTF(u,v)* N m (u,v)+ N a (u,v),
I ' (u,v)= G(u,v)N(u,v) MTF(u,v) ,
x(n)=h(n) i +g(n) j ,
x(N)=h(N) i +g(N) j ,
x T ( N )= h T ( N ) i + g T ( N ) j .
C 0 (u,v)=F(u,v),
W(u,v)=h(N) h T (N) i i +h(N) g T (N) i j +g(N) h T (N) j i +g(N) g T (N) j j ,
Y J (u,v)= C J1 (u,v)W(u,v).
Y J (m,n)= f LL (m,n) i i + f LH (m,n) i j + f HL (m,n) j i + f HH (m,n) j j ,
C J (m,n)= f LL (m,n),
I ˜ ab J (u,v)= G ˜ ab J (u,v) N ˜ (u,v) MTF LL J (u,v) ,
E local =( c=1 1 d=1 1 [ f( x+c,y+d ) ( c=1 1 d=1 1 f( x+c,y+d ) ) /9 ] 2 ) / ( 2K+1 ) 2 ,

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