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Sparse-view ultrasound diffraction tomography using compressed sensing with nonuniform FFT.

Hua S, Ding M, Yuchi M - Comput Math Methods Med (2014)

Bottom Line: Simulation results show the effectiveness of the proposed method that the main characteristics of the object can be properly presented with only 16 views.Compared to interpolation and multiband method, the proposed method can provide higher resolution and lower artifacts with the same view number.The robustness to noise and the computation complexity are also discussed.

View Article: PubMed Central - PubMed

Affiliation: Image Processing and Intelligence Control Key Laboratory of Education Ministry of China, Department of Biomedical Engineering, School of Life Science and Technology, Huazhong University of Science and Technology, Wuhan 430074, China.

ABSTRACT
Accurate reconstruction of the object from sparse-view sampling data is an appealing issue for ultrasound diffraction tomography (UDT). In this paper, we present a reconstruction method based on compressed sensing framework for sparse-view UDT. Due to the piecewise uniform characteristics of anatomy structures, the total variation is introduced into the cost function to find a more faithful sparse representation of the object. The inverse problem of UDT is iteratively resolved by conjugate gradient with nonuniform fast Fourier transform. Simulation results show the effectiveness of the proposed method that the main characteristics of the object can be properly presented with only 16 views. Compared to interpolation and multiband method, the proposed method can provide higher resolution and lower artifacts with the same view number. The robustness to noise and the computation complexity are also discussed.

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Magnitude of error in frequency domain. (a) Interpolation method; (b) error value of interpolation method within [0, 300]; (c) broadband method; (d) CS method.
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fig5: Magnitude of error in frequency domain. (a) Interpolation method; (b) error value of interpolation method within [0, 300]; (c) broadband method; (d) CS method.

Mentions: Figure 5 shows the magnitude of error in the frequency domains. Since the maximum error of the interpolation method in Figure 5(a) is 4311, which is much bigger than the corresponding ones of the broadband method in Figure 5(c) (249.6) and the proposed method in Figure 5(d) (54.2), we also show the magnitude of error within the interval of [0,300] for the interpolation method (Figure 5(b)). From Figure 5, we can find that the error of interpolation method around center frequency is significantly larger than the remaining two methods, which accords with Figure 4(b) that the details of the features are seriously distorted comparing to other two methods. In Figure 5(c), the maximum error around center frequency is lower than that of Figure 5(b); however, the error of frequencies other than center frequency area is generally higher than the corresponding ones in Figure 5(b). This means the noises in the reconstructed image through broadband method are higher than the reconstructed image through interpolation method. Figure 5(d) shows that the proposed method can markedly reduce the frequency domain error particularly in the low frequency components. This indicates that the reconstructed image can faithfully represent the feature details while efficiently suppressing the noises for sparse-view sampling data. Table 1 gives the relative mean square error (RMSE) in frequency domains, which is defined as(26)RMSE=//F−F^//22//F//22;F and are the distribution function of the original phantom and the reconstructed object in frequency domain, respectively. Table 1 also lists the structural similarity (SSIM) index for different methods. Compared with RMSE, the SSIM has proven to be consistent with human eye perception [56]. In this paper, the original object (Figure 4(a)) is the reference image for SSIM. Compared to interpolation method, the proposed method has relatively smaller RMSE and higher SSIM values which coincides with the description above.


Sparse-view ultrasound diffraction tomography using compressed sensing with nonuniform FFT.

Hua S, Ding M, Yuchi M - Comput Math Methods Med (2014)

Magnitude of error in frequency domain. (a) Interpolation method; (b) error value of interpolation method within [0, 300]; (c) broadband method; (d) CS method.
© Copyright Policy - open-access
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC4020553&req=5

fig5: Magnitude of error in frequency domain. (a) Interpolation method; (b) error value of interpolation method within [0, 300]; (c) broadband method; (d) CS method.
Mentions: Figure 5 shows the magnitude of error in the frequency domains. Since the maximum error of the interpolation method in Figure 5(a) is 4311, which is much bigger than the corresponding ones of the broadband method in Figure 5(c) (249.6) and the proposed method in Figure 5(d) (54.2), we also show the magnitude of error within the interval of [0,300] for the interpolation method (Figure 5(b)). From Figure 5, we can find that the error of interpolation method around center frequency is significantly larger than the remaining two methods, which accords with Figure 4(b) that the details of the features are seriously distorted comparing to other two methods. In Figure 5(c), the maximum error around center frequency is lower than that of Figure 5(b); however, the error of frequencies other than center frequency area is generally higher than the corresponding ones in Figure 5(b). This means the noises in the reconstructed image through broadband method are higher than the reconstructed image through interpolation method. Figure 5(d) shows that the proposed method can markedly reduce the frequency domain error particularly in the low frequency components. This indicates that the reconstructed image can faithfully represent the feature details while efficiently suppressing the noises for sparse-view sampling data. Table 1 gives the relative mean square error (RMSE) in frequency domains, which is defined as(26)RMSE=//F−F^//22//F//22;F and are the distribution function of the original phantom and the reconstructed object in frequency domain, respectively. Table 1 also lists the structural similarity (SSIM) index for different methods. Compared with RMSE, the SSIM has proven to be consistent with human eye perception [56]. In this paper, the original object (Figure 4(a)) is the reference image for SSIM. Compared to interpolation method, the proposed method has relatively smaller RMSE and higher SSIM values which coincides with the description above.

Bottom Line: Simulation results show the effectiveness of the proposed method that the main characteristics of the object can be properly presented with only 16 views.Compared to interpolation and multiband method, the proposed method can provide higher resolution and lower artifacts with the same view number.The robustness to noise and the computation complexity are also discussed.

View Article: PubMed Central - PubMed

Affiliation: Image Processing and Intelligence Control Key Laboratory of Education Ministry of China, Department of Biomedical Engineering, School of Life Science and Technology, Huazhong University of Science and Technology, Wuhan 430074, China.

ABSTRACT
Accurate reconstruction of the object from sparse-view sampling data is an appealing issue for ultrasound diffraction tomography (UDT). In this paper, we present a reconstruction method based on compressed sensing framework for sparse-view UDT. Due to the piecewise uniform characteristics of anatomy structures, the total variation is introduced into the cost function to find a more faithful sparse representation of the object. The inverse problem of UDT is iteratively resolved by conjugate gradient with nonuniform fast Fourier transform. Simulation results show the effectiveness of the proposed method that the main characteristics of the object can be properly presented with only 16 views. Compared to interpolation and multiband method, the proposed method can provide higher resolution and lower artifacts with the same view number. The robustness to noise and the computation complexity are also discussed.

Show MeSH