To improve the anti-noise performance of the time-domain Bregman iterative algorithm,an adaptive frequency-domain Bregman sparse-spike deconvolution algorithm is proposed.By solving the Bregman algorithm in the freque...To improve the anti-noise performance of the time-domain Bregman iterative algorithm,an adaptive frequency-domain Bregman sparse-spike deconvolution algorithm is proposed.By solving the Bregman algorithm in the frequency domain,the influence of Gaussian as well as outlier noise on the convergence of the algorithm is effectively avoided.In other words,the proposed algorithm avoids data noise effects by implementing the calculations in the frequency domain.Moreover,the computational efficiency is greatly improved compared with the conventional method.Generalized cross validation is introduced in the solving process to optimize the regularization parameter and thus the algorithm is equipped with strong self-adaptation.Different theoretical models are built and solved using the algorithms in both time and frequency domains.Finally,the proposed and the conventional methods are both used to process actual seismic data.The comparison of the results confirms the superiority of the proposed algorithm due to its noise resistance and self-adaptation capability.展开更多
X-ray computed tomography （CT） is one of widely used diagnostic tools for medical and dental tomographic imaging of the human body. However, the standard filtered back- projection reconstruction method requires the ...X-ray computed tomography （CT） is one of widely used diagnostic tools for medical and dental tomographic imaging of the human body. However, the standard filtered back- projection reconstruction method requires the complete knowledge of the projection data. In the case of limited data, the inverse problem of CT becomes more ill-posed, which makes the reconstructed image deteriorated by the artifacts. In this paper, we consider two dimensional CT reconstruction using the projections truncated along the spatial direc- tion in the Radon domain. Over the decades, the numerous results including the sparsity model based approach has enabled the reconstruction of the image inside the region of interest （ROI） from the limited knowledge of the data. However, unlike these existing methods, we try to reconstruct the entire CT image from the limited knowledge of the sinogram via the tight frame regularization and the simultaneous sinogram extrapolation. Our proposed model shows more promising numerical simulation results compared with the existing sparsity model based approach.展开更多
As X-ray computed tomography （CT） is widely used in diagnosis and radiotherapy, it is important to reduce the radiation dose as low as reasonably achievable. For this pur- pose, one may use the TV based methods or w...As X-ray computed tomography （CT） is widely used in diagnosis and radiotherapy, it is important to reduce the radiation dose as low as reasonably achievable. For this pur- pose, one may use the TV based methods or wavelet frame based methods to reconstruct high quality images from reduced number of projections. Furthermore, by using the in- terior tomography scheme which only illuminates a region-of-interest （ROI）, one can save more radiation dose. In this paper, a robust wavelet frame regularization based model is proposed for both global reconstruction and interior tomography. The model can help to reduce the errors caused by mismatch of the huge sparse projection matrix. A three-system decomposition scheme is applied to decompose the reconstructed images into three differ- ent parts： cartoon, artifacts and noise. Therefore, by discarding the estimated artifacts and noise parts, the reconstructed images can be obtained with less noise and artifacts. Similar to other frame based image restoration models, the model can be efficiently solved by the split Bregman algorithm. Numerical simulations show that the proposed model outperforms the FBP and SART＋TV methods in terms of preservation of sharp edges, mean structural similarity （SSIM）, contrast-to-noise ratio, relative error and correlation- s. For example, for real sheep lung reconstruction, the proposed method can reach the mean structural similarity as high as 0.75 using only 100 projections while the FBP and the SART^TV methods need more than 200 projections. Additionally, the proposed ro- bust method is applicable for interior and exterior tomography with better performance compared to the FBP and the SART＋TV methods.展开更多
In this paper, we consider two variational models for speckle reduction of ultrasound images. By employing the F-convergence argument we show that the solution of the SO model coincides with the minimizer of the JY mo...In this paper, we consider two variational models for speckle reduction of ultrasound images. By employing the F-convergence argument we show that the solution of the SO model coincides with the minimizer of the JY model. Furthermore, we incorporate the split Bregman technique to propose a fast alterative algorithm to solve the JY model. Some numericalexperiments are presented to illustrate the efficiency of the proposed algorithm.展开更多
基金supported by the National Natural Science Foundation of China(No.NSFC 41204101)Open Projects Fund of the State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation(No.PLN201733)+1 种基金Youth Innovation Promotion Association of the Chinese Academy of Sciences(No.2015051)Open Projects Fund of the Natural Gas and Geology Key Laboratory of Sichuan Province(No.2015trqdz03)
文摘To improve the anti-noise performance of the time-domain Bregman iterative algorithm,an adaptive frequency-domain Bregman sparse-spike deconvolution algorithm is proposed.By solving the Bregman algorithm in the frequency domain,the influence of Gaussian as well as outlier noise on the convergence of the algorithm is effectively avoided.In other words,the proposed algorithm avoids data noise effects by implementing the calculations in the frequency domain.Moreover,the computational efficiency is greatly improved compared with the conventional method.Generalized cross validation is introduced in the solving process to optimize the regularization parameter and thus the algorithm is equipped with strong self-adaptation.Different theoretical models are built and solved using the algorithms in both time and frequency domains.Finally,the proposed and the conventional methods are both used to process actual seismic data.The comparison of the results confirms the superiority of the proposed algorithm due to its noise resistance and self-adaptation capability.
文摘X-ray computed tomography （CT） is one of widely used diagnostic tools for medical and dental tomographic imaging of the human body. However, the standard filtered back- projection reconstruction method requires the complete knowledge of the projection data. In the case of limited data, the inverse problem of CT becomes more ill-posed, which makes the reconstructed image deteriorated by the artifacts. In this paper, we consider two dimensional CT reconstruction using the projections truncated along the spatial direc- tion in the Radon domain. Over the decades, the numerous results including the sparsity model based approach has enabled the reconstruction of the image inside the region of interest （ROI） from the limited knowledge of the data. However, unlike these existing methods, we try to reconstruct the entire CT image from the limited knowledge of the sinogram via the tight frame regularization and the simultaneous sinogram extrapolation. Our proposed model shows more promising numerical simulation results compared with the existing sparsity model based approach.
文摘As X-ray computed tomography （CT） is widely used in diagnosis and radiotherapy, it is important to reduce the radiation dose as low as reasonably achievable. For this pur- pose, one may use the TV based methods or wavelet frame based methods to reconstruct high quality images from reduced number of projections. Furthermore, by using the in- terior tomography scheme which only illuminates a region-of-interest （ROI）, one can save more radiation dose. In this paper, a robust wavelet frame regularization based model is proposed for both global reconstruction and interior tomography. The model can help to reduce the errors caused by mismatch of the huge sparse projection matrix. A three-system decomposition scheme is applied to decompose the reconstructed images into three differ- ent parts： cartoon, artifacts and noise. Therefore, by discarding the estimated artifacts and noise parts, the reconstructed images can be obtained with less noise and artifacts. Similar to other frame based image restoration models, the model can be efficiently solved by the split Bregman algorithm. Numerical simulations show that the proposed model outperforms the FBP and SART＋TV methods in terms of preservation of sharp edges, mean structural similarity （SSIM）, contrast-to-noise ratio, relative error and correlation- s. For example, for real sheep lung reconstruction, the proposed method can reach the mean structural similarity as high as 0.75 using only 100 projections while the FBP and the SART^TV methods need more than 200 projections. Additionally, the proposed ro- bust method is applicable for interior and exterior tomography with better performance compared to the FBP and the SART＋TV methods.
基金Supported by the National Natural Science Foundation of China under Grants No.11671004 and 91330101Natural Science Foundation for Colleges and Universities in Jiangsu Province under Grants No.15KJB110018 and 14KJB110020
文摘In this paper, we consider two variational models for speckle reduction of ultrasound images. By employing the F-convergence argument we show that the solution of the SO model coincides with the minimizer of the JY model. Furthermore, we incorporate the split Bregman technique to propose a fast alterative algorithm to solve the JY model. Some numericalexperiments are presented to illustrate the efficiency of the proposed algorithm.
