The local reconstruction from truncated projection data is one area of interest in image reconstruction for com- puted tomography （CT）, which creates the possibility for dose reduction. In this paper, a filtered-bac...The local reconstruction from truncated projection data is one area of interest in image reconstruction for com- puted tomography （CT）, which creates the possibility for dose reduction. In this paper, a filtered-backprojection （FBP） algorithm based on the Radon inversion transform is presented to deal with the three-dimensional （3D） local recon- struction in the circular geometry. The algorithm achieves the data filtering in two steps. The first step is the derivative of projections, which acts locally on the data and can thus be carried out accurately even in the presence of data trun- cation. The second step is the nonlocal Hilbert filtering. The numerical simulations and the real data reconstructions have been conducted to validate the new reconstruction algorithm. Compared with the approximate truncation resistant algorithm for computed tomography （ATRACT）, not only it has a comparable ability to restrain truncation artifacts, but also its reconstruction efficiency is improved. It is about twice as fast as that of the ATRACT. Therefore, this work provides a simple and efficient approach for the approximate reconstruction from truncated projections in the circular cone-beam CT.展开更多
Let X=Rn +×R denote the underlying manifold of polyradial functions on the Heisenberg group H n. We construct a generalized translation on X=Rn +×R, and establish the Plancherel formula on L2(X,dμ). Usin...Let X=Rn +×R denote the underlying manifold of polyradial functions on the Heisenberg group H n. We construct a generalized translation on X=Rn +×R, and establish the Plancherel formula on L2(X,dμ). Using the Gelfand transform we give the condition of generalized wavelets on L2(X,dμ). Moreover, we show the reconstruction formulas for wavelet packet trnasforms and an inversion formula of the Radon transform on X.展开更多
The warhead of a ballistic missile may precess due to lateral moments during release. The resulting micro-Doppler effect is determined by parameters such as the target's motion state and size. A three-dimensional ...The warhead of a ballistic missile may precess due to lateral moments during release. The resulting micro-Doppler effect is determined by parameters such as the target's motion state and size. A three-dimensional reconstruction method for the precession warhead via the micro-Doppler analysis and inverse Radon transform(IRT) is proposed in this paper. The precession parameters are extracted by the micro-Doppler analysis from three radars, and the IRT is used to estimate the size of targe. The scatterers of the target can be reconstructed based on the above parameters. Simulation experimental results illustrate the effectiveness of the proposed method in this paper.展开更多
Let be the quaternion Heisenberg group, and let P be the affine automorphism group of . We develop the theory of continuous wavelet transform on the quaternion Heisenberg group via the unitary representations of P on...Let be the quaternion Heisenberg group, and let P be the affine automorphism group of . We develop the theory of continuous wavelet transform on the quaternion Heisenberg group via the unitary representations of P on L2（ ）. A class of radial wavelets is constructed. The inverse wavelet transform is simplified by using radial wavelets. Then we investigate the Radon transform on . . A Semyanistyi-Lizorkin space is introduced, on which the Radon transform is a bijection. We deal with the Radon transform on both by the Euclidean Fourier transform and the group Fourier transform. These two treatments are essentially equivalent. We also give an inversion formula by using wavelets, which does not require the smoothness of functions if the wavelet is smooth. In addition, we obtain an inversion formula of the Radon transform associated with the sub-Laplacian on .展开更多
基金Project supported by the National High Technology Research and Development Program of China (Grant No. 2012AA011603)
文摘The local reconstruction from truncated projection data is one area of interest in image reconstruction for com- puted tomography （CT）, which creates the possibility for dose reduction. In this paper, a filtered-backprojection （FBP） algorithm based on the Radon inversion transform is presented to deal with the three-dimensional （3D） local recon- struction in the circular geometry. The algorithm achieves the data filtering in two steps. The first step is the derivative of projections, which acts locally on the data and can thus be carried out accurately even in the presence of data trun- cation. The second step is the nonlocal Hilbert filtering. The numerical simulations and the real data reconstructions have been conducted to validate the new reconstruction algorithm. Compared with the approximate truncation resistant algorithm for computed tomography （ATRACT）, not only it has a comparable ability to restrain truncation artifacts, but also its reconstruction efficiency is improved. It is about twice as fast as that of the ATRACT. Therefore, this work provides a simple and efficient approach for the approximate reconstruction from truncated projections in the circular cone-beam CT.
基金Supported by the Foundation of the National Natural Science of China( No.1 0 0 71 0 39) and the Foundation of Edu-cation Commission of Jiangsu Province
文摘Let X=Rn +×R denote the underlying manifold of polyradial functions on the Heisenberg group H n. We construct a generalized translation on X=Rn +×R, and establish the Plancherel formula on L2(X,dμ). Using the Gelfand transform we give the condition of generalized wavelets on L2(X,dμ). Moreover, we show the reconstruction formulas for wavelet packet trnasforms and an inversion formula of the Radon transform on X.
基金supported by the National Natural Science Foundation of China (61871146)the Fundamental Research Funds for the Central Universities (FRFCU5710093720)。
文摘The warhead of a ballistic missile may precess due to lateral moments during release. The resulting micro-Doppler effect is determined by parameters such as the target's motion state and size. A three-dimensional reconstruction method for the precession warhead via the micro-Doppler analysis and inverse Radon transform(IRT) is proposed in this paper. The precession parameters are extracted by the micro-Doppler analysis from three radars, and the IRT is used to estimate the size of targe. The scatterers of the target can be reconstructed based on the above parameters. Simulation experimental results illustrate the effectiveness of the proposed method in this paper.
基金supported by National Natural Science Foundation of China(Grant Nos.10971039 and 11271091)the second author is supported by National Natural Science Foundation of China(Grant No.10990012)the Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.2012000110059)
文摘Let be the quaternion Heisenberg group, and let P be the affine automorphism group of . We develop the theory of continuous wavelet transform on the quaternion Heisenberg group via the unitary representations of P on L2（ ）. A class of radial wavelets is constructed. The inverse wavelet transform is simplified by using radial wavelets. Then we investigate the Radon transform on . . A Semyanistyi-Lizorkin space is introduced, on which the Radon transform is a bijection. We deal with the Radon transform on both by the Euclidean Fourier transform and the group Fourier transform. These two treatments are essentially equivalent. We also give an inversion formula by using wavelets, which does not require the smoothness of functions if the wavelet is smooth. In addition, we obtain an inversion formula of the Radon transform associated with the sub-Laplacian on .
