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
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
The interior Radon transform arises from a limited data problem in computerized tomography. The corresponding operator R is investigated as a mapping between wightedL 2-spaces. Our result is the explicit construction ...The interior Radon transform arises from a limited data problem in computerized tomography. The corresponding operator R is investigated as a mapping between wightedL 2-spaces. Our result is the explicit construction of a singular value decomposition for R. This immediately leads to an inversion formula by series expansion and range characterizations.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 exponential Radon transform, a generalization of the Radon transform, is defined and studied as a mapping of function spaces. It is represented in terms of Fourier transform of its domain and range, and this leads...The exponential Radon transform, a generalization of the Radon transform, is defined and studied as a mapping of function spaces. It is represented in terms of Fourier transform of its domain and range, and this leads to the harmonic decomposition reconstruction. The results are similar results of Tretiak and Metz.展开更多
The Radon transform fits badly Single Photon Emission Tomography (SPECT). However, Thin Holes Collimator (THC) and Radon model are widely used. The CACAO project has been proposed to enhance the quality of SPECT image...The Radon transform fits badly Single Photon Emission Tomography (SPECT). However, Thin Holes Collimator (THC) and Radon model are widely used. The CACAO project has been proposed to enhance the quality of SPECT images. CACAO is a short hand notation for computer aided collimation tomography. The main idea of this project is to use collimators with much larger holes to increase the sensitivity, and slightly longer holes to increase the spatial resolution. The acquisition sequence includes a translation. The Radon projection is replaced by a 2D sum. A dedicated reconstruction algorithm has been developed. If the physical advantage of the project in terms of sensitivity and spatial resolution is generally admitted, a question remains unanswered: Would the ill-posedness of the inverse problem ruin the quality of the reconstructed images? In this article, a representation of the 2D direct problem matrix is derived. This allows us to compare the two inverse problems (CACAO versus THC). The condition number was used for this comparison. We studied the variation of these condition numbers with several parameters. For a proper set of parameters, the CACAO inverse problem may appear easier to solve and more accurately than the THC one.展开更多
对于频率交叠严重且频率成分接近的多分量信号,常用的短时傅里叶变换(Short Time Fourier Transform,STFT)和S方法(S-Method,SM)频率分辨能力不足,重构精度低.针对该问题,本文结合逆Radon变换提出了基于短时迭代自适应-逆Radon变换(Shor...对于频率交叠严重且频率成分接近的多分量信号,常用的短时傅里叶变换(Short Time Fourier Transform,STFT)和S方法(S-Method,SM)频率分辨能力不足,重构精度低.针对该问题,本文结合逆Radon变换提出了基于短时迭代自适应-逆Radon变换(Short Time Iterative Adaptive Approach-Inverse Radon Transform,STIAA-IRT)的微多普勒特征提取方法.首先采用基于加权迭代自适应的STIAA时频分析方法分析了散射点模型的微多普勒特性,然后利用逆Radon变换分离重构不同散射点的微多普勒分量.该方法在低信噪比、邻近时频分布情况下能获得高分辨的多分量信号的完整微多普勒信息,性能分析显示STIAA-IRT重构精度较高,明显优于STFT-IRT(Short Time Fourier Transform-Inverse Radon Transform)和SM-IRT(S-Method-Inverse Radon Transform)特征提取方法.展开更多
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 Ministry of Education of China and the Science Foundation of Wuhan University
文摘The interior Radon transform arises from a limited data problem in computerized tomography. The corresponding operator R is investigated as a mapping between wightedL 2-spaces. Our result is the explicit construction of a singular value decomposition for R. This immediately leads to an inversion formula by series expansion and range characterizations.
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 F oundation of China( No.199710 6 4) ,Key Project of Science and Tech-nology of Hubei Province Education Com mittee
文摘The exponential Radon transform, a generalization of the Radon transform, is defined and studied as a mapping of function spaces. It is represented in terms of Fourier transform of its domain and range, and this leads to the harmonic decomposition reconstruction. The results are similar results of Tretiak and Metz.
文摘The Radon transform fits badly Single Photon Emission Tomography (SPECT). However, Thin Holes Collimator (THC) and Radon model are widely used. The CACAO project has been proposed to enhance the quality of SPECT images. CACAO is a short hand notation for computer aided collimation tomography. The main idea of this project is to use collimators with much larger holes to increase the sensitivity, and slightly longer holes to increase the spatial resolution. The acquisition sequence includes a translation. The Radon projection is replaced by a 2D sum. A dedicated reconstruction algorithm has been developed. If the physical advantage of the project in terms of sensitivity and spatial resolution is generally admitted, a question remains unanswered: Would the ill-posedness of the inverse problem ruin the quality of the reconstructed images? In this article, a representation of the 2D direct problem matrix is derived. This allows us to compare the two inverse problems (CACAO versus THC). The condition number was used for this comparison. We studied the variation of these condition numbers with several parameters. For a proper set of parameters, the CACAO inverse problem may appear easier to solve and more accurately than the THC one.
