Accurate reconstruction from a reduced data set is highly essential for computed tomography in fast and/or low dose imaging applications. Conventional total variation（TV）-based algorithms apply the L1 norm-based pen...Accurate reconstruction from a reduced data set is highly essential for computed tomography in fast and/or low dose imaging applications. Conventional total variation（TV）-based algorithms apply the L1 norm-based penalties, which are not as efficient as Lp（0〈p〈1） quasi-norm-based penalties. TV with a p-th power-based norm can serve as a feasible alternative of the conventional TV, which is referred to as total p-variation（TpV）. This paper proposes a TpV-based reconstruction model and develops an efficient algorithm. The total p-variation and Kullback-Leibler（KL） data divergence, which has better noise suppression capability compared with the often-used quadratic term, are combined to build the reconstruction model. The proposed algorithm is derived by the alternating direction method（ADM） which offers a stable, efficient, and easily coded implementation. We apply the proposed method in the reconstructions from very few views of projections（7 views evenly acquired within 180°）. The images reconstructed by the new method show clearer edges and higher numerical accuracy than the conventional TV method. Both the simulations and real CT data experiments indicate that the proposed method may be promising for practical applications.展开更多
In this paper we prove the behaviour in weighted Lp spaces of the oscillation and variation of the Hilbert transform and the Riesz transform associated with the Hermite operator of dimension 1. We prove that this oper...In this paper we prove the behaviour in weighted Lp spaces of the oscillation and variation of the Hilbert transform and the Riesz transform associated with the Hermite operator of dimension 1. We prove that this operator maps LP（R, w（x）dx） into itself when w is a weight in the Ap class for 1 〈 p 〈 ∞. For p = 1 we get weak type for the A1 class. Weighted estimated are also obtained in the extreme case p = ∞.展开更多
针对有限投影角度的CT图像重建问题,提出一种改进的基于自适应图像全变差(Total p Variation,TpV)约束的代数迭代重建算法。改进算法采用两相式重建结构,首先利用代数重建技术(ART)算法重建中间图像并做非负修正,然后利用自适应TpV正则...针对有限投影角度的CT图像重建问题,提出一种改进的基于自适应图像全变差(Total p Variation,TpV)约束的代数迭代重建算法。改进算法采用两相式重建结构,首先利用代数重建技术(ART)算法重建中间图像并做非负修正,然后利用自适应TpV正则项约束图像稀疏特性,进一步优化重建结果,其中正则项可根据图像区域特性自适应的调整决定平滑强度的参数p,两项交替进行直到满足收敛要求。本文应用经典的Shepp-Logan体模对改进算法进行仿真重建,以重建图像及其局部放大图作为主观分析依据,以profile图和归一化绝对距离值作为客观评估标准,与经典的ART-TV算法进行比较,对比分析重建结果发现:本文算法重建图像不仅与真实体模更接近,重建误差更小,而且能更好地保护图像的边缘特性。展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61372172 and 61601518)
文摘Accurate reconstruction from a reduced data set is highly essential for computed tomography in fast and/or low dose imaging applications. Conventional total variation（TV）-based algorithms apply the L1 norm-based penalties, which are not as efficient as Lp（0〈p〈1） quasi-norm-based penalties. TV with a p-th power-based norm can serve as a feasible alternative of the conventional TV, which is referred to as total p-variation（TpV）. This paper proposes a TpV-based reconstruction model and develops an efficient algorithm. The total p-variation and Kullback-Leibler（KL） data divergence, which has better noise suppression capability compared with the often-used quadratic term, are combined to build the reconstruction model. The proposed algorithm is derived by the alternating direction method（ADM） which offers a stable, efficient, and easily coded implementation. We apply the proposed method in the reconstructions from very few views of projections（7 views evenly acquired within 180°）. The images reconstructed by the new method show clearer edges and higher numerical accuracy than the conventional TV method. Both the simulations and real CT data experiments indicate that the proposed method may be promising for practical applications.
基金Supported by Ministerio de Educación y Ciencia (Spain), Grants MTM 2008-066621-C02-01/02Junta de Andalucía, Grants FQM-354 and P06-FQM-01509supported by Fundación Carolina, Ministerio de Cultura y Educación de la República Argentina and Universidad Nacional del Comahue
文摘In this paper we prove the behaviour in weighted Lp spaces of the oscillation and variation of the Hilbert transform and the Riesz transform associated with the Hermite operator of dimension 1. We prove that this operator maps LP（R, w（x）dx） into itself when w is a weight in the Ap class for 1 〈 p 〈 ∞. For p = 1 we get weak type for the A1 class. Weighted estimated are also obtained in the extreme case p = ∞.
文摘针对有限投影角度的CT图像重建问题,提出一种改进的基于自适应图像全变差(Total p Variation,TpV)约束的代数迭代重建算法。改进算法采用两相式重建结构,首先利用代数重建技术(ART)算法重建中间图像并做非负修正,然后利用自适应TpV正则项约束图像稀疏特性,进一步优化重建结果,其中正则项可根据图像区域特性自适应的调整决定平滑强度的参数p,两项交替进行直到满足收敛要求。本文应用经典的Shepp-Logan体模对改进算法进行仿真重建,以重建图像及其局部放大图作为主观分析依据,以profile图和归一化绝对距离值作为客观评估标准,与经典的ART-TV算法进行比较,对比分析重建结果发现:本文算法重建图像不仅与真实体模更接近,重建误差更小,而且能更好地保护图像的边缘特性。
