Lanzavecchia S, Bellon PL, Radermacher M
Dipartimento di Chimica Strutturale, Universita' degli Studi, via G. Venezian 21, Milan, 20133, Italy.
J Struct Biol. 1999 Dec 15;128(2):152-64. doi: 10.1006/jsbi.1999.4185.
A new algorithm for three-dimensional reconstruction from randomly oriented projections has been developed. The algorithm recovers the 3D Radon transform from the 2D Radon transforms (sinograms) of the projections. The structure in direct space is obtained by an inversion of the 3D Radon transform. The mathematical properties of the Radon transform are exploited to design a special filter that can be used to correct inconsistencies in a data set and to fill the gaps in the Radon transform that originate from missing projections. Several versions of the algorithm have been implemented, with and without a filter and with different interpolation methods for merging the sinograms into the 3D Radon transform. The algorithms have been tested on analytical phantoms and experimental data and have been compared with a weighted back projection algorithm (WBP). A quantitative analysis of phantoms reconstructed from noise-free and noise-corrupted projections shows that the new algorithms are more accurate than WBP when the number of projections is small. Experimental structures obtained by the new methods are strictly comparable to those obtained by WBP. Moreover, the algorithm is more than 10 times faster than WPB when applied to a data set of 1000-5000 projections. Copyright 1999 Academic Press.
一种用于从随机取向投影进行三维重建的新算法已被开发出来。该算法从投影的二维拉东变换（正弦图）中恢复三维拉东变换。通过对三维拉东变换进行反演得到直接空间中的结构。利用拉东变换的数学性质设计了一种特殊滤波器，可用于校正数据集中的不一致性，并填补拉东变换中因缺失投影而产生的间隙。已实现了该算法的几个版本，有滤波器和无滤波器的版本，以及将正弦图合并到三维拉东变换时采用不同插值方法的版本。这些算法已在解析模型和实验数据上进行了测试，并与加权反投影算法（WBP）进行了比较。对从无噪声和有噪声投影重建的模型进行的定量分析表明，当投影数量较少时，新算法比WBP更准确。用新方法获得的实验结构与用WBP获得的结构严格可比。此外，当应用于1000 - 5000个投影的数据集时，该算法比WBP快10倍以上。版权所有1999年学术出版社。
