Appropriate regularization parameter specification is the linchpin for solving ill-posed inverse problems when regularization method is applied. This paper presents a novel technique to determine cut off singular values in the truncated singular value decomposition (TSVD) methods. Simple formulae are presented to calculate the index number of the singular value, beyond which all the smaller singular values and the corresponding vectors are truncated. The determination method of optimal truncation threshold is firstly theoretically inferred. Two-dimensional inverse problems processing Radon transform are then exemplified. Formulae to solve the problem with insufficient image resolution and projection angle number are derived by the currently proposed method. The results show that accuracy of the current method is similar to that of TSVD but with much superior efficiency. On the other hand, insufficiency in input data affects the output accuracy of the inverse solution, a least square method can be engaged to establish formulae calculating the truncation threshold. For an insufficient set of input data, the percentage difference between inversely reconstructed signal and TSVD reconstructed signal is about 3%. The current formulae offer reliable and more efficient approach to calculate the truncation threshold when TSVD is applied to solve inverse problems with known system characteristics.

当应用正则化方法时，适当的正则化参数规范是解决不适定逆问题的关键。本文提出了一种在截断奇异值分解 (TSVD) 方法中确定截止奇异值的新技术。给出了简单的公式来计算奇异值的索引号，超过此值的所有较小的奇异值和相应的向量都被截断。首先从理论上推导了最佳截断阈值的确定方法。然后举例说明处理Radon变换的二维逆问题。通过目前提出的方法推导出解决图像分辨率和投影角数不足问题的公式。结果表明，当前方法的准确性与 TSVD 相似，但效率更高。另一方面，输入数据的不足会影响逆解的输出精度，可以采用最小二乘法建立计算截断阈值的公式。对于一组不足的输入数据，逆重构信号与TSVD重构信号之间的百分比差异约为3%。当应用 TSVD 解决具有已知系统特性的逆问题时，当前的公式提供了计算截断阈值的可靠和更有效的方法。可以采用最小二乘法来建立计算截断阈值的公式。对于一组不足的输入数据，逆重构信号与TSVD重构信号之间的百分比差异约为3%。当应用 TSVD 解决具有已知系统特性的逆问题时，当前的公式提供了计算截断阈值的可靠和更有效的方法。可以采用最小二乘法来建立计算截断阈值的公式。对于一组不足的输入数据，逆重构信号与TSVD重构信号之间的百分比差异约为3%。当应用 TSVD 解决具有已知系统特性的逆问题时，当前的公式提供了计算截断阈值的可靠和更有效的方法。