Verly J G, Bracewell R N
J Comput Assist Tomogr. 1979 Oct;3(5):662-78. doi: 10.1097/00004728-197910000-00017.
Tomographic reconstruction has ordinarily assumed that the measurement data can be regarded as line integrals, but the finite width of the X-ray beam invalidates this assumption. The data can however be expressed in the form of integrals over a strip rather than a line. The strip integral kernel is calculated allowing for extended source and detector, as well as for nonuniform photon emission and detector sensitivity. Strip eccentricity, which occurs in practice, is also taken into account. Even if the measurement data were to cover all scanning angles, there would be imperfect reconstruction expressible as a space-variant point spread function deducible from the strip integral kernel. To deal with this it is convenient to introduce the concepts of generalized projection and generalized Radon transform. Point-spread functions are given for cases involving piecewise-uniform symmetrical source distributions and uniform detectors.
断层重建通常假定测量数据可被视为线积分，但X射线束的有限宽度使这一假设无效。然而，数据可以表示为带状区域上的积分形式而非线积分形式。计算带状积分核时考虑了扩展源和探测器，以及光子发射不均匀性和探测器灵敏度。实际中出现的带状偏心也予以考虑。即使测量数据覆盖所有扫描角度，重建也会存在不完美之处，可表示为从带状积分核推导得出的空间可变点扩散函数。为处理这一问题，引入广义投影和广义拉东变换的概念很方便。给出了涉及分段均匀对称源分布和均匀探测器情况的点扩散函数。
