平面圆Radon变换的值域描述
A range description for the planar circular Radon transform
摘要：
本文所考虑的变换将一个支持在单位圆盘上的函数在以该圆盘边界为中心的所有圆上积分。这种圆形Radon变换出现在几种当代成像技术以及其他应用中。由于Radon型变换的普遍性，它的值域在标准函数空间中具有无穷余维。已知这种变换的范围描述对于计算机断层摄影是非常重要的，例如当处理不完整的数据、误差校正和其他问题时。得到了圆Radon变换的完整的距离描述。范围条件包括最近发现的一组矩型条件，它碰巧是不完整的，以及其余的条件，具有较少的标准式。为了更好地解释这个过程，首先描述了一个类似的（非标准的）治疗的范围条件通常的拉东变换的平面上。
英文摘要：
The transform considered in the paper integrates a function supported in the unit disk on the plane over all circles centered at the boundary of this disk. Such circular Radon transform arises in several contemporary imaging techniques, as well as in other applications. As it is common for transforms of Radon type, its range has infinite co-dimension in standard function spaces. Range descriptions for such transforms are known to be very important for computed tomography, for instance when dealing with incomplete data, error correction, and other issues. A complete range description for the circular Radon transform is obtained. Range conditions include the recently found set of moment type conditions, which happens to be incomplete, as well as the rest of conditions that have less standard form. In order to explain the procedure better, a similar (non-standard) treatment of the range conditions is described first for the usual Radon transform on the plane.
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