Anastasio M A, Pan X
Appl Opt. 2001 Jul 10;40(20):3334-45. doi: 10.1364/ao.40.003334.
Diffraction tomography (DT) is a tomographic inversion technique that reconstructs the spatially variant refractive-index distribution of a scattering object. In fan-beam DT, the interrogating radiation is not a plane wave but rather a cylindrical wave front emanating from a line source located a finite distance from the scattering object. We reveal and examine the redundant information that is inherent in the fan-beam DT data function. Such redundant information can be exploited to reduce the reconstructed image variance or, alternatively, to reduce the angular scanning requirements of the fan-beam DT experiment. We develop novel filtered backpropagation and estimate-combination reconstruction algorithms for full-scan and minimal-scan fan-beam DT. The full-scan algorithms utilize measurements taken over the angular range 0 </= phi </= 2pi, whereas the minimal-scan reconstruction algorithms utilize only measurements taken over the angular range 0 </= phi </= phi(min), where pi </= phi(min) </= 3pi/2 is a specified function that describes the fan-beam geometry. We demonstrate that the full- and minimal-scan fan-beam algorithms are mathematically equivalent. An implementation of the algorithms and numerical results obtained with noiseless and noisy simulated data are presented.
衍射层析成像（DT）是一种层析反演技术，用于重建散射物体的空间变化折射率分布。在扇形束DT中，探测辐射不是平面波，而是来自与散射物体相距有限距离的线源发出的柱面波前。我们揭示并研究了扇形束DT数据函数中固有的冗余信息。这种冗余信息可用于减少重建图像的方差，或者减少扇形束DT实验的角度扫描要求。我们为全扫描和最小扫描扇形束DT开发了新颖的滤波反传播和估计组合重建算法。全扫描算法利用在0≤φ≤2π角度范围内进行的测量，而最小扫描重建算法仅利用在0≤φ≤φ(min)角度范围内进行的测量，其中π≤φ(min)≤3π/2是描述扇形束几何形状的指定函数。我们证明了全扫描和最小扫描扇形束算法在数学上是等效的。给出了算法的实现以及使用无噪声和有噪声模拟数据获得的数值结果。
