Albert M, Maidment A D
Thomas Jefferson University, Department of Radiology, Philadelphia, Pennsylvania 19107-5563, USA.
Med Phys. 2000 Oct;27(10):2417-34. doi: 10.1118/1.1286592.
The optical transfer function (OTF) and the noise power or Wiener spectrum are defined for detectors consisting of a lattice of discrete elements with the assumptions of linear response, Gaussian statistics, and stationarity under the discrete group of translations which leave the lattice fixed. For the idealized classification task of determining the presence or absence of a signal under signal known exactly/background known exactly (SKE/BKE) conditions, the Wiener spectrum, the OTF, along with an analog of the gray-scale transfer characteristic, determine the signal-to-noise ratio (SNR), which quantifies the ability of an ideal observer to perform this task. While this result is similar to the established result for continuous detectors, such as screen-film systems, the theory of discrete lattices of detectors must take into account the fact that the lattice only supports a bounded but (in the limit of a detector of arbitrarily great extent) continuous range of frequencies. Incident signals with higher spatial frequencies appear in the data at lower aliased frequencies, and there are pairs of signals which are not distinguishable by the detector (the SNR vanishes for the task of distinguishing such signals). Further, the SNR will in general change if the signal is spatially displaced by a fraction of the lattice spacing, although this change will be small for objects larger than a single pixel. Some of the trade-offs involved in detectors of this sort, particularly in dealing with signal frequencies above those supported by the lattice, are studied in a simple model.
光学传递函数（OTF）以及噪声功率或维纳频谱是针对由离散元件晶格组成的探测器定义的，其假设包括线性响应、高斯统计以及在使晶格保持固定的离散平移群下的平稳性。对于在信号完全已知/背景完全已知（SKE/BKE）条件下确定信号是否存在的理想化分类任务，维纳频谱、OTF以及灰度传递特性的类似物决定了信噪比（SNR），该信噪比量化了理想观察者执行此任务的能力。虽然此结果与诸如屏-片系统等连续探测器的既定结果相似，但探测器离散晶格理论必须考虑到这样一个事实，即晶格仅支持有限但（在探测器范围任意大的极限情况下）连续的频率范围。具有较高空间频率的入射信号在数据中以较低的混叠频率出现，并且存在探测器无法区分的信号对（对于区分此类信号的任务，SNR为零）。此外，如果信号在空间上移动晶格间距的一部分，SNR通常会发生变化，尽管对于大于单个像素的物体，这种变化会很小。在一个简单模型中研究了这类探测器所涉及的一些权衡，特别是在处理高于晶格支持频率的信号频率时。
