Sezione di Med. Nucl., Firenze.
IEEE Trans Med Imaging. 1993;12(1):90-100. doi: 10.1109/42.222672.
An accurate model of the nonstationary geometrical response of a camera-collimator system is discussed. The algorithm is compared to three other algorithms that are specialized for region-of-interest evaluation, as well as to the conventional method for summing the reconstructed quantity over the regions of interest. For noise-free data and for regions of accurate shape, least-squares estimates were unbiased within roundoff errors. For noisy data, estimates were still unbiased but precision worsened for regions smaller than resolution: simulating typical statistics of brain perfusion studies performed with a collimated camera, the estimated standard deviation for a 1-cm-square region was 10% with an ultra-high-resolution collimator and 7% with a low-energy all-purpose collimator. Conventional region-of-interest estimates show comparable precision but are heavily biased if filtered backprojection is used for image reconstruction. Using the conjugate-gradient iterative algorithm and the model of nonstationary geometrical response, bias of estimates decreased on increasing the number of iterations, but precision worsened, thus achieving an estimated standard deviation of more than 25% for the same 1-cm region.
讨论了相机准直器系统非平稳几何响应的精确模型。将该算法与专门用于感兴趣区域评估的其他三种算法以及用于在感兴趣区域中对重建量求和的常规方法进行了比较。对于无噪声数据和形状准确的区域，最小二乘估计在舍入误差内是无偏的。对于噪声数据，估计仍然是无偏的，但对于小于分辨率的区域，精度会恶化：模拟使用准直相机进行脑灌注研究的典型统计数据，使用超高分辨率准直器和低能通用准直器，对于 1 平方厘米的区域，估计的标准偏差分别为 10%和 7%。如果使用滤波反投影进行图像重建，常规的感兴趣区域估计具有可比的精度，但会受到严重的偏差影响。使用共轭梯度迭代算法和非平稳几何响应模型，随着迭代次数的增加，估计值的偏差减小，但精度恶化，因此对于相同的 1 平方厘米区域，估计的标准偏差超过 25%。
