Howard Hughes Medical Institute and Department of Biochemistry, Rosenstiel Basic Medical Sciences Research Center, Brandeis University, 415 South Street, Waltham, MA 02454, USA.
J Struct Biol. 2011 Oct;176(1):60-74. doi: 10.1016/j.jsb.2011.06.010. Epub 2011 Jul 2.
The Wiener filter is a standard means of optimizing the signal in sums of aligned, noisy images obtained by electron cryo-microscopy (cryo-EM). However, estimation of the resolution-dependent ("spectral") signal-to-noise ratio (SSNR) from the input data has remained problematic, and error reduction due to specific application of the SSNR term within a Wiener filter has not been reported. Here we describe an adjustment to the Wiener filter for optimal summation of images of isolated particles surrounded by large regions of featureless background, as is typically the case in single-particle cryo-EM applications. We show that the density within the particle area can be optimized, in the least-squares sense, by scaling the SSNR term found in the conventional Wiener filter by a factor that reflects the fraction of the image field occupied by the particle. We also give related expressions that allow the SSNR to be computed for application in this new filter, by incorporating a masking step into a Fourier Ring Correlation (FRC), a standard resolution measure. Furthermore, we show that this masked FRC estimation scheme substantially improves on the accuracy of conventional SSNR estimation methods. We demonstrate the validity of our new approach in numeric tests with simulated data corresponding to realistic cryo-EM imaging conditions. This variation of the Wiener filter and accompanying derivation should prove useful for a variety of single-particle cryo-EM applications, including 3D reconstruction.
维纳滤波器是优化通过电子冷冻电子显微镜（cryo-EM）获得的对齐的、有噪声的图像总和中的信号的标准方法。然而，从输入数据中估计与分辨率相关的（“谱”）信噪比（SSNR）一直存在问题，并且由于在维纳滤波器内特定应用 SSNR 项而导致的误差减少尚未得到报道。在这里，我们描述了一种针对孤立粒子图像的最佳总和的维纳滤波器的调整，这些粒子被无特征的背景大区域包围，这在单粒子 cryo-EM 应用中通常是这种情况。我们表明，可以通过按反映粒子占据图像区域的分数来缩放常规维纳滤波器中的 SSNR 项，从而以最小二乘的方式优化粒子区域内的密度。我们还给出了相关的表达式，通过将掩蔽步骤合并到标准分辨率测量的傅里叶环相关（FRC）中，允许在这个新滤波器中应用 SSNR。此外，我们表明，这种掩蔽的 FRC 估计方案大大提高了传统 SSNR 估计方法的准确性。我们在与 cryo-EM 成像条件相对应的模拟数据的数值测试中证明了我们新方法的有效性。这种维纳滤波器的变体和伴随的推导应该对各种单粒子 cryo-EM 应用（包括 3D 重建）有用。
