When using an electron microscope for imaging of particles embedded in vitreous ice, the recorded image, or micrograph, is a significantly degraded version of the tomographic projection of the sample. Apart from noise, the image is affected by the optical configuration of the microscope. This transformation is typically modeled as a convolution with a point spread function. The Fourier transform of this function, known as the contrast transfer function (CTF), is oscillatory, attenuating and amplifying different frequency bands, and sometimes flipping their signs. High-resolution reconstruction requires this CTF to be accounted for, but as its form depends on experimental parameters, it must first be estimated from the micrograph. We present a new method for CTF estimation based on multitaper techniques that reduce bias and variance in the estimate. We also use known properties of the CTF and the background power spectrum to further reduce the variance through background subtraction and steerable basis projection. We show that the resulting power spectrum estimates better capture the zero-crossings of the CTF and yield accurate CTF estimates on several experimental micrographs.

中文翻译：

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减少单粒子 Cryo-EM 中 CTF 估计的偏差和方差

当使用电子显微镜对嵌入玻璃冰中的颗粒进行成像时，记录的图像或显微照片是样品层析投影的显着退化版本。除了噪声，图像还受到显微镜光学配置的影响。这种转换通常被建模为具有点扩散函数的卷积。该函数的傅里叶变换称为对比传递函数 (CTF)，它是振荡的，衰减和放大不同的频带，有时会翻转它们的符号。高分辨率重建需要考虑此 CTF，但由于其形式取决于实验参数，因此必须首先从显微照片中对其进行估计。我们提出了一种基于多锥技术的 CTF 估计新方法，可减少估计中的偏差和方差。我们还使用 CTF 和背景功率谱的已知属性，通过背景减法和可控基投影进一步减少方差。我们表明，由此产生的功率谱估计可以更好地捕获 CTF 的零交叉点，并在几张实验显微照片上产生准确的 CTF 估计。