Two-Dimensional Averaging Techniques
This chapter starts by listing the common sources of noise in the EM and how they can be addressed by averaging techniques. Conditions for digital sampling, or for the representation of an effectively continuous image by an array of discrete density measurements, are discussed. The concept of image alignment is defined, and alignment is introduced as a precondition for averaging as well as for making any meaningful comparison of experimental images. The cross-correlation function is then introduced as one of the most important tools to achieve alignment. Averages of aligned images are characterized by statistical measures such as variance and signal-to-noise ratio. Measures of resolution are introduced based on a comparison, in Fourier space, of two independent averages from halfsets of the data. Among these are the differential phase residual and the Fourier ring correlation. The chapter ends with a discussion of the resolution-limiting factors, and with an outline of rank sum analysis, a method of statistical validation.
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