Error analysis in correlation computation of single particle reconstruction technique

The single particle reconstruction technique has become particularly important in the structure analysis of biomacromolecules. The problem of reconstructing a picture from identical samples polluted by colored noises is studied, and the alignment error in the correlation computation of single particle reconstruction technique is analyzed systematically. The concept of systematic error is introduced, and the explicit form of the systematic error is given under the weak noise approximation. The influence of the systematic error on the reconstructed picture is discussed also, and an analytical formula for correcting the distortion in the picture reconstruction is obtained.