Error analysis and distortion correction in reconstructing a picture from noisy identical samples

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