Circular harmonic averaging of noisy single-molecule images.

A new method for averaging of noisy single-molecule images has been developed. Averaging is done over the circular harmonic components of the images instead of over the images themselves. Those images which show different molecules or molecules in different projections can be separated into classes by comparing the power of their circular harmonic components, which is rotationally invariant. Orientational alignment, based on the rotational correlation of each image with all others, and averaging is performed separately for each class. Applying a quality measure to the circular harmonic averages allows separation of significant and nonsignificant components. Computer simulations indicate that the method is quite stable against noise. One of the main advantages of "circular harmonic averaging" over existing methods is that no reference images are needed in the averaging procedure.