We previously developed an algorithm that made use of redundant measurements of
image shifts between all sub-frames to derive a least squares estimate of relative motions
between neighboring sub-frames. This algorithm, implemented in the program MotionCorr,
provided an efficient correction of image motions with sufficient accuracy
6
to enable the
determination of numerous near atomic resolution 3D reconstructions
11,15
. Around the same time
or soon afterwards, a number of different strategies were devised that either assume particles
located nearby have similar motions or assume uniform motion of the entire frame or patches of
the frame. Programs based on the former assumption include RELION that provides a movie-
processing mode but uses a 3D reconstruction to track particle motions
8,16
, Xmipp that
implemented an Optic Flow algorithm
17
, and alignparts_lmbfgs that implemented a regularized
Fourier Space optimization algorithm to track neighboring particles
18
. Programs based on
tracking the full frame or parts of the frame include MotionCorr
6
and iterative whole frame
alignment procedures such as Unblur
19
or those used in electron tomography
20
. All of these
algorithms have demonstrated the ability to recover high-resolution signals to varying degrees
and have improved the resolution of the resultant 3D reconstructions.
Ideally, single particle cryo-EM images should be acquired with the smallest possible
defocus to enhance high-resolution information, and with the shortest sub-frame exposure times
to reduce motion trapped within individual sub-frames, in particular for the first few frames
where the sample has the least radiation damage but moves most rapidly
21
. Additionally, motion
detection should be done on the smallest possible local area to best capture the anisotropic
motion. Unfortunately, minimizing time and or area significantly reduces the SNR in each sub-
frame, ultimately leading to incorrect motion estimates. For example, previous experiments with
MotionCorr revealed that subdividing the images into areas smaller than ~2000 × ~2000 pixels
or going to sub-frame integration times of less than 100 milliseconds worsened resolution due to
increased errors in motion tracking.
Another recent advance, where a model of radiation damage is used to weight the
individual sub-frames in Fourier space, allows collection to very high doses (80-100e
-
/Å
2
)
producing a high contrast image without degradation of the high-resolution signal
19
. While
having a single correctly weighted high contrast image has clear advantages for particle picking,
orientation refinement, and overall computability, taking advantage of this strategy requires that
each of the sub-frames be optimally aligned over the full image area. Therefore, improving