In the above analysis, an underlying assumption is that the translational motion is compensated ideally and only the rotational motion is involved.
Then, the translational motion errors in the horizontal and vertical directions were measured by the sequential two-point method, where influence of the angular motion errors on the translational measurement was compensated by utilizing the measured angular motion errors.
The image stretching resulting from the sinusoidal motion of the resonant optical scanner was compensated by estimating the distortion from images of a Ronchi ruling, and then re-sampling the images over a grid of equally spaced pixels.
To compensate for this breathing motion by image processing methods two problems have to be overcome: The motion to be compensated for itself, and the rather strong intensity change that is induced by the contrast agent.
The top plot shows the changes in contrast recovery when motion compensation is fully performed (DUAL, as in dual-gated studies), or only ECG gating is performed (ECG, one cardiac gate blurred by the respiratory motion) or if ECG gating is performed starting from a dataset where the respiratory motion has been compensated (ECG+R, one cardiac gate, less noisy).
For one-step MOCO, range-dependent motion error is compensated before RCMC.
For the two-step MOCO algorithm, the range-independent component of motion error is compensated in the first step.
In ISAR scenarios, the target is often engaged in complicated maneuvers and the translational motion should be compensated before performing imaging processing.
Then, the range-dependent motion error is compensated in range time domain by multiplying H MOCO r,X), where {H_{text{MOCO}}}left({r,X} right) = exp left[ { - {jK}_{rc}Delta {R_{r}}left({r,X} right)} right] (22).
