What mathematical technique allows for the reconstruction of motion-free images from helically acquired CT data?

Interpolation is a mathematical technique used in the reconstruction of motion-free images from helically acquired CT data. In helical or spiral CT scanning, images are acquired continuously while the patient moves through the scanner. This results in a dataset where the data points are not evenly spaced in the axial plane, particularly due to motion artifacts such as breathing.

Interpolation helps to estimate the values of pixels in the image where direct measurements may not exist. By using surrounding data points, interpolation fills in gaps and produces a continuous image. This method ensures that the reconstructed images are smooth and coherent, despite any inconsistencies caused by patient motion during the scan.

Other techniques mentioned, such as the Fourier transform, play roles in different aspects of image processing and analysis but do not specifically address the reconstruction needed in this context. Regressive analysis and differential analysis also do not pertain to the direct reconstruction process in helical CT imaging.