Alias-free image reconstruction using Fresnel transform in the phase-scrambling Fourier imaging technique

An image reconstruction technique that reduces aliasing artifacts by scalable image reconstruction in magnetic resonance imaging (MRI) is proposed. The signal obtained by the phase-scrambling Fourier transform (PSFT) imaging technique can be transformed to the signal described in the Fresnel transform equation of the objects. Therefore, image reconstruction can be performed not only by inverse FT but also by inverse Fresnel transform. When a phase-scrambling coefficient is given in a certain range, image reconstruction by inverse Fresnel transform allows shrinking of images over rather wide scales. Thus, reduced aliasing images can be reconstructed even from signals that produce serious aliasing artifacts by standard inverse FT reconstruction. Simulation and experimental studies reveal that the proposed method can be used to produce reduced aliasing images.