New Algorithm for Closed Form Image Reconstruction from Fourier Transform Magnitude

摘要

Signal reconstruction from Fourier transform magnitude (FTM) has been the topic of much interest in the literature. It has been recently shown that if the support of the image is known, then most images can be reconstructed from knowledge of only its FTM modulo a rotation by 180 degrees and a sign change. Several algorithms have been proposed for reconstruction from FTM. A class of iterative algorithms has been extensively studied by Fienup. A difficulty with present iterative algorithms is that they often stagnate before converging to a solution. The unsatisfactory behavior of iterative algorithms has prompted the development of several non-iterative algorithms. However, these closed form algorithms require a computational load which increases exponentially with image size. Thus, they are applicable to small images only. This reprint presents a new closed form algorithm which avoids the computational complexity of previous closed form algorithms while still guaranteeing a solution. In the next section several results from complex analysis which form the theoretical basis of the algorithms are reviewed, while section 3 describes the actual algorithm. Section 4 presents some images which have been reconstructed via the new algorithm.