A gridding algorithm for efficient density compensation of arbitrarily sampled Fourier-domain data

Uniformly sampled data is sometimes not directly available in engineering applications ranging from synthetic aperture radars to magnetic resonance imaging. However, certain signal processing techniques, such as the fast Fourier transform, cannot be applied to non-equispaced data. It is therefore desirable to resample the data on a regular grid. Various interpolation schemes have been proposed for this purpose, such as gridding reconstruction. A computationally expensive step in the gridding algorithm is the estimation of the data sampling density. The paper presents a method for improving both the efficiency and the quality of gridding density estimation based on partial Voronoi diagrams. It is shown that significantly higher computational efficiency is achieved by this method over existing schemes. Lower spreading and greater sidelobe suppression of the point spread function demonstrate the superiority of the proposed reconstruction method