Accurate algorithms for nonuniform fast forward and inverse Fourier transforms and their applications

Regular fast Fourier transform (FFT) algorithms require uniformly sampled data. In many practical situations, however, the input data is nonuniform, and hence the regular FFT does not apply. To overcome this difficulty the authors have proposed an accurate algorithm for the nonuniform forward FFT (NUFFT) based on a new class of matrices, the regular Fourier matrices. For the nonuniform inverse FFT (NU-IFFT) algorithm, the conjugate-gradient method and the regular FFT algorithm are combined to speed up a matrix inversion. Numerical results show that these algorithms are more than one order of magnitude more accurate than existing algorithms.