Computationally efficient fourier transform of nonequidistant sampled data

We present an approximate method of performing the Fourier transform of the data sampled in nonequidistant readouts. It is shown that the data can be recalculated as equidistant readouts by using a nonuniform convolution, i.e., convolution of a certain function whose form depends on the calculated element and the character of nonequidistance. Thus, this recalculation does not require calculation of the values of the initial data in intermediate readouts (unlike the linear approximation, spline, or other recalculations). Since the size of the kernel of this nonuniform convolution is about 9, the proposed method can be the basis for an efficient computational algorithm. Applicability of the proposed approach to spectral optical coherence tomography is demonstrated.