Interpolation of 2-D fractional Brownian motion using first order increments

This paper presents an new method to interpolate 2-D fractional Brownian motion (fBm). This interpolation problem differs from standard image interpolation because noise must be added to the interpolated points to obtain an interpolated image with the proper second-order statistics. Our interpolation method is based on the first order increments of both the original and interpolated fBms. These increments are stationary and yield interpolation equations with a Toeplitz-block-Toeplitz (TBT) structure which can be approximated by a circulant-block-circulant (CBC) matrix. By taking advantage of FFT, the computational complexity is O(N²log₂ N) for N×N image interpolation. Simulation shows this method achieves good second order statistics even for small size images