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A new reconstruction method of complex-valued fractional Brownian motion(CV-fBm) field based on Compressive Sampling (CS) is proposed. The decayproperty of Fourier coefficients magnitude of the fBm signals/ fields indicatesthat fBms are compressible. Therefore, a few numbers of samples will besufficient for a CS based method to reconstruct the full field. Theeffectiveness of the proposed method is showed by simulating, random sampling,and reconstructing CV-fBm fields. Performance evaluation shows advantages ofthe proposed method over boxcar filtering and thin plate methods. It is alsofound that the reconstruction performance depends on both of the fBm's Hurstparameter and the number of samples, which in fact is consistent with the CSreconstruction theory. In contrast to other fBm or fractal interpolationmethods, the proposed CS based method does not require the knowledge of fractalparameters in the reconstruction process; the inherent sparsity is justsufficient for the CS to do the reconstruction. Potential applicability of theproposed method in weak gravitational lensing survey, particularly forinterpolating non-smooth PSF (Point Spread Function) distribution representingdistortion by a turbulent field is also discussed.

Reconstruction of Complex-Valued Fractional Brownian Motion Fields Based  on Compressive Sampling and Its Application to PSF Interpolation in Weak  Lensing Survey