Reconstruction of Complex-Valued Fractional Brownian Motion Fields Based
  on Compressive Sampling and Its Application to PSF Interpolation in Weak
  Lensing Survey
  A new reconstruction method of complex-valued fractional Brownian motion
(CV-fBm) field based on Compressive Sampling (CS) is proposed. The decay
property of Fourier coefficients magnitude of the fBm signals/ fields indicates
that fBms are compressible. Therefore, a few numbers of samples will be
sufficient for a CS based method to reconstruct the full field. The
effectiveness of the proposed method is showed by simulating, random sampling,
and reconstructing CV-fBm fields. Performance evaluation shows advantages of
the proposed method over boxcar filtering and thin plate methods. It is also
found that the reconstruction performance depends on both of the fBm's Hurst
parameter and the number of samples, which in fact is consistent with the CS
reconstruction theory. In contrast to other fBm or fractal interpolation
methods, the proposed CS based method does not require the knowledge of fractal
parameters in the reconstruction process; the inherent sparsity is just
sufficient for the CS to do the reconstruction. Potential applicability of the
proposed method in weak gravitational lensing survey, particularly for
interpolating non-smooth PSF (Point Spread Function) distribution representing
distortion by a turbulent field is also discussed.
