Reconstruction of turbulence-degraded images using the vector Wiener filter

Adaptive optics and speckle imaging are common methods for improving Fourier domain signal-to-noise ratio (SNR) in astronomical images. These techniques may benefit from linear processing to deconvolve blurring due to the attenuation of high spatial frequencies in the compensated images. Typical linear deconvolution methods require an explicit estimate of the random atmospheric-optical system point spread function or optical transfer function (OTF). In addition, a priori knowledge of the object class and noise are not used in an optimal manner. We apply a vector Wiener filter to photon-limited images degraded by atmospheric turbulence to demonstrate the potential advantages of optimal deconvolution processing. This filter incorporates model-based information about object, OTF, and noise. To our knowledge, this is the first application of complete OTF correlation statistics to the reconstruction of turbulence-degraded images. Computer simulation of binary star images show the vector Wiener filter provides superior reconstructions when compared to the traditional scalar Wiener filter for non-wide-sense stationary objects. Much of this performance improvement can be attributed to variance reduction in the noisy Fourier data at spatial frequencies where the mean OTF is severely attenuated. However, vector Wiener filter performance is substantially degraded with respect to both mean square error and mean square phase error at spatial frequencies where the OTF SNR is less than unity. ©1998 Society of Photo-Optical Instrumentation Engineers