Constrained deconvolution from wavefront sensing using the frozen flow hypothesis and complex wavelet regularization

Deconvolution from wavefront sensing (DWFS) is a high-performance image restoration technique designed to compensate for atmospheric turbulence-induced wavefront distortions. It uses simultaneously recorded short-exposure images of the object and high cadence wavefront sensor (WFS) data to estimate both the wavefronts and the object. Conventional DWFS takes no account of the temporal correlations in WFS data, which limits the reconstruction of high-spatial frequency components of wavefront distortion and then the recovery of the object. This paper takes the frozen flow hypothesis (FFH) to model the temporal evolution of atmospheric turbulence. Under this assumption, a joint estimation is performed in a Bayesian framework to simultaneously estimate the object and the turbulence phases with strict constraints imposed by WFS data and the FFH. It takes into account the temporal correlations in WFS data as well as the available a priori knowledge about the object and turbulence phases. Taking advantage of the sparse analysis prior of the object in the wavelet domain, a sparse regularization of the object based on the 2D dual-tree complex wavelet transform is proposed. Numerical experiments show that the proposed method is robust and effective for high-resolution image restoration in different seeing conditions.