Blind deconvolution of astronomical images with band limitation determined by optical system parameters
Lei Luo, Mingming Fan, Minxian Shen · Acta Astronomica Sinica · 2007
Atmospheric turbulence greatly limits the spatial resolution of astronomi- cal images acquired by the large ground-based telescope.The record image obtained from telescope was thought as a convolution result of the object function and the point spread function.The statistic relationship of the images measured data,the estimated object and point spread function was in accord with the Bayes conditional probability distribution,and the maximum-likelihood formulation was found.A blind deconvolution approach based on the maximum-likelihood estimation technique with real optical band limitation constraint is presented for removing the effect of atmospheric turbulence on this class images through the minimization of the convolution error function by use of the conjugation gradient opti- mization algorithm.As a result,the object function and the point spread function could be estimated from a few record images at the same time by the blind deconvolution algorithm. According to the principle of Fourier optics,the relationship between the telescope optical system parameters and the image band constraint in the frequency domain was formulated during the image processing transformation between the spatial domain and the frequency domain.The convergence of the algorithm was increased by use of having the estimated function variable(also is the object function and the point spread function)nonnegative and the point-spread function band limited.Avoiding Fourier transform frequency compo- nents beyond the cut off frequency lost during the image processing transformation when the size of the sampled image data,image spatial domain and frequency domain were the same respectively,the detector element(e.g.a pixels in the CCD)should be less than the quarter of the diffraction speckle diameter of the telescope for acquiring the images on the focal plane.The proposed method can easily be applied to the case of wide field-view turbulent-degraded images restoration because of no using the object support constraint in the algorithm.The performance validity of the method is examined by the computer simulation and the restoration of the real Alpha Psc astronomical image data.The results suggest that the blind deconvolution with the real optical band constraint can remove the effect of the atmospheric turbulence on the observed images and the spatial resolution of the object image can arrive at or exceed the diffraction-limited level.