An adaptive version of the Richardson-Lucy iterative algorithm of deconvolution has been presented. This method using some additional constraints gives a solution very close to the one given by the Maximum Likelihood principle. The crucial point in this approach is spatially varying regularization achieved by a spatially varying number of iterations, contrary to the original scheme, where each image point is processed by the same number of iterations set by the operator. This leads to a spatially varying resolution. The number of iterations is controlled via the sigmoid function by the local difference between the object signal and the noisy background. When the difference between the object and the noisy background increases, the number of iterations also increases to attain its maximum value assigned by the operator. Due to this adaptivity, the background noise is highly diminished and artefacts of the restoration procedure almost vanish, which is not the case with the original Richardson-Lucy scheme. Moreover, in the new approach the mean number of iterations per one pixel is substantially less than the maximum value assigned by the operator.
To evaluate properties of both algorithms one- and two-dimensional profiles consisting of objects lying on the background were convolved with theoretical and observationally obtained PSF profiles and restored using both schemes. Photometric and astrometric properties of both methods have been evaluated from aperture photometry and brightness centre astrometry of the synthetic stellar cluster. The overall conclusion is that the computational efficiency of the modified iterative scheme is substantially greater, the quality of restored images and photometric fidelity substantially better than that of the original one. This is generally due to the adaptivity of the newly elaborated approach. Its predominance over the basic algorithm is especially evident in the case of the restoration of crowded star fields.
Acknowledgements
The author is very grateful to Dr. H.-M. Adorf and Dr. Roques, referees of this paper, for many helpful comments on an initial version of this work.