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Elimination of distortions of weak images of astronomical objects on the example of Saturn, Jupiter and their satellites

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Methods and algorithms for restoring smeared and noisy images by numerically solving integral equations (IE) are considered. The algorithms are illustrated by the restoration of distorted images of celestial bodies using the example of images of Saturn, Jupiter and their satellites against the background of the starry sky. Images of objects may be weak, which will require increased exposure and may lead to a mismatch between the rotations of the Earth and a telescope, and then a smear image of the object will occur. The article proposes to eliminate smear by mathematical and computer processing of the distorted image. In this case, the type and the parameters of a smear may be practically unknown or known inaccurately. The novelty of the proposed solution lies in the fact that the type and the parameters of a distortion, and therefore the kernel of an IE or the point spread function (PSF), are determined by the original “spectral method”. In the direct problem, modeling the smear and noise in receivers (telescopes) is performed by calculating convolutiontype integrals. In the inverse problem, image smearing is performed by IE solving with the Wiener parametric filtering method using the new “spectral method” for determining the kernel of the IE as well as filtering the noise by the Tukey median filter and the new modified filter. Error estimates for each operation are obtained. A technique has been proposed that makes it possible to eliminate, through the use of mathematical and software tools, images of planets, natural and instrumental noise, image smear, and also to obtain the clear images of Saturn, Jupiter and their satellites. Undistorted images of Saturn and Jupiter with their satellites were taken from astronomical catalogs. By modeling, we have obtained a distorted (smeared and noisy) image of Saturn with given distortion parameters (smear angle θ and smear value Δ) and a truly distorted image of Jupiter with unknown distortion parameters determined by the spectral method. Next, the image of Saturn with its satellites was restored by solving the IE. Image processing of Jupiter was also carried out, in which, to eliminate image smear by solving the integral equation, the “spectral method” was used to determine the smear parameters, and therefore the PSF and the kernel of the integral equation. The performance of the proposed method is determined both by visual assessment of the reconstructed image and by calculating the reconstruction error. The proposed technique makes it possible to eliminate in images of various space objects, in particular, Saturn and Jupiter, the natural or instrumental noise, as well as image smear, and to highlight faint objects (satellites, etc.) against the background of stars.

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