Context. Due to the presence of atmospheric turbulence, the quality of solar images tends to be significantly degraded when observed by ground-based telescopes. The adaptive optics (AO) system can achieve partial correction but stops short of reaching the diffraction limit. In order to further improve the imaging quality, post-processing for AO closed-loop images is still necessary. Methods based on deep learning (DL) have been proposed for AO image reconstruction, but the most of them are based on the assumption that the point spread function (PSF) is spatially invariant. Aims. Our goal is to construct clear solar images by using a sophisticated spatially variant end-to-end blind restoration network. Methods. The proposed channel sharing spatio-temporal network (CSSTN) consists of three sub-networks: a feature extraction network (FEN), channel sharing spatio-temporal filter adaptive network (CSSTFAN), and a reconstruction network (RN). First, CSST-FAN generates two filters adaptively according to features generated from three inputs. Then these filters are delivered to the proposed channel sharing filter adaptive convolutional (CSFAC) layer in CSSTFAN to convolve with the previous or current step features. Finally, the convolved features are concatenated as input of RN to restore a clear image. Ultimately, CSSTN and the other three supervised DL methods are trained on the binding real 705nm photospheric and 656nm chromospheric AO correction images as well as the corresponding speckle reconstructed images. Results. The results of CSSTN, the three DL methods, and one classic blind deconvolution method evaluated on four test sets are shown. The imaging condition of the first photospheric and second chromospheric set is the same as training set, except for the different time given in the same hour. The imaging condition of the third chromospheric and fourth photospheric set is the same as the first and second, except for the Sun region and time. Our method restores clearer images and performs best in both the peak signal-to-noise ratio (PSNR) and contrast among these methods.

A series of short-exposure images are often used for rich, small-scale structure, high-quality, and high-resolution astronomical observations. Postprocessing of the closed-loop adaptive optics (AO) image using ground-based astronomical telescopes plays an important role in astronomical observations due to it further improving image quality after AO processing. These images show several main characteristics: random spatial variation blur kernel, unclear model after AO correction, unclear physical characteristics of observation objects, etc. Our goal is to propose a multiframe correction blind deconvolution (MFCBD) algorithm to restore AO closed-loop solar images. MFCBD introduces a denoiser and corrector to help estimate the intermediate latent image and proposes using an L q norm of the kernel as the sparse constraint to acquire a compact blur kernel. MFCBD also uses the half-quadratic splitting strategy to optimize the objective function, which makes the algorithm not only simple to solve, but also easy to adapt to different fidelity terms and prior terms. In tests on three data sets observed from the photosphere and chromosphere of the Sun, MFCBD not only restored clearer and more detailed images, but also converged smoothly and monotonically in terms of the peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) after a few iterations. Taking the speckle-reconstructed image as a reference, the clear image restored by our method performs best both in PSNR and SSIM compared with the state-of-the-art traditional methods OBD and BATUD.