In deep exploration, we often use high-noise and high-resolution astronomical images because of long distance transmission, cosmic noise interference, or other disturbances. Designing an effective method for high-noise astronomical image denoising plays a crucial role in this field. The famous compressed sensing (CS) has shown to be a successful technique for high-resolution image reconstruction. CS is employed to solve the denoising problem in high-noise astronomical images, and a CS reconstruction model and a CS curvelet soft thresholding (NCCST) reconstruction algorithm are proposed simultaneously. In image denoising, the l₁-norm reconstruction model based on CS cannot fully consider the internal structure of the image, thus affecting the reconstruction quality. Combined with the l₁-norm reconstruction model and group sparse total variation method, the CS reconstruction model is first established. In this framework, the NCCST algorithm uses an adaptive curvelet adjustment operator proposed to select the sparse coefficients in the stage of image sparsity transform, and then a descending VisuShrink threshold is adopted to pick out these reconstructed astronomical image coefficients in each iteration. The experimental results demonstrate that the algorithm proposed can reconstruct clear images from high-noise and high-resolution astronomical images. Meanwhile, it can preserve more astronomical image details, edges, and textures. Even at a low-compression sampling ratio, this algorithm can achieve superior reconstruction performance. The proposed algorithm can be applied in the satellite receiving station to quickly and accurately reconstruct high-resolution astronomical images with high quality.