  Remote sensing images are essential for many applications of the earth's
sciences, but their quality can usually be degraded due to limitations in
sensor technology and complex imaging environments. To address this, various
remote sensing image deblurring methods have been developed to restore sharp
and high-quality images from degraded observational data. However, most
traditional model-based deblurring methods usually require predefined
{hand-crafted} prior assumptions, which are difficult to handle in complex
applications. On the other hand, deep learning-based deblurring methods are
often considered as black boxes, lacking transparency and interpretability. In
this work, we propose a new blind deblurring learning framework that utilizes
alternating iterations of shrinkage thresholds. This framework involves
updating blurring kernels and images, with a theoretical foundation in network
design. Additionally, we propose a learnable blur kernel proximal mapping
module to improve the accuracy of the blur kernel reconstruction. Furthermore,
we propose a deep proximal mapping module in the image domain, which combines a
generalized shrinkage threshold with a multi-scale prior feature extraction
block. This module also incorporates an attention mechanism to learn adaptively
the importance of prior information, improving the flexibility and robustness
of prior terms, and avoiding limitations similar to hand-crafted image prior
terms. Consequently, we design a novel multi-scale generalized shrinkage
threshold network (MGSTNet) that focuses specifically on learning deep
geometric prior features to enhance image restoration. Experimental results on
real and synthetic remote sensing image datasets demonstrate the superiority of
our MGSTNet framework compared to existing deblurring methods.
