System noise poses significant challenges for image quality and data analysis in satellite imaging. This paper addresses the issue of system noise removal in area-array satellite images, highlighting the limitations of existing methods that aggregate multiple noisy images without capturing the consistent properties of system noise, which leads to inaccurate system noise estimates and imposes considerable computational burdens. Additionally, current system noise estimation methods rely on cloud-free images, which are particularly challenging to obtain for large-swath satellites such as Gaofen-4. Furthermore, the spatial non-uniformity and mixed characteristics of system noise complicate its modeling, rendering standard additive white Gaussian noise (AWGN) frameworks inadequate. To address these challenges, a novel system noise estimation method that considers self-constraint and graph regularized row sparse coding (SC-GRSC) is proposed. By applying data fidelity constraints directly to the system noise, our method leverages the consistent property of system noise across multiple images and mitigates biases and inefficiencies associated with multiple noisy images. Cloud region masks are introduced to characterize the unique statistical characteristics of system noise in cloud-covered areas, addressing the dependency on cloud-free images. Moreover, graph-regularized row sparse coding is employed to represent image priors and weight matrices are incorporated to characterize the spatial non-uniformity of system noise, enabling more accurate system noise estimation. A series of experiments conducted on simulated images and real Gaofen-4 satellite images demonstrate that the proposed SC-GRSC method outperforms comparable methods in removing system noise. The source code for SC-GRSC is available at: https://github.com/2015114000/SC-GRSC.