Synthetic Aperture Radar (SAR) imagery are widely utilized in remote sensing due to their all-weather, all-day imaging capabilities. However, SAR images are highly susceptible to noise, particularly speckle noise, caused by the coherent imaging process, which severely degrades image quality. This has driven increasing research interest in SAR despeckling. Sparse representation-based methods have been extensively applied in natural image processing, yet SAR despeckling requires addressing non-Gaussian assumption and ensuring sparsity in the transform domain. In this work, we propose a simple, intuitive, and efficient SAR despeckling approach grounded in compressive sensing theory. By applying Log-Yeo-Johnson transformation, we convert gamma-distributed noise into an approximate Gaussian distribution to noise sparse assumption. The method incorporates noise and sparsity priors, leveraging a non-local sparse representation through auxiliary matrices: one capturing varying noise characteristics across regions and the other encoding adaptive sparsity information. Extensive experiments validate the effectiveness of our method.

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