Synthetic aperture radar (SAR) images are contaminated by multiplicative noise during the imaging process because of flaws in SAR's innate imaging mechanism; the image noise makes it difficult to analyze targets and detect changes. Existing denoising algorithms cannot adaptively estimate the noise size, and the edge preservation effect is not ideal. Additionally, it can be difficult to work out how to adaptively analyze images with different noise sizes. As a result, this work proposes a sparse denoising algorithm for SAR images based on bilateral filtering and blind estimation. First, bilateral filtering was employed to obtain preprocessed images with good edge-preserving properties, and then the blind estimation was utilized to determine the global noise level of the images, which acted as a residual threshold in the sparse reconstruction process. To achieve the goal of image denoising, sparse coding and dictionary learning algorithms were employed for representing the image using the least amount of atomic information possible. The experimental findings demonstrate that the sparse reconstruction algorithm combined with blind estimation not only effectively removes image noise and improves the equivalent numbers of looks, but also performs well for peak signal-to-noise ratio and edge-preserving index, effectively preserving the detailed texture information of the original image.