Speckle noise seriously degrades the quality of SAR images and complicates the image exploitation using automated image analysis techniques. Recently, the application of compressed sensing (CS) is explored in the SAR signal processing. In this paper, first, a linear model is derived for speckled SAR data. Then, using this model and the compressed sensing theory, a speckle reduction method is proposed. In the proposed method, the image backgrounds as well as the bright point targets are also reconstructed together with noise reduction. The important feature of the proposed method is the joint noise reduction simultaneous with the SAR image formation. Moreover, using simulated and real SAR images, the performance of the proposed method in noise reduction and preserving image features is evaluated and compared to the performance of some de-noising approaches.