Recently Compressive Sensing (CS) has shown great potential in the field of Image processing applications. In this paper we propose a novel CS based technique for simultaneous compression and despeckling of Synthetic Aperture Radar (SAR) images. We incorporate Dual Tree Complex Wavelet Transform (DT-CWT) based denoising within a sparse regularization frame work and solve by a fast projected Landweber reconstrution algorithm. The proposed work contributes in three ways. First the processing is done on data acquired in spatial domain under sub Nyquist rate sampling. Then a two stage denoising in the recovery process eliminates speckles in an excellent way, preserving edges and details effectively. Finally simultaneous compression and denoising is achieved in a simple fast and efficient manner saving the computational cost substantially in both time and memory. © 2015 IEEE.