Synthetic aperture radar (SAR) has been widely used for remote sensing applications in the past three decades. It provides hight-resolution two-dimentional images independent from daylight, cloudcoverage and weather conditions. A particular drawback of SAR image is speckle effect. This effect is caused by the presence of several elementary scatterers with a random distribution within each resolution cell. As a result, the radar image looks visually very noisy and has a salt-and-pepper appearance with strong variations from pixel to pixel. This noise is usually reduced before any image exploitation. There are two common approaches for speckle reduction or despeckling: a) multilook processing and b) filtering. Multilook processing improves the appearance of SAR image by non-coherent averaging of the intensity image. Filtering methods, known as post-image formation methods apply a speckle removal filter to the SAR data after the image is formed. Recently, compressed sensing (CS) has been explored in the SAR imaging context. CS provides the ability to reconstruct sparse or compressible signals and images with far fewer samples or measurements than that Nyquist requires. This thesis investigates the potential of CS in speckle reduction of SAR images. In this thesis, common despeckling methods are reviewed and compared. Then, a CS-based despeckling method is proposed. In this method, speckle reduction and image reconstruction are done simultaneously. Moreover, two CS-based approaches are developed to jointly preserve the bright point targets and reduce the speckle. Finally, effectiveness of the proposed approaches is illustrated with computer simulation. Keywords: Synthetic aperture radar (SAR), Speckle reduction, Multilook processing (ML), Filtering methods, compressed sensing (CS).