The performance of an image compression scheme is affected by the presence of noise, and the achievable compression may be reduced significantly. We investigated the effects of specific signal-dependent-noise (SDN) sources, such as film-grain and speckle noise, on image compression, using JPEG (Joint Photographic Experts Group) standard image compression. For the improvement of compression ratios noisy images are preprocessed for noise suppression before compression is applied. Two approaches are employed for noise suppression. In one approach an estimator designed specifically for the SDN model is used. In an alternate approach, the noise is first transformed into signal-independent noise (SIN) and then an estimator designed for SIN is employed. The performances of these two schemes are compared. The compression results achieved for noiseless, noisy, and restored images are also presented.