Lossy compression of noise-free and noisy images differs from each other. While in the first case image quality is decreasing with an increase of compression ratio, in the second case coding image quality evaluated with respect to a noise-free image can be improved for some range of compression ratios. This paper is devoted to the problem of lossy compression of noisy images that can take place, e.g., in compression of remote sensing data. The efficiency of several approaches to this problem is studied. Image pre-filtering is shown to be expedient for coded image quality improvement and/or increase of compression ratio. Some recommendations on how to set the compression ratio to provide quasioptimal quality of coded images are given. A novel DCT-based image compression method is briefly described and its performance is compared to JPEG and JPEG2000 with application to lossy noisy image coding.