This paper concerns lossy compression of images corrupted by additive noise. The main contribution of the paper is that analysis is carried out from the viewpoint of compressed image visual quality. Several coders for which the compression ratio is controlled in different manner are considered. Visual quality metrics that are the most adequate for the considered application (WSNR, MSSIM, PSNR-HVS-M, and PSNR-HVS) are used. It is demonstrated that under certain conditions visual quality of compressed images can be slightly better than quality of original noisy images due to image filtering through lossy compression. The "optimal" parameters of coders for which this positive effect can be observed depend upon standard deviation of the noise. This allows proposing automatic procedure for compressing noisy images in the neighborhood of optimal operation point, that is, when visual quality either improves or degrades insufficiently. Comparison results for a set of grayscale test images and several variances of noise are presented.
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