image compression versus image denoising
Perceptually lossless (but actually lossy) image compression aims to maintain visually the same image while reducing the number of bits necessary to represent it. If you try to compress aggressively however, visually apparent compression artifacts will show up.

Wavelet based image denoising aims to change the appearance of an image by getting rid of what is considered as noise. We expect the denoised image to look better, compared to the noisy version.

One side effect of image denoising is also a reduction in the size of the image, as you are effectievely discarding some data from the image. But it will never be as efficient as a compression algorithm.

Furthermore, since noise is always considered as irrelevant information, it can be useful to denoise an image (if necessary) before compressing it, allowing you to achieve higher compression rations.

However, note that image denoisers are not perfect algorithms in terms of discriminating noise from true image data, and they may and will discard not only noise but also some very critical image information (especially at high frequencies, textures an edges).