Random Noise Removal In Images
There are a lot of ways to do image denoising.

I will give several known examples:


Hard/soft thrsholding of the wavelet decomposition: Do a wavelet decomposition of the image and for zero all coefficients less than some minimum value and linear the other values.

Non Local Means: We use the fact that for "natural images" for each patch in the image we can find very similar other patches in the image. So for each pixel we look at the neighborhood around him and we search for other pixels that has the same neighborhood and than we use those patches to calculate the value of the original pixel.using the fact that the patches are very coorelated but the noise isn't.





Block Match 3D: We do the same as before finding similar patches around the image and than we arrange them as a 3D block and apply wavelet thresholding. This is more complicated and you can read about this. A basic scheme for this is:




There a lot more ways and just by googling it you will get a lot of information hope this basic intro will help you enough.