A very basic explanation of removal of jpg artifacts in the Noise Reduction filter, discussing the potential tensions between different aims. Improves, but does not produce a high quality image.
An interesting approach using Lab Colour mode to separate out the lightness, colour and contrast channels of the image. Artifacts are most evident in the colour and contrast A and B channels. Add Gaussian blur to A and B channels. Higher values give a sort of watercolour effect. Sharpen the lightness channel. Go back to RGB at the end to use filters etc again.
Duplicate the image. On top layer use surface blur – avoids blurring the edges. Change to colour blend mode to get rid of colour noise. Mask areas if necessary. Duplicate again and use dust and scratches filter gets rid of luminance noise. Again use masks to [reserve details. Duplicate again and Reduce Noise filter and use preserve details slider.