Read here: http://www.lightvortexastronomy.com/tutorial-sharpening-fine-details.html
This tutorial covers the process of sharpening fine details in one's images, be they monochrome or colour. The tutorial covers the in-depth use of Deconvolution with DynamicPSF on linear images (linearity is required for this) and MultiscaleLinearTransform on linear and non-linear images. ATrousWaveletTransform is normally used but as it is being phased out to obsolete by PixInsight developers, MultiscaleLinearTransform replaces it completely.
[UPDATE]: This tutorial is now back online after a corrective update. Deconvolution with DynamicPSF is now described strictly with linear images (as it should be). The order of presentation of Deconvolution and MultiscaleLinearTransform has been reversed to nail in the idea that both can be used - Deconvolution while the image is linear and MultiscaleLinearTransform later, ideally when the image is non-linear. Also made some edits to the text to ensure correctness and fluidity.