One principal objective of noise suppression is to give an image the perception of sharpness. Online discussions of sharpness emphasize that it depends on factors external to an image as well as the properties of the image itself. Principally, viewing distance and enlargement factor affect our impression of image sharpness. An image that appears wonderfully sharp when viewed from 1m away and displayed as 8x10 may look noisy and blurry if viewed from a closer distance or at greater enlargement. Some internet sites provide equations to help with this relationship, but the point is, at some distance or at some size, virtually every image will be unsatisfactorily noisy. So, target the image processing for the intended viewing conditions.
Next issue is that noise reduction, good noise reduction anyway, tries to smooth regions that are smooth (subject to viewing conditions) while preserving edges. What you see as large-scale noise is what the algorithm sees as edges around homogeneous regions. So, the game is to blur or otherwise smooth-out noise in the regions between 'true' edges but leave the edges themselves unscathed. To do this the algorithm needs to work with some definition of edge--some definition that says, "a rapid change in color or intensity at a particular scale (or larger) is not noise--it's signal!"
Generally, the parameters you set in the PI procedure tell the algorithm what the change-over scale between noise and edge is--unless it's a primitive algorithm that just smooths everything without regard for edges. So, decide how the image is to be view, and proceed accordingly--and inspect your image just as closely as you intend to display it, and no closer!
BTW TGV is an 'edge-aware' algorithm, some others are not.