Difficulty changing fabric to crisp white

[Melancholy_Tangerine]

I have several images with deep purple towels that my client wants turned pure crisp white, and I have tried every trick I know (and a youtube rabbithole) and I cannot get pure crisp white without losing the texture of the towel... the closest I can get without losing texture still have far too much grey - especially with the real white towels already in the image (which it should match).

Even if I get it *almost* there on some images, the edge lines are so harsh feathering/blurring is doing nothing. I have been playing mostly with hue/saturation adjustment layers on the selection (saturation & lightness) and a curve adjustment layer helps, but it's still not a crisp, clean white.

Any suggestions? P.S. Please be kind, I am still learning. See some samples below

[S_Gans]

I would love to see your curves adjustment on this. I'm thinking you may not be pinpointing the location of the adjustment, so it may be coming out more heavy-handed than you're prefer?

You can have crisp white, but you want to be sure not to blow it out to specular. So, pick a place on the high end of the biggest lump on the histogram and pull up - making certain to have NONE of it attach to the top of the viewing area (specular white). Then, pick one shadow with the finger icon, to pull down on, and increase contrast in the area. 

Attached, is a rough selection, but the general idea I'm getting at. I hope it helps.

[Melancholy_Tangerine]

Thank you so much this was tremendously help I do believe it was my curves, I will continue to play aroudn with them more but I couldn't pinpoint where the curves where going wrong. Your kindness is deeply appreciated!

[Bojan Živković]

You can also try using Hue/Saturation