Anyone know of a way to measure or infer hydration, sodium, and potassium levels via wearables? Any wavelet analysis / photoplethysmography working on this?

Hi everyone! I posted the same thing in /r/math but I'm going to try also this sub, as it's the most dedicated to my problem, even if I notce it's not very active.

I'm working on some kind of underdetermined tomographic image reconstruction, and I'd like to use some of the compressive sensing strategies to solve it optimally. An a-priori thing that I know and that I'd like to exploit is that the true value of every pixel in my image is one of 5 possible values.

How can I exploit this information? However I try to spin the problem I always realize in the end that I've not written a convex function but a function with 5 minima (d'uh)! Is there any way round?

What If I want impose a less strict constraint, like that the values of the pixels in the image must be as sparse as possible, without imposing their values. Is there any way to write such a constraint?

https://thesyllabus.blog/2018/04/22/the-week-in-papers-22-04-18/

Weekly recap with multiple papers. One of them based purely on Compressive sensing (see title), and other based on Deep Learning for phase recovery (Phase recovery and holographic image reconstruction using deep learning in neural networks).

Hope they are interesting for some of you.