[ENH]: Add a low rank denoiser

[paquiteau]

Hi there,

Among the classical denoising technique, low-rank approximation (a.k.a PCA) is a widely known technique, and the so-called singular value threshold corresponds to the proximal operator of the nuclear norm ¹. It is used in particular in hyperspectral imaging but also for dynamic imaging problem (like functional or cardiac MRI). Having this into deepinv would be a nice addition.

I might propose a PR doing this the coming days/weeks.

PS: Local low rank denoising (where the low-rankness is enforced patch-wise) is also possible, in fact I have a package just doing that ² (sadly with no working GPU acceleration for now (see cupy/cupy#8009).

Footnotes

1. Cai, J.-F., Candès, E. J., & Shen, Z. (2010). A Singular Value Thresholding Algorithm for Matrix Completion. SIAM Journal on Optimization, 20(4), 1956–1982. https://doi.org/10/bqxph7 ↩

2. https://github.com/paquiteau/patch-denoising ↩

[tachella]

Hey!

This would be a nice idea, did you make any progress?

[paquiteau]

Hello again ! I plan to resume the work on this in the coming weeks. There was some bug in Pytorch (pytorch/pytorch#122312) that has been recently fixed.

So adding this should be fairly easy now (for both real and complex-valued data; as an MRI guy, I am more interested in the latter)