Single-view phase retrieval of an extended sample by exploiting edge detection and sparsity

Ashish just sent me the following:

Hi Igor,

awesome blog you run.

I've got a recent paper on using compressive sensing (L0/L1 regularization) to make phase retrieval more robust. Paper is here:

https://www.osapublishing.org/oe/abstract.cfm?uri=oe-24-21-24719

Just thought I'd bring it to your attention and maybe someone on the blog might be interested.

Thanks Ashish ! This problem in eq (7) very much looks like a co-sparsity one. Here is the paper: Single-view phase retrieval of an extended sample by exploiting edge detection and sparsity by Ashish Tripathi, Ian McNulty, Todd Munson, and Stefan M. Wild

We propose a new approach to robustly retrieve the exit wave of an extended sample from its coherent diffraction pattern by exploiting sparsity of the sample’s edges. This approach enables imaging of an extended sample with a single view, without ptychography. We introduce nonlinear optimization methods that promote sparsity, and we derive update rules to robustly recover the sample’s exit wave. We test these methods on simulated samples by varying the sparsity of the edge-detected representation of the exit wave. Our tests illustrate the strengths and limitations of the proposed method in imaging extended samples. 

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