# Phase retrieval via SDP (semidefinite program) of 2D test image (Matrix completion)

In SDP based phase retrieval we have intensity measurement (abs(FFT2(x))^2) of the form

A(xo) = |ak,x|^2 =b^2, phase retrieval is then

find x that obeys A(xo)=b

The quadratic measurements can be lifted and interpreted as linear about rank 1 matrix X =xx*

|ak,x|^2 = b^2 = Tr(AX), with X =xx* and we want to recover the phase (x - signal to recover).

In the standard approach named as phase lift we imagine lift of dimension X =xx* and we look to minimize rank of Tr(X), subject to A(X)=b, X>=0

And we need roughly 4n measurement for n length signal if I understand it correctly.

This is fine for 1D problems. When we have 2D pahse retrieval going to 4D in X doesnt look good approach.What is the trick for phase recover in the case of 2D phase retrieval problems?

I would like to ask how to construct phase retrieval of test picture 2D, let say phantom (phantom('Modified Shepp-Logan',50) in matlab) with semidefinite programing like phaselift.

http://web.stanford.edu/~mahdisol/PhaseRetrieval_CDP.pdf Phase lift method

Examples in 1D online.

http://web.stanford.edu/~mahdisol/PhaseRetrieval_CDP.html

via semidefinite method like phaselift

Thank you.

• Most of these links are broken. Commented Jul 21, 2016 at 10:46
• yes they are but cant fix them Commented Jul 23, 2016 at 18:33