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?
Just few reference links.
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
http://web.stanford.edu/~mahdisol/PRcode.html code
or http://arxiv.org/pdf/1111.6323v3.pdf
http://users.isy.liu.se/en/rt/ohlsson/code.html code
Thank you.