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I'm trying to solve the phase problem from single intensity measurement. I implemented error reduction algorithm in Matlab for my problem but it does not give any result. Is there anybody uses this algorithm for phase problem?

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    $\begingroup$ Could you describe the problem you're trying to solve in more detail. Also, it would be helpful if you describe your error reduction algorithm explicitly in terms of equations. Posting relevant code portions may also help us to help you better. $\endgroup$
    – Paul
    Jan 30 '17 at 17:52
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I assume you refer to what's become known as the error reduction algorithm for phase retrieval (e.g. as defined in the Wikipedia article on Phase retrieval). I've used ER in several contexts, but since this algorithm relies on a very simpler alternating projections scheme between the two spaces, convergence tends to be slow. It also tends to get stuck in local minima, where the most direct developments (HIO is mentioned in the article, in my group we have been using RAAR quite a bit) can perform much better.

However, I would also look seriously into whether the problem, as you specify it, is expected to be solvable at all. You say very little on the structure of your problem, and it is very easy to specify something which is seriously underdetermined, at least when you take experimental noise into account. That is, there are a plethora of feasible "solution" which are nothing alike a proper recovery, and it can even be that the very best global optimum, would one find it, is too far removed from the true object to be of relevance. Having a proper support constraint, and possibly constraints on positivity/reality (no imaginary part) in the object space can make a significant difference, in practice.

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