Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Phase retrieval seeks to recover a signal $$x \in {\mathbb {C}}^p$$ x ? C p from the amplitude $$|A x|$$ | A x | of linear measurements $$Ax \in {\mathbb {C}}^n$$ A x ? C n .  cast the phase retrieval problem as a non-convex quadratic program over a complex phase vector and formulate a tractable relaxation (called PhaseCut) similar to the classical MaxCut semidefinite program.  solve this problem using a provably convergent block coordinate descent algorithm whose structure is similar to that of the original greedy algorithm in Gerchberg and Saxton (Optik 35:237---246, 1972), where each iteration is a matrix vector product. Numerical results show the performance of this approach over three different phase retrieval problems, in comparison with greedy phase retrieval algorithms and matrix completion formulations.
['Irène Waldspurger', "Alexandre d'Aspremont", 'Stéphane Mallat']
I am writing a research paper on a idea Phase recovery, MaxCut and complex semidefinite programming
[{"from": "human", "value": "I am writing a research paper on a idea Phase recovery, MaxCut and complex semidefinite programming"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Phase retrieval seeks to recover a signal $$x \\in {\\mathbb {C}}^p$$ x ? C p from the amplitude $$|A x|$$ | A x | of linear measurements $$Ax \\in {\\mathbb {C}}^n$$ A x ? C n .  cast the phase retrieval problem as a non-convex quadratic program over a complex phase vector and formulate a tractable relaxation (called PhaseCut) similar to the classical MaxCut semidefinite program.  solve this problem using a provably convergent block coordinate descent algorithm whose structure is similar to that of the original greedy algorithm in Gerchberg and Saxton (Optik 35:237---246, 1972), where each iteration is a matrix vector product. Numerical results show the performance of this approach over three different phase retrieval problems, in comparison with greedy phase retrieval algorithms and matrix completion formulations."}]