Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The state of the art for solving the phase retrieval problem in two dimensions relies heavily on the algorithms proposed by Gerchbercy, Saxton, and Fienup. Despite the widespread use of these algorithms, current mathematical theory cannot explain their remarkable success. It is already known that the Gerchberg-Saxton algorithm is a nonconvex version of method of alternating projections. ,  show that two other prominent phase retrieval methods also have ll known counterparts in the world of convex optimization algorithms: Fienup's basic input-output algorithm corresponds to Dykstra's algorithm, and Fienup's hybrid input-output algorithm can be vied as an instance of the Douglas-Rachford algorithm. This work provides a theoretical framework to better understand and, potentially, improve existing phase recovery algorithms.
['Heinz H. Bauschke', 'Patrick L. Combettes', 'David Russell Luke']
I am writing a research paper on a idea On the structure of some phase retrieval algorithms
[{"from": "human", "value": "I am writing a research paper on a idea On the structure of some phase retrieval algorithms"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The state of the art for solving the phase retrieval problem in two dimensions relies heavily on the algorithms proposed by Gerchbercy, Saxton, and Fienup. Despite the widespread use of these algorithms, current mathematical theory cannot explain their remarkable success. It is already known that the Gerchberg-Saxton algorithm is a nonconvex version of method of alternating projections. ,  show that two other prominent phase retrieval methods also have ll known counterparts in the world of convex optimization algorithms: Fienup's basic input-output algorithm corresponds to Dykstra's algorithm, and Fienup's hybrid input-output algorithm can be vied as an instance of the Douglas-Rachford algorithm. This work provides a theoretical framework to better understand and, potentially, improve existing phase recovery algorithms."}]