AI Article Synopsis
- This work highlights the significance of using approximate Fourier phase information in tackling the phase retrieval problem.
- The study reveals that having a rough phase estimate (within π/2 radians) enables the creation of highly efficient algorithms that are significantly faster than the existing leading method, known as the hybrid input-output (HIO) algorithm.
- Additionally, the authors explain why traditional optimization methods struggle with phase retrieval and how using approximate phase information can help overcome these challenges, supported by numerical simulations that prove the effectiveness of their new reconstruction method, especially in difficult scenarios where HIO fails.
Article Abstract
This work evaluates the importance of approximate Fourier phase information in the phase retrieval problem. The main discovery is that a rough phase estimate (up to π/2 rad) allows development of very efficient algorithms whose reconstruction time is an order of magnitude faster than that of the current method of choice--the hybrid input-output (HIO) algorithm. Moreover, a heuristic explanation is provided of why continuous optimization methods like gradient descent or Newton-type algorithms fail when applied to the phase retrieval problem and how the approximate phase information can remedy this situation. Numerical simulations are presented to demonstrate the validity of our analysis and success of our reconstruction method even in cases where the HIO algorithm fails, namely, complex-valued signals without tight support information.
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| http://dx.doi.org/10.1364/JOSAA.28.002124 | DOI Listing |
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