Denoised Wigner distribution deconvolution via low-rank matrix completion.

Area of Science:

• Optics
• Image Processing
• Computational Science

Background:

• Wigner distribution deconvolution (WDD) is a linear method for phase retrieval from intensity measurements.
• WDD's adoption is limited by high computational costs and noise sensitivity.
• Existing phase retrieval methods include iterative techniques like ptychography.

Purpose of the Study:

• To propose a novel noise suppression method for WDD.
• To enhance the accuracy and applicability of WDD in noisy conditions.
• To compare the proposed method against existing WDD algorithms and iterative phase retrieval techniques.

Main Methods:

• Implementation of low-rank noisy matrix completion for WDD.
• Exploitation of phase space redundancy for denoising WDD reconstructions.
• Model calculations to validate the proposed technique.

Main Results:

• The proposed method effectively suppresses noise in WDD.
• The technique demonstrates superior performance compared to traditional WDD algorithms.
• Outperformed modern iterative phase retrieval methods like ptychography in model calculations.

Conclusions:

• Low-rank noisy matrix completion offers effective noise suppression for WDD.
• Regularized direct inversion methods can yield accurate quantitative phase information in high-noise environments.
• This approach broadens the applicability of WDD for phase retrieval.