Denoising Poisson phaseless measurements via orthogonal dictionary learning.

Area of Science:

• Computational imaging
• Image processing
• Scientific computing

Background:

• Phaseless diffraction measurements are crucial for imaging but susceptible to Poisson noise.
• Existing denoising methods may not adequately preserve texture features in these measurements.

Purpose of the Study:

• To develop a dictionary learning model for denoising Poisson noise in phaseless diffraction measurements.
• To improve the accuracy and visual quality of reconstructed images in phase retrieval.

Main Methods:

• A novel dictionary learning model incorporating orthogonal dictionary representation, L0 pseudo-norm sparsity, and Kullback-Leibler divergence for Poisson data fitting.
• Utilizing fast alternating minimization method (AMM) and proximal alternating linearized minimization (PALM) for model optimization, with theoretical convergence guarantees for PALM.
• Developing fast solvers for sparse coding and dictionary updating, leveraging the orthogonality of learned dictionaries.

Main Results:

• The proposed model effectively denoises phaseless Poisson measurements, preserving essential texture features.
• Numerical experiments using coded diffraction and ptychographic patterns demonstrate superior performance compared to methods without regularization or local sparsity promotion.
• Restored images exhibit significant visual and quantitative improvements.

Conclusions:

• The proposed dictionary learning approach offers an efficient and robust solution for denoising phaseless diffraction measurements affected by Poisson noise.
• This method advances phase retrieval techniques by providing higher-fidelity image reconstruction.
• The developed algorithms ensure fast convergence and accurate sparse representation for improved imaging outcomes.