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Phase Retrieval Based on DC and DnCNN

Xueming Li, Bing Guo

TL;DR

This work tackles phase retrieval in noisy settings by proposing two algorithms that integrate DC programming with denoising-based regularization. By rewriting the nonconvex objective as a difference of convex functions and applying DCA, $prDeep$-DC enhances the proximal-gradient step, while $prDeep$-L2 introduces a 2-norm denoising regularization within a RED-like framework using DnCNN. The methods are solved efficiently with a FASTA-based scheme and validated on Fourier measurements with Poisson noise on 128×128 images, showing consistent PSNR/SSIM gains and better detail preservation over $prDeep$ and HIO across multiple noise levels. The results suggest robust reconstruction in practical imaging scenarios (e.g., microscopy and spectroscopy) where phase information is corrupted by noise, offering a data-driven yet principled approach to improve phase retrieval fidelity.

Abstract

This paper investigates noise-robust phase retrieval by enhancing the prDeep architecture with difference of convex functions (DC) and DnCNN-based denoising regularization. This research introduces two novel algorithms, prDeep-DC and prDeep-L2, which demonstrably achieve excellent quantitative and visual performance, as confirmed by extensive numerical experiments.

Phase Retrieval Based on DC and DnCNN

TL;DR

This work tackles phase retrieval in noisy settings by proposing two algorithms that integrate DC programming with denoising-based regularization. By rewriting the nonconvex objective as a difference of convex functions and applying DCA, -DC enhances the proximal-gradient step, while -L2 introduces a 2-norm denoising regularization within a RED-like framework using DnCNN. The methods are solved efficiently with a FASTA-based scheme and validated on Fourier measurements with Poisson noise on 128×128 images, showing consistent PSNR/SSIM gains and better detail preservation over and HIO across multiple noise levels. The results suggest robust reconstruction in practical imaging scenarios (e.g., microscopy and spectroscopy) where phase information is corrupted by noise, offering a data-driven yet principled approach to improve phase retrieval fidelity.

Abstract

This paper investigates noise-robust phase retrieval by enhancing the prDeep architecture with difference of convex functions (DC) and DnCNN-based denoising regularization. This research introduces two novel algorithms, prDeep-DC and prDeep-L2, which demonstrably achieve excellent quantitative and visual performance, as confirmed by extensive numerical experiments.

Paper Structure

This paper contains 13 sections, 30 equations, 8 figures, 2 tables, 7 algorithms.

Table of Contents

  1. Introduction
  2. Preliminary knowledge
  3. Image denoising engine
  4. DCA
  5. FBS algorithm and its improvement
  6. Our work
  7. Numerical simulation
  8. Experimental setup
  9. Measurement and Noise Model
  10. Parameter tuning and initialization
  11. Experimental analysis of phase retrieval based on prDeep-DC
  12. Experimental analysis of phase retrieval based on prDeep-L2
  13. Conclusion

Figures (8)

  • Figure 1: BM3D.
  • Figure 2: DnCNN.
  • Figure 3: Test dataset NT-6 which are widely used in phase retrieval.
  • Figure 4: Test dataset UNT-6 which are widely used in phase retrieval.
  • Figure 5: Comparison of reconstruction of UNT-6 test images at $128 \times 128$ for Butterfly,Ecoli and Pillarsof at $\alpha=2$.
  • ...and 3 more figures