[Paper Review] Advanced phase retrieval: maximum likelihood technique with sparse regularization of phase and amplitude

Artem Migukin, Vladimir Katkovnik+1 more|arXiv (Cornell University)|Aug 15, 2011

Advanced X-ray Imaging Techniques3 references3 citations

TL;DR

This paper proposes a novel iterative phase-retrieval algorithm that combines maximum likelihood estimation with sparse regularization of both amplitude and phase to improve image reconstruction accuracy from noisy intensity-only measurements. By leveraging sparse modeling in a constrained maximum likelihood framework, the method achieves superior reconstruction quality over conventional techniques, as validated by numerical simulations showing significant enhancement in imaging fidelity.

ABSTRACT

Sparse modeling is one of the efficient techniques for imaging that allows recovering lost information. In this paper, we present a novel iterative phase-retrieval algorithm using a sparse representation of the object amplitude and phase. The algorithm is derived in terms of a constrained maximum likelihood, where the wave field reconstruction is performed using a number of noisy intensity-only observations with a zero-mean additive Gaussian noise. The developed algorithm enables the optimal solution for the object wave field reconstruction. Our goal is an improvement of the reconstruction quality with respect to the conventional algorithms. Sparse regularization results in advanced reconstruction accuracy, and numerical simulations demonstrate significant enhancement of imaging.

Motivation & Objective

• To improve the quality of wave field reconstruction in phase retrieval by incorporating sparse modeling of both amplitude and phase.
• To address the limitations of conventional phase-retrieval algorithms that lack robustness to noise and poor reconstruction fidelity.
• To develop a statistically optimal solution using constrained maximum likelihood estimation under Gaussian noise assumptions.
• To enhance imaging accuracy through joint sparse regularization of amplitude and phase in iterative reconstruction.
• To demonstrate the superiority of the proposed method over existing techniques via numerical simulations.

Proposed method

• The algorithm is derived within a constrained maximum likelihood framework for wave field reconstruction from noisy intensity-only observations.
• It enforces sparsity in both the amplitude and phase components using regularization terms in the optimization problem.
• The method iteratively updates estimates of the object's complex wave field by minimizing a likelihood function with sparse priors.
• The optimization incorporates zero-mean additive Gaussian noise models to ensure statistical robustness.
• Sparse regularization is applied in a transform domain (e.g., wavelets or Fourier) to promote sparsity in the representation of amplitude and phase.
• The algorithm alternates between data fidelity and sparsity-promoting steps to converge to a high-quality solution.

Experimental results

Research questions

• RQ1 Can joint sparse regularization of amplitude and phase improve phase retrieval accuracy beyond conventional methods?
• RQ2 How does incorporating maximum likelihood estimation with sparse priors enhance reconstruction under noisy intensity measurements?
• RQ3 What is the impact of sparsity in both amplitude and phase on the convergence and fidelity of wave field reconstruction?
• RQ4 How does the proposed method compare quantitatively to standard phase-retrieval algorithms in terms of reconstruction quality?
• RQ5 To what extent does the use of a constrained maximum likelihood framework improve robustness to noise in intensity-only data?

Key findings

• The proposed method achieves significantly higher reconstruction accuracy compared to conventional phase-retrieval algorithms.
• Numerical simulations demonstrate a measurable enhancement in imaging fidelity due to the joint sparse regularization of amplitude and phase.
• The algorithm provides a statistically optimal solution under the assumed Gaussian noise model for intensity observations.
• Sparse regularization effectively suppresses artifacts and noise in the reconstructed wave field.
• The method shows robust performance even with low signal-to-noise ratios in the intensity measurements.
• The improvement in reconstruction quality is particularly evident in recovering fine structural details of the object.