Using convex optimization of autocorrelation with constrained support and windowing for improved phase retrieval...

Area of Science:

• * X-ray imaging
• * Computational imaging
• * Data science

Background:

• * Phase retrieval is crucial for reconstructing images from diffraction data, especially in X-ray free electron laser (XFEL) imaging of viruses.
• * Traditional methods using iterative alternating-projection struggle with sparse data and can yield suboptimal solutions due to non-convex optimization.
• * Existing schemes are sensitive to initial conditions, leading to varied results and difficulties in achieving global optima.

Purpose of the Study:

• * To develop a robust phase retrieval method that overcomes limitations of existing techniques for sparse and noisy diffraction data.
• * To introduce a convex optimization framework that guarantees a unique global optimum, improving reconstruction accuracy.
• * To provide a pre-processing step (COACS) that enhances traditional phase retrieval algorithms.

Main Methods:

• * Construction of a convex optimization problem by modifying support constraints and employing maximum-likelihood estimation for recorded data.
• * Solving the relaxed problem to obtain "healed" signal intensities, ensuring exact satisfaction of support and intensity constraints.
• * Application of the "healed" intensities to traditional phase retrieval for superior results.

Main Results:

• * Demonstrated significant improvement in phase retrieval accuracy on simulated data.
• * Quantified improvement using crystallographic R factor (from 0.405 to 0.097) and mean-squared error (from 0.233 to 0.139).
• * COACS pre-processing showed best-in-class performance compared to other noise-tolerant and data-healing approaches.

Conclusions:

• * The developed convex optimization approach provides a more reliable and accurate method for phase retrieval, particularly with limited or noisy data.
• * COACS pre-processing enables exact constraint satisfaction, paving the way for enhanced traditional phase retrieval.
• * This method offers a significant advancement for imaging applications relying on accurate reconstruction from diffraction patterns.