# Iterative X-ray Spectroscopic Ptychography

## TL;DR

This paper introduces SPA, a novel iterative algorithm for spectroscopic ptychography that improves chemical composition imaging by leveraging spectral redundancy and handling incomplete spectral dictionaries.

## Contribution

The paper presents SPA, an innovative algorithm for spectroscopic ptychography that enhances reconstruction quality and robustness, especially with incomplete spectral information.

## Key findings

- SPA outperforms standard methods in reconstruction quality.
- SPA effectively handles Poisson noise in measurements.
- SPA demonstrates robustness with reduced redundancy data.

## Abstract

Spectroscopic ptychography is a powerful technique to determine the chemical composition of a sample with high spatial resolution. In spectro-ptychography, a sample is rastered through a focused x-ray beam with varying photon energy so that a series of phaseless diffraction data are recorded. Each chemical component in the material under investigation has a characteristic absorption and phase contrast as a function of photon energy. Using a dictionary formed by the set of contrast functions of each energy for each chemical component, it is possible to obtain the chemical composition of the material from high resolution multi-spectral images. This paper presents SPA (Spectroscopic Ptychography with ADMM), a novel algorithm to iteratively solve the spectroscopic blind ptychography problem. We design first a nonlinear spectro-ptychography model based on Poisson maximum likelihood, and construct then the proposed method based on fast iterative splitting operators. SPA can be used to retrieve spectral contrast when considering both a known or an incomplete (partially known) dictionary of reference spectra. By coupling the redundancy across different spectral measurements, the proposed algorithm can achieve higher reconstruction quality when compared to standard state-of-the-art two-step methods. We demonstrate how SPA can recover accurate chemical maps from Poisson-noised measurements, and also show its enhanced robustness when reconstructing reduced redundancy ptychography data using large scanning stepsizes.