Robust retrieval of material chemical states in X-ray microspectroscopy

X-ray microspectroscopic techniques are essential for studying morphological and chemical changes in materials, providing high-resolution structural and spectroscopic information. However, its practical data analysis for reliably retrieving the chemical states remains a major obstacle to accelerating the fundamental understanding of materials in many research fields. In this work, we propose a novel data formulation model for X-ray microspectroscopy and develop a dedicated unmixing framework to solve this problem, which is robust to noise and spectral variability. Moreover, this framework is not limited to analyzing two-state material chemistry, making it an effective alternative to conventional and widely used methods. In addition, an alternative directional multiplier method with explicit or implicit regularization is applied to obtain the solution efficiently. Our framework can accurately identify and characterize chemical states in complex and heterogeneous samples, even under challenging conditions such as low signal-to-noise ratios and overlapping spectral features. By testing six simulated datasets, our method improves the existing methods by up to 151.84% and 136.33% in terms of the peak signal-to-noise ratio (PSNR) and the structural similarity index (SSIM) for the chemical phase map. Extensive experimental results on simulated and real datasets demonstrate its effectiveness and reliability.