Quantitative phase retrieval with low photon counts using an energy resolving quantum detector

PEPI Lab: a flexible compact multi-modal setup for X-ray phase-contrast and spectral imaging

This paper presents a new flexible compact multi-modal imaging setup referred to as PEPI (Photon-counting Edge-illumination Phase-contrast imaging) Lab, which is based on the edge-illumination (EI) technique and a chromatic detector. The system enables both X-ray phase-contrast (XPCI) and spectral (XSI) imaging of samples on the centimeter scale. This work conceptually follows all the stages in its realization, from the design to the first imaging results. The setup can be operated in four different modes, i.e. photon-counting/conventional, spectral, double-mask EI, and single-mask EI, whereby the switch to any modality is fast, software controlled, and does not require any hardware modification or lengthy re-alignment procedures. The system specifications, ranging from the X-ray tube features to the mask material and aspect ratio, have been quantitatively studied and optimized through a dedicated Geant4 simulation platform, guiding the choice of the instrumentation. The realization of the imaging setup, both in terms of hardware and control software, is detailed and discussed with a focus on practical/experimental aspects. Flexibility and compactness (66 cm source-to-detector distance in EI) are ensured by dedicated motion stages, whereas spectral capabilities are enabled by the Pixirad-1/Pixie-III detector in combination with a tungsten anode X-ray source operating in the range 40-100 kVp. The stability of the system, when operated in EI, has been verified, and drifts leading to mask misalignment of less than 1 [Formula: see text]m have been measured over a period of 54 h. The first imaging results, one for each modality, demonstrate that the system fulfills its design requirements. Specifically, XSI tomographic images of an iodine-based phantom demonstrate the system's quantitativeness and sensibility to concentrations in the order of a few mg/ml. Planar XPCI images of a carpenter bee specimen, both in single and double-mask modes, demonstrate that refraction sensitivity (below 0.6 [Formula: see text]rad in double-mask mode) is comparable with other XPCI systems based on microfocus sources. Phase CT capabilities have also been tested on a dedicated plastic phantom, where the phase channel yielded a 15-fold higher signal-to-noise ratio with respect to attenuation.

Poisson Phase Retrieval in Very Low-count Regimes

This paper discusses phase retrieval algorithms for maximum likelihood (ML) estimation from measurements following independent Poisson distributions in very low-count regimes, e.g., 0.25 photon per pixel. To maximize the log-likelihood of the Poisson ML model, we propose a modified Wirtinger flow (WF) algorithm using a step size based on the observed Fisher information. This approach eliminates all parameter tuning except the number of iterations. We also propose a novel curvature for majorize-minimize (MM) algorithms with a quadratic majorizer. We show theoretically that our proposed curvature is sharper than the curvature derived from the supremum of the second derivative of the Poisson ML cost function. We compare the proposed algorithms (WF, MM) with existing optimization methods, including WF using other step-size schemes, quasi-Newton methods such as LBFGS and alternating direction method of multipliers (ADMM) algorithms, under a variety of experimental settings. Simulation experiments with a random Gaussian matrix, a canonical DFT matrix, a masked DFT matrix and an empirical transmission matrix demonstrate the following. 1) As expected, algorithms based on the Poisson ML model consistently produce higher quality reconstructions than algorithms derived from Gaussian noise ML models when applied to low-count data. Furthermore, incorporating regularizers, such as corner-rounded anisotropic total variation (TV) that exploit the assumed properties of the latent image, can further improve the reconstruction quality. 2) For unregularized cases, our proposed WF algorithm with Fisher information for step size converges faster (in terms of cost function and PSNR vs. time) than other WF methods, e.g., WF with empirical step size, backtracking line search, and optimal step size for the Gaussian noise model; it also converges faster than the LBFGS quasi-Newton method. 3) In regularized cases, our proposed WF algorithm converges faster than WF with backtracking line search, LBFGS, MM and ADMM.

Dual-energy phase retrieval algorithm for inline phase sensitive x-ray imaging system

Phase retrieval is vital for quantitative x-ray phase contrast imaging. This work presents an iterative method to simultaneously retrieve the x-ray absorption and phase images from a single x-ray exposure. The proposed approach uses the photon-counting detectors' energy-resolving capability in providing multiple spectrally resolved phase contrast images from a single x-ray exposure. The retrieval method is derived, presented, and experimentally tested with a multi-material phantom in an inline phase contrast imaging setup. By separating the contributions of photoelectric absorption and Compton scattering to the attenuation, the authors divide the phase contrast image into two portions, the attenuation map arises from photoelectric absorption and a pseudo phase contrast image generated by electron density. This way one can apply the Phase Attenuation Dualiby (PAD) algorithm and Fresnel propagation for the iteration. The retrieval results from the experimental images show that this iterative method is fast, accurate, robust against noise, and thus yields noticeable enhancement in contrast to noise ratios.