A comparative study of information retrieval in grating-based x-ray phase-contrast imaging

Iterative signal retrieval for X-ray grating interferometry with dual-shot

BACKGROUND

X-ray grating interferometry normally requires multiple steps and exposures, causing a prolonged imaging time. There is motivation to use fewer steps to reduce scanning time and complexity, while keeping fidelity of the retrieved signals.

OBJECTIVE

We propose an iterative signal retrieval method, extracting attenuation, dark field contrast (DFC), and differential phase contrast (DPC) signals from two X-ray exposures.

METHODS

Two shots were captured at G2 grating positions with difference of 1/4 grating period. The algorithm consists of two stages. At the first stage, amplitude of sample phase stepping curve retrieved by virtual phase stepping (VPS) method, visibility and local phase of background phase stepping curve are used to limit the results to the proximity of the ground truth. After the second stage, three high-quality parameters, amplitude, visibility, and local phase, are retrieved through finetuning, and three signals are calculated. Simulated and real-sample experiments were conducted to validate this method.

RESULTS

We used standard phase stepping result as benchmark and calculated structural similarity (SSIM) and peak signal-to-noise ratio (PSNR) between benchmark and parameters retrieved by our dual-shot method and virtual phase stepping (VPS) method. For both simulated and real-sample experiments, the SSIM and PSNR value of dual-shot method are higher than those of VPS method. For real-sample method, we also conducted a three-step PS, and the SSIM and PSNR value of dual-shot method are slightly lower than those of three-step PS.

CONCLUSION

Using our dual-shot method demonstrates higher performance than other single-shot method in retrieving high-quality signals, and it also reduces radiation dose and time.

Fourier-based interpretation and noise analysis of the moments of small-angle x-ray scattering in grating-based x-ray phase contrast imaging

In grating-based x-ray phase contrast imaging, Fourier component analysis (FCA) is usually recognized as a gold standard to retrieve the contrasts including attenuation, phase and dark-field, since it is well-established on wave optics and is of high computational efficiency. Meanwhile, an alternative approach basing on the particle scattering theory is being developed and can provide similar contrasts with FCA by calculating multi-order moments of deconvolved small-angle x-ray scattering, so called as multi-order moment analysis (MMA). Although originated from quite different physics theories, the high consistency between the contrasts retrieved by FCA and MMA implies us that there may be some intrinsic connections between them, which has not been fully revealed to the best of our knowledge. In this work, we present a Fourier-based interpretation of MMA and conclude that the contrasts retrieved by MMA are actually the weighted compositions of Fourier coefficients, which means MMA delivers similar physical information as FCA. Based on the recognized cosine model, we also provide a truncated analytic MMA method, and its computational efficiency can be hundreds of times faster than the original deconvolution-based MMA method. Moreover, a noise analysis for our proposed truncated method is also conducted to further evaluate its performances. The results of numerical simulation and physical experiments support our analyses and conclusions.

The trigonometric orthogonality of phase-stepping curves in grating-based x-ray phase-contrast imaging: Integral property and its implications for noise optimization

PURPOSE

Grating-based x-ray phase-contrast imaging (GPCI) is a promising technique for clinical applications as it can provide two newly emerging imaging modalities (differential phase-contrast and dark-field contrast) in addition to the conventional absorption contrast. As far, phase-stepping strategy is the most commonly used approach in GPCI to indirectly acquire differential phase-contrast and dark-field contrast. It is known that the obtained phase-stepping curves (PSCs) have the cosine property and the convolution property, leading to two types of information retrieval approaches in literature: the Fourier component analysis and the multi-order moment analysis. The purpose of this paper is to derive a new property of PSCs and apply the property to noise optimization for information retrieval.

METHODS

Based on the cosine expression of the flat PSC without the sample and the well-established convolution relationship between the flat PSC and the sample PSC, we reveal an important integral property of PSCs: the inner product of PSCs and an arbitrary function contains only zero-order and first-order components in the Fourier series. Furthermore, we apply the property to the direct multi-order moment analysis and propose a set of generalized forms including an optimal one in the presence of noise.

RESULTS

To validate the effectiveness of our analysis, we compared the simulated and real experiment results retrieved by the original direct multi-order moment analysis with the ones retrieved by our proposed noise-optimal form. A significant improvement of noise performance by our method is observed and the improvement ratio in differential phase-contrast is consistent with our theoretical calculation (39.2%).

CONCLUSIONS

In this paper, we reveal a new integral property of the acquired PSCs with and without samples in GPCI, which can be applied to information retrieval approaches like the direct multi-order moment analysis. Then we optimize these approaches to improve the noise performance, offering great potentials of dose reduction in practical applications.