Analyzer-less X-ray Interferometry with Super-Resolution Methods

Abstract

X-ray interferometry provides valuable information in terms of attenuation, small-angle scatter, and differential phase contrast. This multi-modal contrast can aid in many clinical applications, such as lung diseases and breast cancer. However, standard interferometry has an analyzer grating that can increase the dose requirement to maintain the same image quality as a standard X-ray. We propose the use of super-resolution methods for X-ray grating interferometry without an analyzer, with detectors that fail to meet the Nyquist sampling rate needed for traditional image recovery algorithms. We use the phase-steps judiciously to nominally recover the sampling and iteratively recover the visibility and the object parameters. This method enables Talbot-Lau interferometry without the X-ray absorbing analyzer. It also allows for smaller fringe periods (Pd) or higher autocorrelation lengths for the analyzer-less Modulated Phase Grating Interferometer. This will allow for reduced X-ray dose and higher autocorrelation lengths than previously accessible. We demonstrate the use of super-resolution methods to iteratively reconstruct attenuation, differential-phase, and dark-field images using simulations of two-dimensional lung phantoms with lesions. We tested a direct detector with 75 micron and 30 micron pixel size, modeled using a box-binning. We also tested scintillator-based detectors with 50 micron and 75 micron pixel sizes, modeled using Gaussian PSFs. We show that our super-resolution iterative reconstruction methods are robust to noise and can be used to improve grating interferometry for cases where traditional algorithms cannot be used.

Figures (11)

• Figure 1: Schematics of the (a) Talbot-Lau Interferometer Schematic, with three gratings G0,G1 and G2 (analyzer) and (b) Modulated Phase Grating Interferometer Schematic with no G2 grating. The G1 grating has modulation of width W and pitch P.
• Figure 2: Flowchart of the Phantom generation with known ground truth of $\mu T$, dark field parameter, $S$ and differential phase-shift(DPC). The interferometery signal is generated by using equation \ref{['eq:object_signal']} by using the above defined parameters. The phase step is obtained by translation of interferometry pattern, but for illusion purposes, only a single phase-step is shown.
• Figure 3: Left: Schematic representation of interlacing five phase-stepped images, $D^k_{obj}(x,y)$, k = 1...5, each with dimension n × m. The first columns from all five images are concatenated in order, followed by the second columns, and so on, until the last or m-th column. The resulting image, $I_{obj}(x,y)$, has dimensions n × 5m. Note: Although the phase-stepped images are shown in distinct colors for illustrative purposes, they are nearly identical in intensity in practice(representing either a set of reference phase steps or reference+object phase steps). The observed intensity variations arise primarily from sub-pixel phase shifts on the order of a few microns. Right: Figure shows the same process for the down-sampled interferometry signal. The downsampled signal, $D^k_{obj}(x,y)$, is interlaced to generate the interleaved image, $I_{obj}(x,y)$
• Figure 4: Stages 1 and 2 (a) Stage 1 to recover $\hat{g}_r$. This essentially recovers the visibility for the reference signal, $I_r(x)$. (b) Stage 2 to recover $\mu T (x)$, $t_{ph}(x)$, and $S(x)$.
• Figure 5: Recovered $\mu T$, $t_{ph}$, and $S$ for a detector of size 50 $\mu m$ and step N = 10 (step-resolution = $5 \: \mu m$. $P_d = 140 \: \mu m$. The images are 10mm x 10mm. The detector model was a Gaussian PSF of $\sigma$ = 50 $\mu m$. RMSE values for the middle row are $7.7410 \times 10^{-4}$ for $\mu T$, 0.1761 for $t_{ph}$, and 0.0262 for $S$.