Phase Unwrapping in Spectral X-Ray Differential Phase-Contrast Imaging With an Energy-Resolving Photon-Counting Pixel Detector

Abstract

Grating-based differential phase-contrast imaging has proven to be feasible with conventional X-ray sources. The polychromatic spectrum generally limits the performance of the interferometer but benefit can be gained with an energy-sensitive detector. In the presented work, we employ the energy-discrimination capability to correct for phase-wrapping artefacts. We propose to use the phase shifts, which are measured in distinct energy bins, to estimate the optimal phase shift in the sense of maximum likelihood. We demonstrate that our method is able to correct for phase-wrapping artefacts, to improve the contrast-to-noise ratio and to reduce beam hardening due to the modelled energy dependency. The method is evaluated on experimental data which are measured with a laboratory Talbot-Lau interferometer equipped with a conventional polychromatic X-ray source and an energy-sensitive photon-counting pixel detector. Our work shows, that spectral imaging is an important step to move differential phase-contrast imaging closer to pre-clinical and clinical applications, where phase wrapping is particularly problematic.

Slit‐scanning differential x‐ray phase‐contrast mammography: Proof‐of‐concept experimental studies

“…Furthermore, energy resolved detection, [25][26][27] as supported by the next generation MicroDose system, can further improve the SNR. [28][29][30] Since our ultimate goal is phase-contrast mammography, future work will also include the imaging of breast samples.…”

Multiple Input Single Output Phase Retrieval

“…where H τ,l and x * i H τ,l x i are defined as in (5), and a is defined in (8). A GD algorithm is adopted to recover the i th mixed signal by minimizing (16).…”

“…where G l and y (i−1)l are represented in (4), a is defined as in (8), and x i0 is a principle eigenvector of F i0 . Then the initialization x i0 of the proposed GD algorithm can be constructed by F i0 .…”

“…The problem of recovering a one-dimensional signal from its Fourier transform magnitude, known as phase retrieval, is of paramount importance in various engineering and scientific applications, such as X-ray crystallography [8,27], optics [11,34], astronomy [9,31], speech recognition [24,32,38,39], and blind channel estimation [1,3]. This problem has a long history and has been studied by many researchers [5,7,10,12,14,18].…”

Applications of Laboratory-Based Phase-Contrast Imaging Using Speckle Tracking Technique towards High Energy X-Rays

“…With the aid of monochromators, the analyzer-based technique has been realized using laboratory sources [15]. Energy-sensitive detectors can potentially enhance the imaging signal-to-noise ratio [16] and loosen a phase-contrast technique's demand on monochromaticity of a beam.…”