Noise texture and signal detectability in propagation‐based x‐ray phase‐contrast tomography

Abstract

X-ray phase-contrast tomography (PCT) is a rapidly emerging imaging modality for reconstructing estimates of an object's three-dimensional x-ray refractive index distribution. Unlike conventional x-ray computed tomography methods, the statistical properties of the reconstructed images in PCT remain unexplored. The purpose of this work is to quantitatively investigate noise propagation in PCT image reconstruction. The authors derived explicit expressions for the autocovariance of the reconstructed absorption and refractive index images to characterize noise texture and understand how the noise properties are influenced by the imaging geometry. Concepts from statistical detection theory were employed to understand how the imaging geometry-dependent statistical properties affect the signal detection performance in a signal-known-exactly/background-known-exactly task. The analytical formulas for the phase and absorption autocovariance functions were implemented numerically and compared to the corresponding empirical values, and excellent agreement was found. They observed that the reconstructed refractive images are highly spatially correlated, while the absorption images are not. The numerical results confirm that the strength of the covariance is scaled by the detector spacing. Signal detection studies were conducted, employing a numerical observer. The detection performance was found to monotonically increase as the detector-plane spacing was increased. The authors have conducted the first quantitative investigation of noise propagation in PCT image reconstruction. The reconstructed refractive images were found to be highly spatially correlated, while absorption images were not. This is due to the presence of a Fourier space singularity in the reconstruction formula for the refraction images. The statistical analysis may facilitate the use of task-based image quality measures to further develop and optimize this emerging modality for specific applications.