Simulated propagation-based x-ray phase contrast (PB-XPC) measurements under laboratory conditions for the design and evaluation of learning-based methods for quantitative phase retrieval

Description of the datasets: Two datasets consisting of measurements acquired via simulations of propagation-based x-ray phase contrast (PB-XPC) imaging under laboratory conditions are provided. These datasets may be employed to develop and test learning-based methods for quantitative phase retrieval. A single training sample can include up to two inputs: a contact plane image and a downstream image, or only the latter. The output corresponds to the target phase map (in radians) at 24 keV, which corresponds to the peak energy in our polychromatic source spectrum. A total of 4000 samples, each consisting of 2 inputs and 1 output, are provided per dataset. Each image is sized 1024×1024 pixels and saved as 32-bit float data. Object description: For dataset 1 (complex phantom), a stochastic object model consisting of 64 structures (small spheres, large spheres, large ellipsoids, thin ellipsoids) in each realization was employed. For generation of the four shapes, the following parameters were specified: small spheres (mean radius: 845 μm, std. dev.: 0.5 × mean), large spheres (mean radius: 422 μm, std. dev.: 0.5 × mean), large ellipsoids (mean semi-axes lengths: 845, 1690, 845 μm, std. dev.: 0.5 × mean), thin ellipsoids (mean semi-axes lengths: 211, 1690, 211 μm, std. dev.: 0.05 × mean). For this dataset, material allocation corresponded to soft tissue. This is a single material phantom. For dataset 2 (4-material phantom), a stochastic object model consisting of 16 spheres was employed. For each realization, the spheres were drawn from a beta distribution with the following parameters: mean: 845 μm, std dev: 20%, range: 422 to 1690 μm. The spheres were placed at random, at least 3.6 mm away from the edge of the detector at the contact plane. For this dataset, four tissue materials: lung, liver, cartilage, and intestine, were allocated to the 16 spheres within each realization. All shapes in both phantoms were described analytically. System description: The source spectrum corresponds to that of an x-ray source with a liquid-metal-jet anode (MetalJet D2, Excillum at 70 kVp, with peak energy 24 keV), filtered by 0.9 mm Aluminum, and discretized into 65 energy levels. This resulted in an equivalent energy of 32 keV. The detector consisted of a CsI(Tl) scintillator-based X-ray imager with a 13 µm pixel pitch. The physical size of the detector was 13.5 × 13.5 mm. Source-to-object distance, and object-to-detector distance were fixed at 1 m and 0.5 m respectively. Oversampling by a factor of 2 was included in all simulations. To obtain the downstream image after propagation, the Fresnel propagator in Fourier domain was employed, followed by the Fresnel scaling theorem to accounts for cone beam effects. Effects of spectral weights of the source, as well as the energy-specific detective sensitivity of the detector were included in this simulation. A system blur of full-width-half-maximum 66 microns, or 5 detector pixels, modeled via Gaussian blurring, was employed. Last, system noise modeled as a mixed Poisson-Gaussian random variable, with zero mean and 5% individual pixel intensity, was added to the simulated image after downsampling. The two datasets differ only in terms of phantoms and material allocation; system parameters are the same. Description of the files: Prefix ‘cx’ indicates the first dataset while prefix ‘t4’ indicates the second dataset. ‘c1’, ‘c2’, and ‘proj’ in the filenames indicate contact plane data, post-propagation data, and phase maps respectively. The contact plane data, as well as the post-propagation data, is split across 8 files for each dataset. The target phase maps are all included in a single file for one dataset. For the second dataset only, log files are provided for each realization in the second dataset. Within each log file, there are 16 lines corresponding to the 16 spheres present in the realization. The six values in a line represent: (1) serial number, (2 - 4) co-ordinates of the sphere center (z, r, c), (5) radius of the sphere, and (6) sphere material. Other files include: (1) the source spectrum, post-filtering and including detective sensitivities across all energy levels (column 1: energy levels, column 2: weights), and (2) the delta and beta values over the entire spectrum for the materials allocated within the two phantoms. The source spectrum and refractive indices are provided as numpy arrays.