Bi-Lipschitz embeddings of the space of unordered -tuples with a partial transportation metric.

Let be non-empty, open and proper. This paper is concerned with , the space of -integrable Borel measures on equipped with the transportation metric introduced by Figalli and Gigli that allows the creation and destruction of mass on . Alternatively, we show that is isometric to a subset of Borel measures with the ordinary Wasserstein distance, on the one point completion of equipped with the shortcut metric In this article we construct bi-Lipschitz embeddings of the set of unordered -tuples in into Hilbert space.

X-ray phase-contrast microtomography of soft tissues using a compact laboratory system with two-directional sensitivity.

X-ray microtomography is a nondestructive, three-dimensional inspection technique applied across a vast range of fields and disciplines, ranging from research to industrial, encompassing engineering, biology, and medical research. Phase-contrast imaging extends the domain of application of x-ray microtomography to classes of samples that exhibit weak attenuation, thus appearing with poor contrast in standard x-ray imaging. Notable examples are low-atomic-number materials, like carbon-fiber composites, soft matter, and biological soft tissues.

Volumetric High-Resolution X-Ray Phase-Contrast Virtual Histology of Breast Specimens With a Compact Laboratory System.

The assessment of margin involvement is a fundamental task in breast conserving surgery to prevent recurrences and reoperations. It is usually performed through histology, which makes the process time consuming and can prevent the complete volumetric analysis of large specimens. X-ray phase contrast tomography combines high resolution, sufficient penetration depth and high soft tissue contrast, and can therefore provide a potential solution to this problem.

Optimization of multipoint phase retrieval in edge illumination X-ray imaging: A theoretical and experimental analysis.

Purpose: In this work, an analytical model describing the noise in the retrieved three contrast channels, transmission, refraction, and ultra small-angle scattering, obtained with edge illumination X-ray phase-based imaging system is presented and compared to experimental data.

Methods: In EI, images acquired at different displacements of the presample mask (i.e.

Detection of involved margins in breast specimens with X-ray phase-contrast computed tomography.

Margins of wide local excisions in breast conserving surgery are tested through histology, which can delay results by days and lead to second operations. Detection of margin involvement intraoperatively would allow the removal of additional tissue during the same intervention. X-ray phase contrast imaging (XPCI) provides soft tissue sensitivity superior to conventional X-rays: we propose its use to detect margin involvement intraoperatively.

A compact system for intraoperative specimen imaging based on edge illumination x-ray phase contrast.

A significant number of patients receiving breast-conserving surgery (BCS) for invasive carcinoma and ductal carcinoma in situ (DCIS) may need reoperation following tumor-positive margins from final histopathology tests. All current intraoperative margin assessment modalities have specific limitations. As a first step towards the development of a compact system for intraoperative specimen imaging based on edge illumination x-ray phase contrast, we prove that the system's dimensions can be reduced without affecting imaging performance.