Abstract: We present the technical/physical foundations of a new imaging technique that combines ordinary radiographic information (generated by conventional X-ray settings) with the patient's volume to derive densitometric images. Traditionally, these images provide quantitative information about tissues densities. In our approach, they graphically enhance either soft or bony regions. After measuring the patient's volume with contour recognition devices, the physical traversed lengths within it (as the Roentgen beam intersects the patient) are calculated and pixel-wise associated with the original radiograph (X). In order to derive this map of lengths (L), the camera equations of the X-ray system and the contour sensor are determined. The patient's surface is also translated to the point-of-view of the X-ray beam and all its entrance/exit points are sought with the help of ray-casting methods. The derived L is applied to X as a physical operation (subtraction), obtaining soft tissue-(D-S) or bone-enhanced (D'(B)) figures. In the D-S type, the contained graphical information can be linearly mapped to the average electronic density (traversed by the X-ray beam). This feature represents an interesting proof-of-concept of associating density data to radiographs, but most important, their intensity histogram is objectively compressed, i.e., the dynamic range is more shrunk (compared against the corresponding X). This leads to other advantages: improvement in the visibility of border/edge areas (high gradient), extended manual window level/width manipulations during screening, and immediate correction of underexposed X instances. In the D-B' type, high-density elements are highlighted and easier to discern. All these results can be achieved with low-energy beam exposures, saving costs and dose. Future work will deepen this clinical side of our research. In contrast with other image-based modifiers, the proposed method is grounded on the measurement of a physical entity: the span of the X-ray beam within a body while undertaking a radiographic examination.

Abstract: We characterize preserved extreme points of the unit ball of Lipschitz-free spaces F (X) in terms of simple geometric conditions on the underlying metric space (X, d). Namely, the preserved extreme points are the elementary molecules corresponding to pairs of points p, q in X such that the triangle inequality d (p, q) <= d (p, r) + d (q, r) is uniformly strict for r away from p, q. For compact X, this condition reduces to the triangle inequality being strict. As a consequence, we give an affirmative answer to a conjecture of N. Weaver that compact spaces are concave if and only if they have no triple of metrically aligned points, and we show that all extreme points are preserved for several classes of compact metric spaces X, including Holder and countable compacta.

Abstract: This paper describes the electronics of NEXT-White (NEW) detector PMT plane, a high pressure xenon TPC with electroluminescent amplification (HPXe-EL) currently operating at the Laboratorio Subterraneo de Canfranc (LSC) in Huesca, Spain. In NEXT-White the energy of the event is measured by a plane of photomultipliers (PMTs) located behind a transparent cathode. The PMTs are Hamamatsu R11410-10 chosen due to their low radioactivity. The electronics have been designed and implemented to fulfill strict requirements: an overall energy resolution below 1% and a radiopurity budget of 20 mBq unit(-1) in the chain of Bi-214. All the components and materials have been carefully screened to assure a low radioactivity level and at the same time meet the required front-end electronics specifications. In order to reduce low frequency noise effects and enhance detector safety a grounded cathode connection has been used for the PMTs. This implies an AC-coupled readout and baseline variations in the PMT signals. A detailed description of the electronics and a novel approach based on a digital baseline restoration to obtain a linear response and handle AC coupling effects is presented. The final PMT channel design has been characterized with linearity better than 0.4% and noise below 0.4 mV.