Sparse spectral techniques for emission imaging

tEmission imaging is based on scanning an object with a photon beam or a stream of particles havinghigh kinetic energy, amplifying the emitted particles with an intensifier device, and guiding its outputsecondary particles onto a position-sensitive detector which sometimes comprises a high frequency clockwhich provides additional separation of the sensed events in time. We show that the image is always aset of elliptical loci of secondary particles with some noise, and that the positions of the primary particlescan be efficiently recognized from the intensifier’s output image and all the geometric noise separated.This requires ad hoc data analysis due to the redundancy of the raw event stream which becomes under-sampled after filtering. A two-phase technique to filter geometric noise and to visualize the acquiredstructures addresses the redundancy and under-sampling/filtering problems. Our filtering is based onthe statistical properties of particle beams which allows us to efficiently “clean” the acquired 2D imagesby handling all the types of inherent artifacts based on the parameters of the spatial distribution of anindividual particle beam. The filtered images suffer from significant under-sampling which should behandled by some missing pixel recovery procedure, usually an interpolation. We present an overviewof various interpolation approaches from 3D approximation to manifold learning, and show that thereconstruction of the distorted spectrum sampled at the locations of beam positions produces the bestimage recovery.