Sub pixel resolution using spectral-spatial encoding in x-ray imaging

Purpose: Previous efforts at increasing spatial resolution have relied on decreasing focal spot and or detector element size. Many “super resolution” methods require physical movement of a component of the imaging system. This work describes a method for achieving spatial resolution on a scale smaller than the detector pixel without motion of the object or detector. Methods: We introduce a weighting of the photon energy spectrum on a length scale smaller than a single pixel using a physical filter that can be placed between the focal spot and the object, between the object and the detector, or integrated into the x-ray source or detector. We refer to the method as sub pixel encoding (SPE). We show that if one acquires multiple measurements (i.e. x-ray projections), information can be synthesized at a spatial scale defined by the spectrum modulation, not the detector element size. Specifically, if one divides a detector pixel into n sub regions, and m photon-matter interactions are present, the number of x-ray measurements needed to solve for the detector response of each sub region is mxn. We discuss realizations of SPE using multiple x-ray spectra with an energy integrating detector, a single spectra with a photon counting detector, and the single photon-matter interaction case. We demonstrate the feasibility of the approach using a simulated energy integrating detector with a detector pitch of 2 mm for 80-140 kV medical and 200-600 kV industrial applications. Phantoms used for both example SPE realization had some features only a 1 mm detector could resolve. We calculate the covariance matrix of SPE output to characterize the and noise propagation and correlation of our test examples. Results: The mathematical foundation of SPE is provided, with details worked out for several detector types and energy ranges. Two numerical simulations were provided to demonstrate feasibility. In both the medical and industrial simulations, some phantom features were only observable with the 1 mm and SPE synthesized 2 mm detector, while the 2 mm detector was not able to visualize them. Covariance matrix analysis demonstrated negative diagonal terms for both example cases. Conclusions: The concept of encoding object information at a length scale smaller than a single pixel element, and then retrieving that information was introduced. SPE simultaneously allows for an increase in spatial resolution and provides “dual energy” like information about the underlying photon-matter interactions.