Accurate, provable, and fast nonlinear tomographic reconstruction: A variational inequality approach
This addresses faster and more efficient computed tomography reconstruction for medical or industrial imaging, though it is incremental as it builds on variational inequality approaches.
The paper tackles nonlinear tomographic reconstruction under a polychromatic X-ray source and noise by developing the EXACT algorithm, which reduces X-ray exposures, source intensity, and computation time while achieving similar quality to existing methods.
We consider the problem of signal reconstruction for computed tomography (CT) under a nonlinear forward model that accounts for exponential signal attenuation, a polychromatic X-ray source, general measurement noise (e.g. Poisson shot noise), and observations acquired over multiple wavelength windows. We develop a simple iterative algorithm for single-material reconstruction, which we call EXACT (EXtragradient Algorithm for Computed Tomography), based on formulating our estimate as the fixed point of a monotone variational inequality. We prove guarantees on the statistical and computational performance of EXACT under practical assumptions on the measurement process. We also consider a recently introduced variant of this model with Gaussian measurements, and present sample and iteration complexity bounds for EXACT that improve upon those of existing algorithms. We apply our EXACT algorithm to a CT phantom image recovery task and show that it often requires fewer X-ray projection exposures, lower source intensity, and less computation time to achieve similar reconstruction quality to existing methods.