Tomographic Reconstruction Using Information-Weighted Spline Smoothing

Abstract

The conventional method for tomographic image reconstruction, convolution backprojection (CBP), attempts to reduce the effects of measurement noise by radial smoothing with a spatially-invariant filter. Spatially-invariant smoothing is suboptimal when the measurement statistics are nonstationary, and often leads to a choice between oversmoothing or streak artifacts. In this paper, we describe a nonstationary sinogram smoothing method that accounts for the relative variances between different detector measurements and for the finite width of tomographic detectors. The method is based on an information-weighted smoothing spline, where the weights are determined from the calibration factors and from the measurements themselves. This weighting diminishes the influence of high variance measurements, such as detectors with relatively poor efficiency, which is shown to reduce streak artifacts. Simulations of emission and transmission tomography applications demonstrate qualitatively improved image noise structure and quantitative improvements in the tradeoffs between bias and variance.