Penalized-likelihood sinogram decomposition for dual-energy computed tomography

Dual-energy techniques in radiography and computed tomography can allow for decomposition of projection images and reconstructed images into two components, representing, for instance, bone and soft tissue. There are a variety of approaches to performing this decomposition in the data domain, including direct solution of the pair of nonlinear equations for each line integral using, in one case, a power-series expansion. After data-domain decomposition into two material-specific sinograms, standard image reconstruction techniques such as filtered backprojection are employed. One potential shortcoming of these approaches is that the data domain decomposition has the potential to amplify noise in the data, which algorithms such as FBP can mitigate only through filter apodization, potentially resulting in oversmoothing. Fessler and collaborators have explored two statistically principled alternatives. The first begins with a standard data-domain decomposition but then applies an iterative penalized weighted least squares algorithm during reconstruction in which the statistics of the decomposed sinograms, including correlations, are modeled in the weighting matrix. The second is an iterative penalized-likelihood based reconstruction approach that works directly with the raw dual-energy data without first decomposing. While the results are promising, these fully iterative reconstruction approaches are very computationally intensive. In this work we propose a middle ground, in which penalized-likelihood methods accurately modeling data statistics are used to perform the sinogram decomposition after which fast analytic algorithms can be used to reconstruct the images. Specifically, we derive a method that is guaranteed to monotonically increase a joint penalized likelihood objective for the two sets of material-specific line integrals.