ITERATIVE IMAGE RECONSTRUCTION FOR DUAL-ENERGY X-RAY CT USING REGULARIZED MATERIAL SINOGRAM ESTIMATES

ABSTRACT X-ray CT images have various applications, including CTbased attenuation correction (CTAC) for PET. Low-dose CT imaging is particularly desirable for CTAC. Dual-energy (DE) CT imaging methods may improve the accuracy of attenuation correction in PET. However, conventional DE CT approaches to sinogram material decomposition use logarithmic transforms that are sensitive to noise in low-dose scans. This paper describes a DE reconstruction method based on statistical models that avoids using a logarithm. We first estimate material sinograms directly from the raw DE data (without any logarithm), with mild regularization to control noise and avoid outliers. We then apply a penalized weighted least squares (PWLS) method to reconstruct images of the two material components. We also propose a joint edgepreserving regularizer that uses the prior knowledge that the two material images have many region edges located in the same positions. Preliminary simulation results suggest that this iterative method improves image quality compared to conventional approaches based on log data for low-dose DE CT scans. I. DUAL-ENERGY RECONSTRUCTION I-A. Measurement model Let μ( x, E) denote the object's linear attenuation coefficient (LAC) which depends on the spatial position x and the photon energy E. For m = 1, . . . , M 0 , i = 1, . . . , N d , the CT measurement data y mi recorded by the ith ray for the mth incident spectrum has the following ensemble mean: where Li · d denotes the line integral along the ith ray, I mi (E) denotes the product of the mth incident source spectrum and the detector gain for the ith ray, and r mi denotes additive background contributions such as room background, dark current, and scatter. We assume that I mi (E) and r mi are known nonnegative constants by [1]-[3]. This work was supported in part by NIH/NCI grant 1R01CA115870. The measurements are finite, but μ( x, E) is a continuous function of x and E. Thus, for reconstruction we parameterize μ( x, E) using basis material decomposition [4] as follows: where β l (E) denotes the energy-dependent mass-attenuation coefficient (MAC) of the lth material type; we use tabulated MAC values for water and bone In DE CT, we usually choose M 0 = 2, L 0 = 2. Substituting (2) into (1) yields the following simplified model for the ensemble means of the measurements : v mi (s) p mi (E)e −β(E)·si dE, for m = 1, . . . , M 0 , l = 1, . . . , L 0 , and I mi = I mi (E) dE denotes the total intensity for the mth incident spectrum and the ith ray, and we define the sinogram vector s i as follows