Penalized-Likelihood Image Reconstruction for Transmission Computed Tomography Using Adaptive Median Regularization

Transmission computed tomography (TCT) is a nondestructive imaging technique that provides cross-sectional images from attenuated transmission measurements. In this work we introduce a penalized-likelihood image reconstruction method for TCT where the penalty term takes the form of a median regularizer. More precisely, we develop a center-weighted median regularizer that assigns a variable weight only to the central pixel of each median window so that the fine details can be better preserved. To select an optimal value of the center weight for each median window, we propose an adaptive method that increases the value of the center weight, as the corresponding center pixel is more likely to belong to an edge, and vice versa. The edge-likeliness is measured by the pixel-wise standard deviation (SD), each of whose pixels is transformed into the center weight for the corresponding pixel via the monotonically non-decreasing function derived from the normalized cumulative histogram of the SD image. By noting that the performance of the weighted median regularization is affected by the smoothing parameter that weights the regularization term with respect to the likelihood term, we also propose a similar method to adaptively select the smoothing parameter for each pixel. The experimental results indicate that our proposed method improves not only the overall reconstruction accuracy in terms of the percentage error, but also the contrast recovery coefficients measured in several regions of interest.