Multi-energy CT material decomposition using Bayesian deep convolutional neural network with explicit penalty of uncertainty and bias

Convolutional neural network (CNN)-based material decomposition has the potential to improve image quality (visual appearance) and quantitative accuracy of material maps. Most methods use deterministic CNNs with mean-square-error loss to provide point-estimates of mass densities. Point estimates can be over-confident as the reliability of CNNs is frequently compromised by bias and two major uncertainties - data and model uncertainties originating from noise in inputs and train-test data dissimilarity, respectively. Also, mean-square-error lacks explicit control of uncertainty and bias. To tackle these problems, a Bayesian dual-task CNN (BDT-CNN) with explicit penalization of uncertainty and bias was developed. It is a probabilistic CNN that concurrently conducts material classification and quantification and allows for pixel-wise modeling of bias, data uncertainty, and model uncertainty. CNN was trained with images of physical and simulated tissue-mimicking inserts at varying mass densities. Hydroxyapatite (nominal density 400mg/cc) and blood (nominal density 1095mg/cc) inserts were placed in different-sized body phantoms (30 - 45cm) and used to evaluate mean-absolute-bias (MAB) in predicted mass densities across different images at routine- and half-routine-dose. Patient CT exams were collected to assess generalizability of BDT-CNN in the presence of anatomical background. Noise insertion was used to simulate patient exams at half- and quarter-routine-dose. The deterministic dual-task CNN was used as baseline. In phantoms, BDT-CNN improved consistency of insert delineation, especially edges, and reduced overall bias (average MAB for hydroxyapatite: BDT-CNN 5.4mgHA/cc, baseline 11.0mgHA/cc and blood: BDT-CNN 8.9mgBlood/cc, baseline 14.0mgBlood/cc). In patient images, BDT-CNN improved detail preservation, lesion conspicuity, and structural consistency across different dose levels.