A general framework of noise suppression in material decomposition for dual‐energy CT - Petrongolo, Michael; Dong, Xue; Zhu, Lei (Medical physics (Lancaster), 2015)
Purpose: As a general problem of dual‐energy CT (DECT), noise amplification in material decomposition severely reduces the signal‐to‐noise ratio on the decomposed images compared to that on the original CT images. In this work, the authors propose a general framework of noise suppression in material decomposition for DECT. The method is based on an iterative algorithm recently developed in their group for image‐domain decomposition of DECT, with an extension to include nonlinear decomposition models. The generalized framework of iterative DECT decomposition enables beam‐hardening correction with simultaneous noise suppression, which improves the clinical benefits of DECT. Methods: The authors propose to suppress noise on the decomposed images of DECT using convex optimization, which is formulated in the form of least‐squares estimation with smoothness regularization. Based on the design principles of a best linear unbiased estimator, the authors include the inverse of the estimated variance–covariance matrix of the decomposed images as the penalty weight in the least‐squares term. Analytical formulas are derived to compute the variance–covariance matrix for decomposed images with general‐form numerical or analytical decomposition. As a demonstration, the authors implement the proposed algorithm on phantom data using an empirical polynomial function of decomposition measured on a calibration scan. The polynomial coefficients are determined from the projection data acquired on a wedge phantom, and the signal decomposition is performed in the projection domain. Results: On the Catphan®600 phantom, the proposed noise suppression method reduces the average noise standard deviation of basis material images by one to two orders of magnitude, with a superior performance on spatial resolution as shown in comparisons of line‐pair images and modulation transfer function measurements. On the synthesized monoenergetic CT images, the noise standard deviation is reduced by a factor of 2–3. By using nonlinear decomposition on projections, the authors’ method effectively suppresses the streaking artifacts of beam hardening and obtains more uniform images than their previous approach based on a linear model. Similar performance of noise suppression is observed in the results of an anthropomorphic head phantom and a pediatric chest phantom generated by the proposed method. With beam‐hardening correction enabled by their approach, the image spatial nonuniformity on the head phantom is reduced from around 10% on the original CT images to 4.9% on the synthesized monoenergetic CT image. On the pediatric chest phantom, their method suppresses image noise standard deviation by a factor of around 7.5, and compared with linear decomposition, it reduces the estimation error of electron densities from 33.3% to 8.6%. Conclusions: The authors propose a general framework of noise suppression in material decomposition for DECT. Phantom studies have shown the proposed method improves the image uniformity and the accuracy of electron density measurements by effective beam‐hardening correction and reduces noise level without noticeable resolution loss.