Noise correlation and its impact on the performance of multi‐material decomposition‐based spectral imaging in photon‐counting CT

PURPOSE: It has been known that noise correlation plays an important role in the determination of the performance of spectral imaging based on two‐material decomposition (2‐MD). To further understand the basics of spectral imaging in photon‐counting CT toward optimal design and implementation, we study the noise correlation in multi‐MD (m‐MD) and its impact on the performance of spectral imaging. METHOD: We derive the equations that characterize the noise and noise correlation in the material‐specific (basis) images in m‐MD, followed by a simulation study to verify the derived equations and study the noise correlation's impact on the performance of spectral imaging. Using a specially designed digital phantom, the study of noise correlation runs over the cases of two‐, three‐, and four‐MD (2‐MD, 3‐MD, and 4‐MD). Then, the noise correlation's impact on the performance of spectral imaging in photon‐counting CT is investigated, using a modified Shepp–Logan phantom. RESULTS: The results in 2‐MD show that, in‐line with what has been reported in the literature, the noise correlation coefficient between the material‐specific images corresponding to the basis materials approaches −1. The results in m‐MD (m ≥ 3) are more complicated and interesting, as the noise correlation coefficients between a pair of the material‐specific images alternate between ±1, and so do in the case of 4‐MD. The m‐MD data show that the noise in virtual monochromatic imaging (a form of spectral imaging) is moderate even though the noises in material‐specific (basis) images vary drastically. CONCLUSIONS: The observation of noise correlation in 3‐MD, 4‐MD, and beyond (i.e., m‐MD) is informative to the community. The relationship between noise correlation and the performance of spectral imaging revealed in this work may help clinical medical physicists understand the fundamentals of spectral imaging based on MD and optimize the performance of spectral imaging in photon‐counting CT and other X‐ray imaging modalities.