Noise power spectrum (NPS) in computed tomography: Enabling local NPS measurement without stationarity and ergodicity assumptions

Abstract

AbstractBackgroundConventional methods for estimating the noise power spectrum (NPS) often necessitate multiple computed tomography (CT) data acquisitions and are required to satisfy stringent stationarity and ergodicity conditions, which prove challenging in CT imaging systems.PurposeThe aim was to revisit the conventional NPS estimation method, leading to a new framework that estimates local NPS without relying on stationarity or ergodicity, thus facilitating experimental NPS estimations.MethodsThe scientific foundation of the conventional CT NPS measurement method, based on the Wiener‐Khintchine theorem, was reexamined, emphasizing the critical conditions of stationarity and ergodicity. This work proposes an alternative framework, characterized by its independence from stationarity and ergodicity, and its ability to facilitate local NPS estimations. A spatial average of local NPS over a Region of Interest (ROI) yields the conventional NPS for that ROI. The connections and differences between the proposed alternative method and the conventional method are discussed. Experimental studies were conducted to validate the new method.Results(1) The NPS estimated using the conventional method was demonstrated to correspond to the spatial average of pointwise NPS from the proposed NPS estimation framework. (2) The NPS estimated over an ROI with the conventional method was shown to be the sum of the NPS estimated from the proposed method and a contribution from measurement uncertainty. (3) Local NPS estimations from the proposed method in this work elucidate the impact of surrounding image content on local NPS variations.ConclusionThe NPS estimation method proposed in this work allows for the estimation of local NPS without relying on stationarity and ergodicity conditions, offering local NPS estimations with significantly improved precision.