Signal detection and location‐dependent noise in cone‐beam computed tomography using the spatial definition of the Hotelling SNR

Abstract

Quality assurance in computed tomography (CT) is commonly performed with the Fourier-based modulation transfer function (MTF) and the noise variance, while more recently the noise power spectrum (NPS) has increased in popularity. The Fourier-based methods make assumptions such as shift-invariance and cyclostationarity. These assumptions are violated in real clinical systems and consequently are expected to result in systematic errors. A spatial approach, based on the object transfer matrix (T) and the covariance matrix (K) theory, does not require these assumptions and can provide a more general description of the imaging system. In this paper, the authors present an experimental methodology and data treatment for quality assessment of a lab cone-beam CT system by comparing the spatial with the Fourier approach in 2D reconstructed slices. In order to have control over all experimental parameters and image reconstruction, a bench-top flat-panel-based cone-beam CT scanner and a cylindrical water-filled poly(methyl methacrylate) (PMMA) phantom were used for the noise measurements. An aluminum foil inserted in the water phantom enabled the estimation of the line response function (LRF) with a limited number of assumptions. The authors evaluated the spatial blur, the noise and the signal-to-noise ratio (SNR) using the spatial approach as well as the Fourier-based approach. In order to evaluate the degree of noise nonstationarity of their cone-beam CT system, the authors evaluated both the local and global CT noise properties and compared them using both approaches. For the laboratory cone-beam CT, the location-dependent noise evaluation showed that in addition to the noise variance, the NPS and covariance eigenvector symmetry depend on the location in the image. The estimated signal transfer was similar for both approaches. Unlike the Fourier approach which uses the same exponential wave function basis for both MTF and NPS, the eigenvectors of T and K were significantly different. By using the eigenvectors of the noise and object transfer to characterize the system, the spatial approach provides additional information to the Fourier approach and is therefore an important tool for a thorough understanding of a CT system.