Data correlation based noise level estimation for cone beam projection data

Ti Bai, Hao Yan, Luo Ouyang, David Staub, Jing Wang, Xun Jia, Steve B. Jiang, Xuanqin Mou
2017 Journal of X-Ray Science and Technology  
BACKGROUND-In regularized iterative reconstruction algorithms, the selection of regularization parameter depends on the noise level of cone beam projection data. OBJECTIVE-Our aim is to propose an algorithm to estimate the noise level of cone beam projection data. METHODS-We first derived the data correlation of cone beam projection data in the Fourier domain, based on which, the signal and the noise were decoupled. Then the noise was extracted and averaged for estimation. An adaptive
more » ... tion parameter selection strategy was introduced based on the estimated noise level. Simulation and real data studies were conducted for performance validation. RESULTS-There exists an approximately zero-energy double-wedge area in the 3D Fourier domain of cone beam projection data. As for the noise level estimation results, the averaged relative errors of the proposed algorithm in the analytical/MC/spotlight-mode simulation experiments were 0.8%, 0.14% and 0.24%, respectively, and outperformed the homogeneous area based as well as the transformation based algorithms. Real studies indicated that the estimated noise levels were inversely proportional to the exposure levels, i.e., the slopes in the log-log plot were −1.0197 and −1.049 with respect to the short-scan and half-fan modes. The introduced regularization parameter selection strategy could deliver promising reconstructed image qualities. CONCLUSIONS-Based on the data correlation of cone beam projection data in Fourier domain, the proposed algorithm could estimate the noise level of cone beam projection data accurately and robustly. The estimated noise level could be used to adaptively select the regularization parameter. CT sinogram exhibits a unique property in its 2D Fourier domain, namely, there exists an approximately zero-energy double-wedge area. Its theoretical formalism has been introduced in an earlier paper [23] . Here, we will briefly present this data correlation for completeness. Equal-spaced fan beam geometry with a circle orbit will be used as an example. Let us consider an object composed of a delta function point, which located at distance r from the origin and at angle ϕ with respect to the x-axis. It could be denoted by δ(r, ϕ) in the polar coordinate system. Then, the Radon transform of δ(r, ϕ) can be expressed as (2) where Bai et al.
doi:10.3233/xst-17266 pmid:28697578 pmcid:PMC5714667 fatcat:a7xdo52d7vb5rfc3w6bqcrjlfm