Abstract
Purpose:To develop a Hessian‐based norm penalty for cone‐beam CT (CBCT) reconstruction that has a similar ability in suppressing noise as the total variation (TV) penalty while avoiding the staircase effect and better preserving low‐contrast objects.Methods:We extended the TV penalty to a Hessian‐based norm penalty based on the Frobenius norm of the Hessian matrix of an image for CBCT reconstruction. The objective function was constructed using the penalized weighted least‐square (PWLS) principle. An effective algorithm was developed to minimize the objective function using a majorization‐minimization (MM) approach. We evaluated and compared the proposed penalty with the TV penalty on a CatPhan 600 phantom and an anthropomorphic head phantom, each acquired at a low‐dose protocol (10mA/10ms) and a high‐dose protocol (80mA/12ms). For both penalties, contrast‐to‐noise (CNR) in four low‐contrast regions‐of‐interest (ROIs) and the full‐width‐at‐half‐maximum (FWHM) of two point‐like objects in constructed images were calculated and compared.Results:In the experiment of CatPhan 600 phantom, the Hessian‐based norm penalty has slightly higher CNRs and approximately equivalent FWHM values compared with the TV penalty. In the experiment of the anthropomorphic head phantom at the low‐dose protocol, the TV penalty result has several artificial piece‐wise constant areas known as the staircase effect while in the Hessian‐based norm penalty the image appears smoother and more similar to that of the FDK result using the high‐dose protocol.Conclusion:The proposed Hessian‐based norm penalty has a similar performance in suppressing noise to the TV penalty, but has a potential advantage in suppressing the staircase effect and preserving low‐contrast objects.This work was supported in part by National Natural Science Foundation of China (NNSFC), under Grant Nos. 60971112 and 61375018, and Fundamental Research Funds for the Central Universities, under Grant No. 2012QN086.
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