Department of Mathemtics, Uniersity of Bologna, Italy.
Comput Med Imaging Graph. 2012 Jan;36(1):38-46. doi: 10.1016/j.compmedimag.2011.07.002. Epub 2011 Aug 6.
Medical images obtained with emission processes are corrupted by noise of Poisson type. In the paper the denoising problem is modeled in a Bayesian statistical setting by a nonnegatively constrained minimization problem, where the objective function is constituted by a data fitting term, the Kullback-Leibler divergence, plus a regularization term, the Total Variation function, weighted by a regularization parameter. Aim of the paper is to propose an efficient numerical method for the solution of the constrained problem. The method is a Newton projection method, where the inner system is solved by the Conjugate Gradient method, preconditioned and implemented in an efficient way for this specific application. The numerical results on simulated and real medical images prove the effectiveness of the method, both for the accuracy and the computational cost.
采用发射过程获得的医学图像会受到泊松噪声的干扰。本文在贝叶斯统计环境下通过非负约束最小化问题对去噪问题进行建模，其中目标函数由数据拟合项、Kullback-Leibler 散度和正则化项、总变差函数构成，由正则化参数加权。本文的目的是提出一种有效的数值方法来求解约束问题。该方法是牛顿投影法，其中内系统通过共轭梯度法求解，并针对这种特定应用进行了有效的预处理和实现。对模拟和真实医学图像的数值结果证明了该方法的有效性，无论是在准确性还是计算成本方面。
