Istituto per le Applicazioni del Calcolo, CNR, Rome.
IEEE Trans Med Imaging. 1995;14(3):434-41. doi: 10.1109/42.414607.
A new statistical method is proposed for reduction of truncation artifacts when reconstructing a function by a finite number of its Fourier series coefficients. Following the Bayesian approach, it is possible to take into account both the errors induced by the truncation of the Fourier series and some specific characteristics of the function. A suitable Markov random field is used for modeling these characteristics. Furthermore, in applications like Magnetic Resonance Imaging, where these coefficients are the measured data, the experimental random noise in the data can also be taken into account. Monte Carlo Markov chain methods are used to make statistical inference. Parameter selection in the Bayesian model is also addressed and a solution for selecting the parameters automatically is proposed. The method is applied successfully to both simulated and real magnetic resonance images.
提出了一种新的统计方法，用于在通过有限数量的傅里叶级数系数重建函数时减少截断伪影。通过贝叶斯方法，可以同时考虑到傅里叶级数截断引起的误差和函数的某些特定特征。使用合适的马尔可夫随机场来模拟这些特征。此外，在磁共振成像等应用中，这些系数是测量数据，也可以考虑数据中的实验随机噪声。使用蒙特卡罗马尔可夫链方法进行统计推断。还解决了贝叶斯模型中的参数选择问题，并提出了一种自动选择参数的解决方案。该方法成功应用于模拟和真实磁共振图像。
