熵正则化磁共振成像理论及迭代算法

ON ITERATIVE METHOD FOR ENTROPY REGULARIZED RECONSTRUCTION IN MRI

实际的磁共振成像系统 ,通常仅能收集有限的频谱数据 ,傅立叶变换法重建的图像存在Gibbs伪影 ,且分辨率有限。我们提出的熵正则化磁共振成像方法是考虑与原始频谱数据一致性的条件下 ,熵极大化而获得的结果。重建的图像具有无限的分辨率 ,降低Gibbs伪影及信号中的噪声。本算法的稳定性优于模型最大熵法[12 ] 。

In magnetic resonance imaging, only a limited amount of sampled data could be collected. The limitation of available experimental data led to the infamous problem of diffraction which manifested itself by causing ringing in the image. This ringing was due to interference phenomena in optics and was known as the Gibbs phenomenon in engineering. Here, an iterative entropy regularization algorithm for MRI was developed, which produced a super redsolution and optimal signal to noise solution to the problem of reconstructing a source from partial Fourier transform data. This method was capable, in principle, of unlimited resolution and was robust with respect to Gaussian white noise perturbation. Comparisons of the IMER method with the conventional Fourier transform method was carried out with the real magnetic resonance data to illustrate the proposed method.