一种基于Fourier-小波矩的PET图像重建方法

正电子发射断层图像(PET)重建问题是一种不适定问题,通常需要采用正则化方法以抑制噪声,提高重建质量.本文提出一种新的非正则化重建方法,即基于Fourier-小波基函数的特征重建算法.Fourier-小波基函数结合了小波基函数和Fourier调和函数的特征,使我们便于对其进行小波分析和Fourier分析.在本文的算法中,我们采用迭代方法,计算图像的Fourier-小波矩(FWM),并由FWM恢复图像.此外我们利用Fourier-小波基函数的旋转不变性节省算法存储空间,简化计算,并且利用此性质,推导出一种类似Row-Action(RA)方法的快速收敛算法,以提高收敛速度.我们将FWM算法同几种常用算法进行了比较,实验结果表明,FWM算法的重建效果同传统的MAP算法接近,具有较好的应用前景.

A New PET Reconstruction Method Based on Fourier-Wavelet Moment

The problem of Positron emission tomography(PET) image reconstruction is well-known ill-posed, thus regularization methods are usually considered to suppress the noise effect. In this paper, a new non-regularization method is proposed, which is a feature-based reconstruction method using Fourier-Wavelet basis. The Fourier-Wavelet basis combines Fourier harmonic and Wavelet function, and provides us with convenience performing both Wavelet and Fourier analysis. In order to obtain the reconstructions, we only have to recover the Fourier-Wavelet moment(FWM) from the measurements. To achieve the FWMs the authors employ iterative method. With the aid of the rotation invariance property of the proposed basis, both the online memory storage and computational costs can be reduced. In addition, the property allows us to generate a Row-Action(RA) like fast convergent algorithm. In experiment, the proposed method is compared with several others. The results suggest that the proposed method offer good reconstruction quality comparable to conventional MAP method.