小波分析在层析图像重构中的应用研究

Application of wavelet in CT for image reconstruction

小波分析作为一种非平稳信号分析方法，具有良好的时（ 空）、频局部化特性和多分辨率特性。介绍了小波分析的基本原理和应用，引入小波分析进行图像重构，利用小波分解后得到的多分辨率的稀疏矩阵表示，设计了一迭代重构算法。通过计算机仿真试验，验证了小波分析在计算层析（ＣＴ） 成像光谱技术中能够应用于图像重构，并证实了小波分析的迭代重构算法是稳定、多分辨率和快速收敛的。

As a powerful tool in handling transient signal, wavelet analysis possesses multiresolution and localization in time(space) domain or frequency domain. The principle of wavelet is presented. The wavelet transformation in solving the perturbation equation is introduced. After the wavelet decomposition, we can get a multiresolution sparse matrix representation of the inverse problem, which make us induce an iterative algorithm. The computer simulation results show that wavelet analysis is efficient in image reconstruction for computed-tomography, and that the iterative algorithm is robust and converges rapidly.