Zhu W, Wang Y, Deng Y, Yao Y, Barbour R L
Department of Electrical Engineering, Polytechnic University, Brooklyn, NY 11203, USA.
IEEE Trans Med Imaging. 1997 Apr;16(2):210-7. doi: 10.1109/42.563666.
In this paper, we present a wavelet-based multigrid approach to solve the perturbation equation encountered in optical tomography. With this scheme, the unknown image, the data, as well as the weight matrix are all represented by wavelet expansions, thus yielding a multiresolution representation of the original perturbation equation in the wavelet domain. This transformed equation is then solved using a multigrid scheme, by which an increasing portion of wavelet coefficients of the unknown image are solved in successive approximations. One can also quickly identify regions of interest (ROI's) from a coarse level reconstruction and restrict the reconstruction in the following fine resolutions to those regions. At each resolution level a regularized least squares solution is obtained using the conjugate gradient descent method. This approach has been applied to continuous wave data calculated based on the diffusion approximation of several two-dimensional (2-D) test media. Compared to a previously reported one grid algorithm, the multigrid method requires substantially shorter computation time under the same reconstruction quality criterion.
在本文中，我们提出了一种基于小波的多重网格方法来求解光学层析成像中遇到的扰动方程。采用该方案，未知图像、数据以及权重矩阵均由小波展开表示，从而在小波域中得到原始扰动方程的多分辨率表示。然后使用多重网格方案求解这个变换后的方程，通过该方案，未知图像的小波系数在逐次逼近中被求解的比例不断增加。还可以从粗分辨率重建中快速识别感兴趣区域（ROI），并将后续细分辨率的重建限制在这些区域。在每个分辨率级别，使用共轭梯度下降法获得正则化最小二乘解。该方法已应用于基于几种二维（2-D）测试介质的扩散近似计算得到的连续波数据。与先前报道的单网格算法相比，在相同的重建质量标准下，多重网格方法所需的计算时间大幅缩短。
