# Multiresolution Regularized Least Squares Image Reconstruction Based on Wavelet Trandform in Optical Tomography

### W. Zhu *et al.* (1995)

#### Summary

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 weight matrix are all represented by
wavelet expansions, and thus yielding a multi–resoltuion 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) 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 a
Conjugate Gradient Descent (CGD) method. Compared to a previously reported one grid algorithm, the multigrid method
requires substantially shorter computation time under the same reconstruction quality criterion.