# A wavelet–based multiresolution regularized least squares reconstruction approach for optical tomography

### W. Zhu *et al.* (1997)

#### 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, tha 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 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.