Multiresolution total least squares reconstruction algorithm based on wavelet in medical optical tomography

In this paper, we present a wavelet based multiresolution total least squares (TLS) approach to solve the perturbation equation encountered in medical optical tomography. With this scheme, the unknown image, the data, as well as the weight matrix are all represented by wavelet expansions, and thus yielding a multi-resolution representation of the original Rayleigh quotient function in the wavelet domain. This transformed Rayleigh quotient function is then minimized 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 TLS solution is obtained iteratively using a conjugate gradient (CG) method. Compared to a previously reported one grid iterative TLS algorithm, the multigrid method requires substantially shorter computation time under the same reconstruction quality criterion.