Wavelet Based Multigrid Reconstruction Algorithm for Optical Tomography

Abstract

In this paper, we present a wavelet based multigrid approach to solve the perturbation encountered in optical tomography. The wavelet based multigrid representation has been applied to obtain regularized least squares (RLS) and total least squares (TLS) solutions. The unknown image, the data, as well as the weight matrix are all represented by wavelet expansions, thus yielding a multi-resolution representation of the perturbation Then, the transformed perturbation is solved by either the RLS or TLS method, using a multigrid scheme, by which an increasing portion of wavelet coefficients of the unknown image are solved in successive approximations. The experimental results show that the multigrid method can achieve similar reconstruction quality with a significantly reduced amount of time than the one-grid algorithm.