<title>Efficient noise tolerant reconstructions in diffuse optical tomography through computation of Jacobian in wavelet domain</title>

Abstract

In this paper, we present a wavelet -based approach to solve the reconstruction problem encountered in diffuse optical tomography (DOT). The DOT reconstruction problem using model based iterative image reconstruction (MoBIIR) procedure involves repeated implementation of the three steps: (i) solution to the diffusion equation (DE) to generate the simulated data from the current optical properties, (ii) estimation of the Jacobian for the current optical property values and (iii) inversion of the perturbation equation leading to the update vectors for the optical properties. Consequently, there are three approaches to a wavelet based solution to the DOT problem: (i) waveletization of the perturbation equation, (ii) application of wavelets for computation of the Jacobian for use in the perturbation equation and (iii) the solution to the DE in the wavelet domain. While the first of these approaches has been addressed earlier, the other two have not been attempted to the best of our knowledge. In this work, we have attempted the second approach, i.e., waveletization of the perturbation equation for each measurement, which requires computing the Jacobian in the wavelet domain. Our results show that this method outperforms the earlier method. With each measurement appropriately represented in wavelet domain, the localization and de-noising property of wavelets are exploited. Our simulation results show that the mean-square-error at convergence is not affected by the increase in noise in data (up to 4% additive Gaussian noise). In addition, the usual Vcycle strategy of wavelets is attempted.