Nonlinear inverse scattering methods for thermal-wave slice tomography: a wavelet domain approach

A wavelet domain, nonlinear inverse scattering approach is presented for imaging subsurface defects in a material sample, given observations of scattered thermal waves. Unlike methods using the Born linearization, our inversion scheme is based on the full wave-field model describing the propagation of thermal waves. Multiresolution techniques are employed to regularize and to lower the computational burden of this ill-posed imaging problem. We use newly developed wavelet-based regularization methods to resolve better the edge structures of defects relative to reconstructions obtained with smoothness-type regularizers. A nonlinear approximation to the exact forward-scattering model is introduced to simplify the inversion with little loss in accuracy. We demonstrate this approach on cross-section imaging problems by using synthetically generated scattering data from transmission and backprojection geometries.