A Contrast Source Inversion Method In The Wavelet Domain

We present a contrast source inversion (CSI) algorithm using truncated wavelet representations. Specifically, we represent the unknown contrast sources and the contrast function in terms of the wavelet basis functions. In order to reduce the number of wavelet coefficients for these unknowns, we apply a progressive multiscale truncation scheme based on the reconstructed contrast function. This approach increases the robustness of the CSI algorithm for noisy or limited data, and decreases the computation time as well as the memory usage. We tested the wavelet-domain CSI method using both synthetic and experimental data. The numerical experiments show that similar results with the regular spatial-domain CSI method are obtained when the number of (independent) measurement data points is comparable to the number of the unknowns in the contrast function. The advantages of the wavelet-domain CSI method become apparent as we deal with cases where the number of measurement data points is smaller than the number of unknowns in the contrast function.