A numerical inversion scheme for recovering a map of the absolute conductivity from the absorbed power density map that is conventionally reconstructed in thermacoustic imaging is described. This offers the prospect of obtaining an image that is more closely related to the underlying tissue structure and physiology. The inversion scheme employs a full 3D full wave model of electromagnetic propagation in tissue which is iteratively fitted to the measured absorbed power density map using a simple

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... recursive method. The reconstruction is demonstrated numerically using three examples of absorbers of varying geometries, tissue realistic complex permittivity values and noise. In these examples, the reconstruction is shown to rapidly converge to within good estimates of the true conductivity in less than 20 iterations.