1. A method of multi-spectral opto-acoustic tomography (MSOT) imaging of a target tissue including a target tissue biomarker, comprising: illuminating the target tissue with an illumination device emitting at least one pulsed illumination pattern at several illumination wavelengths; detecting pressure signals from the target tissue biomarker with a detector device, wherein the pressure signals being produced in the target tissue are in response to the said illumination; and reconstructing a quantitative tomographic image of a distribution of the target tissue biomarker in the target tissue, wherein the pressure signals are analyzed using a photon propagation model which depends on an illuminating light fluence in the target tissue and on the illumination wavelengths; at least one spectral processing scheme; and an inversion scheme providing the tomographic image.