1. A method of multi-spectral opto-acoustic tomography (MSOT) imaging of a target tissue including at least one target tissue biomarker, the method comprising: illuminating the target tissue using several different illumination wavelengths; detecting pressure signals from the at least one target tissue biomarker with a detector, wherein the pressure signals are produced in the target tissue in response to said illuminating the target tissue; and reconstructing a quantitative tomographic image of a spatial distribution of a concentration of the at least one target tissue biomarker in the target tissue, said reconstructing of the quantitative tomographic image comprising: applying an inversion scheme to the pressure signals to provide a reconstructed optoacoustic image ψ k (λ) at each of the different illumination wavelengths; separating contributions of a light fluence U k (λ) and an absorption coefficient μ k (λ) to the reconstructed image ψ k (λ) at each of the illumination wavelengths using a blind source separation method, whereby the absorption coefficient μ k (λ) is obtained at each of the illumination wavelengths; and using at least one spectral processing scheme to resolve the at least one target tissue biomarker, wherein the spectral processing scheme processes, on a pixel-by-pixel basis, the absorption coefficient μ k (λ) obtained at each of the illumination wavelengths to resolve the spatial distribution of the concentration of the at least one target tissue biomarker.