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Multifrequency electrical impedance tomography (MFEIT) exploits the dependence of tissue impedance on frequency to recover an image of conductivity. MFEIT could provide emergency diagnosis of pathologies such as acute stroke, brain injury and breast cancer. We present a method for performing MFEIT using spectral constraints. Boundary voltage data is employed directly to reconstruct the volume fraction distribution of component tissues using a nonlinear method. Given that the reconstructed parameter is frequency independent, this approach allows for the simultaneous use of all multifrequency data, thus reducing the degrees of freedom of the reconstruction problem. Furthermore, this method allows for the use of frequency difference data in a nonlinear reconstruction algorithm. Results from empirical phantom measurements suggest that our fraction reconstruction method points to a new direction for the development of multifrequency EIT algorithms in the case that the spectral constraints are known, and may provide a unifying framework for static EIT imaging.