We study the seismic inverse problem for the recovery of subsurface properties in acousticmedia. In order to reduce the ill-posedness of the problem, the heterogeneous wave speedparameter is represented using a limited number of coefficients associated with a basis ofeigenvectors of a diffusion equation, following theregularization by discretizationapproach.We compare several choices for the diffusion coefficient in the partial differential equations,which are extracted from the field of image processing. We first investigate their efficiency forimage decomposition (accuracy of the representation with respect to the number of variables).Next, we implement the method in the quantitative reconstruction procedure for seismicimaging, following the full waveform inversion method, where the difficulty resides in thatthe basis is defined from an initial model where none of the actual structures is known. Inparticular, we demonstrate that the method may be relevant for the reconstruction of mediawith salt-domes. We use the method in 2-D and 3-D experiments, and show that the eigenvectorrepresentation compensates for the lack of low-frequency information, it eventually serves usto extract guidelines for the implementation of the method.