The Linear Sampling Method (LSM) aims to image the shape of defects in a known medium from measurements of scattered fields and generally provides satisfactory solutions if multi-static (far field) data is available. However, this method becomes less effective for cluttered defects (for instance a network of cracks). In this talk, we shall present a recently introduced imaging method based on the LSM formalism but that exploits the spectrum of an eigenvalue problem. This eigenvalue problem is specifically designed by the introduction of a modified background so that its analysis in terms of defects size is possible. We prove that the eigenvalues of this problem can be identified from multi-static data. We then exploit this fact to construct an indicator function of the defects density based on the sensitivity of the eigenvalues to the presence and size of these defects. We shall illustrate the obtained inverse algorithm and its performances on some synthetic numerical experiments.