Guided waves have gained popularity in structural health monitoring (SHM) due to their ability to inspect large areas with little attenuation, while providing rich interactions with defects. For thin-walled structures, the propagating waves are Lamb waves, which are a complex but well understood type of guided waves. Recent works have cast the defect localization problem of Lamb wave based SHM within the sparse reconstruction framework. These methods make use of a linear model relating the measurements with the scene reflectivity under the assumption of point-like defects. However, most structural defects are not perfect points but tend to assume specific forms, such as surface cracks or internal cracks. Knowledge of the "type" of defects is useful in the assessment phase of SHM. In this paper, we present a dual purpose sparsity-based imaging scheme which, in addition to accurately localizing defects, properly classifies the defects present simultaneously. The proposed approach takes advantage of the bias exhibited by certain types of defects toward a specific Lamb wave mode. For example, some defects strongly interact with the anti-symmetric modes, while others strongly interact with the symmetric modes. We build model based dictionaries for the fundamental symmetric and anti-symmetric wave modes, which are then utilized in unison to properly localize and classify the defects present. Simulated data of surface and internal defects in a thin Aluminum plate are used to validate the proposed scheme.