This work introduces a method for the detection and triangulation of anomalous features in solid media. The strategy leverages an algorithm which demixes the dynamic system response data into two distinct components: the first characterized by spatially sparse, persistent features and the second comprising the relatively large, smooth features of the bulk response. In performing this demixing, we select a topologically suitable basis for each component and we seek an accurate representation of the data in terms of the respective bases. This task is cast in the form of a Group Lasso optimization problem and solved using a Block Coordinate Descent algorithmic approach. The resulting representation distills the signatures of potential anomalies from the bulk dynamic response, thus allowing an effortless determination of their location. The proposed method is baseline free, automated, unsupervised (it makes no use of training sets), and model agnostic (it makes virtually no use of material knowledge or constitutive behavior). These attributes are appealing in systems where there exists limited or unreliable a priori constitutive knowledge of the model, or when the physical domain is highly heterogeneous or compromised by large damage zones. The method is tested against synthetically generated data and experimental data obtained using a scanning laser Doppler vibrometer.