Anomaly-Sensitive Dictionary Learning for Unsupervised Diagnostics of Solid Media

Abstract: This paper proposes a strategy for the detection and triangulation of structural anomalies in solid media. The method revolves around the construction of sparse representations of the medium's dynamic response, obtained by learning instructive dictionaries which form a suitable basis for the response data. The resulting sparse coding problem is recast as a modified dictionary learning task with additional spatial sparsity constraints enforced on the atoms of the learned dictionaries, which provides them with a prescribed spatial topology that is designed to unveil anomalous regions in the physical domain. The proposed methodology is model agnostic, i.e., it forsakes the need for a physical model and requires virtually no a priori knowledge of the structure's material properties, as all the inferences are exclusively informed by the data through the layers of information that are available in the intrinsic salient structure of the material's dynamic response. This characteristic makes the approach powerful for anomaly identification in systems with unknown or heterogeneous property distribution, for which a model is unsuitable or unreliable. The method is validated using both synthetically