Low-rank decomposition-based anomaly detection

With high spectral resolution hyperspectral imaging is capable of uncovering many subtle signal sources which cannot be known a priori or visually inspected. Such signal sources generally appear as anomalies in the data. Due to high correlation among spectral bands and sparsity of anomalies, a hyperspectral image can be e decomposed into two subspaces: a background subspace specified by a matrix with low rank dimensionality and an anomaly subspace specified by a sparse matrix with high rank dimensionality. This paper develops an approach to finding such low-high rank decomposition to identify anomaly subspace. Its idea is to formulate a convex constrained optimization problem that minimizes the nuclear norm of the background subspace and little ι1 norm of the anomaly subspace subject to a decomposition of data space into background and anomaly subspaces. By virtue of such a background-anomaly decomposition the commonly used RX detector can be implemented in the sense that anomalies can be separated in the anomaly subspace specified by a sparse matrix. Experimental results demonstrate that the background-anomaly subspace decomposition can actually improve and enhance RXD performance.