$\mathrm{D}^{3}$T: Deep Denoising Dictionary Tensor for Hyperspectral Anomaly Detection

Hyperspectral anomaly detection (HAD) approaches with tensor low-rank representation (TLRR) have shown engaging performance, which are capable of capturing abundant spectral and spatial information and, hence, extracting sparse anomalies from the low-rank background without ruining the intrinsic geometric structures of tensor data. However, existing HAD approaches construct the low-rank representation by a handcrafted dictionary that still contains the anomalies, resulting in an inferior representation. To this end, we propose a deep denoising dictionary tensor for hyperspectral anomaly detection (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathrm{D}^{3}$</tex-math></inline-formula>T), which can balance performance and interpretability by fusing two intuitive priors, i.e., low-rankness and deep denoising, into the dictionary tensor and coefficient tensor. In particular, the proposed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathrm{D}^{3}$</tex-math></inline-formula>T first designs a tensor recovery module for dividing the low-rank background and sparse anomalies, where the background is optimized as a denoising dictionary tensor by the joint low-rankness and deep denoising. Following that, we build the TLRR model based on the denoising dictionary tensor to explore the latent representation of the input hyperspectral images, and hence, each background pixel is represented by the other clear background pixels in place of the anomaly pixels. Meanwhile, the coefficient tensor in TLRR is also optimized by the two priors to fully explore the spatial and spectral correlations in the background, and hence, the anomalies can be accurately detected. Numerous experimental results from various real-world datasets validate the effectiveness of our <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathrm{D}^{3}$</tex-math></inline-formula>T.