Detecting targets in hyperspectral image under compressive sensing (CS) is crucial for real-time applications in front-ends. However, applying existing deep learning methods directly to compressed hyperspectral image has been challenging, including the uncertainty introduced by the random sensing matrix in the CS acquisition model, and the ineffectuality of traditional similarity metrics. In this paper, we present a solution to these challenges by introducing a Compressive Sensing-based Triplet Transformer Detector (CS-TTD). Our approach involves data augmentation using the Restricted Distribution Property (RDP) to generate samples for a balanced number of positive samples. followed by the Siamese Network with a triplet transformer to transition spectral vectors from the compressed domain to an embedding space. In addition, we introduce a Combine Convolution Net (CCN) classification module to replace traditional metrics for obtaining classification results. To improve the training and make full use of dataset labels, we also present a two-stage training approach, known as intercategory separation and intracategory aggregation (ISIA), combined with Hard-negative mining, Semi Hard-negative mining. Besides, to estimate the minimal number of compressed bands for sufficient detection performance, we introduce a kernel distribution estimation-based sequential iteration (KDE-SI). Our method achieves hyperspectral target detection without reconstruction, and experimental results demonstrate its performance at 0.16 compression ratio is comparative to existing methods in the original domain.

Compressive sensing (CS) is a widely utilized technique in hyperspectral imaging front end, and hyperspectral target detection (HTD) in the CS domain is crucial for conserving computational and storage resources on front-end platforms and achieving real-time detection. However, existing HTD methods can only handle reconstructed hyperspectral images. To address this limitation, this study investigates a novel property under hyperspectral CS and proposes an algorithm framework for HTD without reconstruction. The newly proposed property, named restricted distribution property (RDP), is based on assumptions about spectral random vectors and derivations from the CS model. It indicates that the spectral vectors in the compressed hyperspectral follow a deterministic Gaussian distribution under specific conditions and provide a generalized expression for their covariance matrix. Building upon this property, a Kullback–Leibler (KL) divergence subspace distribution estimator is developed, enabling HTD without reconstruction. Experimental result demonstrates that the performance of the proposed detector in compressed hyperspectral data is comparable to or even superior to conventional methods in original hyperspectral images. The result is inspiring for future research.