As most optical satellites remotely acquire multispectral images (MSIs) with limited spatial resolution, multispectral unmixing (MU) becomes a critical signal processing technology for analyzing the pure material spectra for high-precision classification and identification. Unlike the widely investigated hyperspectral unmixing (HU) problem, MU is much more challenging as it corresponds to the underdetermined blind source separation (BSS) problem, where the number of sources is larger than the number of available multispectral bands. In this article, we transform MU into its overdetermined counterpart (i.e., HU) by inventing a radically new quantum deep image prior (QDIP), which relies on the virtual band-splitting task conducted on the observed MSI for generating the virtual hyperspectral image (HSI). Then, we perform HU on the virtual HSI to obtain the virtual hyperspectral sources. Though HU is overdetermined, it still suffers from the ill-posed issue, for which we employ the convex geometry structure of the HSI pixels to customize a weighted simplex shrinkage (WSS) regularizer to mitigate the ill-posedness. Finally, the virtual hyperspectral sources are spectrally downsampled to obtain the desired multispectral sources. The proposed geometry/quantum-empowered MU (GQ- $\mu $ ) algorithm can also effectively obtain the spatial abundance distribution map for each source, where the geometric WSS regularization is adaptively and automatically controlled based on the sparsity pattern of the abundance tensor. Simulation and real-world data experiments demonstrate the practicality of our unsupervised GQ- $\mu $ algorithm for the challenging MU task. Ablation study demonstrates the strength of QDIP, not achieved by classical DIP, and validates the mechanics-inspired WSS geometry regularizer. The associated code will be available at https://github.com/IHCLab/GQ-mu.

Quantum machine intelligence starts showing its impact on satellite remote sensing (SRS). Also, recent literature exhibits that quantum generative intelligences encompass superior potential than their classical counterpart, motivating us to develop quantum generative adversarial networks (GANs) for SRS. However, existing quantum GANs are restricted by the limited quantum bit (qubit) resources of current quantum computers and process merely a small 2 × 2 grayscale image, far from being applicable to SRS. Recently, the novel concept of hybrid quantum-classical GAN, a quantum generator with a classical discriminator, has upgraded the order to 28 × 28 (still grayscale), whereas it is still insufficient for SRS. This motivates us to design a radically new hybrid framework, where both generator and discriminator are hybrid architectures. We demonstrate this feasibility, leading to a breakthrough of processing 128×128 hyperspectral images for SRS. Specifically, we design the quantum part with mathematically provable quantum full expressibility (FE) to address core signal processing tasks, wherein the FE property allows the quantum network to realize any valid quantum operator with appropriate training. The classical part, composed of convolutional layers, treats the read-in (compressing the optical information into limited qubits) and read-out (addressing the quantum collapse effect) procedures. The proposed innovative hybrid quantum GAN, named “Hyperspectral Knot-like IntelligeNt dIscrimiNator and Generator” (HyperKING), where “knot” partly symbolizes the quantum entanglement and partly the compressed quantum domain in the central part of the network architecture. HyperKING significantly surpasses the classical approaches in hyperspectral tensor completion, mixed noise removal (about 3dB improvement), and blind source separation results.

Hyperspectral anomaly detection (HAD), a challenging inverse problem, has found numerous scientific applications. Although extant HAD algorithms have achieved remarkable results, there are still several issues remained unresolved: 1) low spatial resolution (and spectral redundancy) in typical hyperspectral images prevents effectively distinguishing the abnormal pixels from those normal ones and 2) the reconstruction from existing residual-based frameworks would not completely remove anomaly effects, making the detection solely from the residual impractical. In this article, we propose a novel HAD method, termed transformer-guided fractional attention within the abundance domain (TGFA-AD), which substitutes raw input image with the abundance matrix obtained via blind source separation (BSS). First, the proposed abundance spatial-channel reconstruction transformer (ASCR-Former) is customized for rebuilding the abundance matrix. According to the image self-similarity, the abundance is patch-wisely encoded with class (CLS) tokens. The transformer encoders intensify the spatial and channel characteristics between tokens for reconstructing the abundance, followed by deriving the initial detection from the abundance residual matrix. Second, a novel fractional abundance attention (FAA) mechanism is proposed, where the attention weights coming from a specific linear combination of abundances are guided by the initial detection with convex $ Q$ -quadratic norm. Finally, the fractional convolution is incorporated to fuse the abundance and residual into the fractional feature for yielding the final detection result. Real data experiments quantitatively and qualitatively exhibit the state-of-the-art performance of TGFA-AD.

Adversarial learning is of paramount importance in numerous recent computing areas, while quantum entanglement has also revealed its role in efficient computing. This motivated us to bring quantum computing into adversarial learning. Though there are some preliminary theoretical studies of quantum adversarial learning (QAL), there has no demonstration of advanced real-world applications. For the first time, we design and implement a QAL framework, and demonstrate the feasibility of QAL-based hyperspectral image processing for remote sensing. This research line aims to lay the foundation for the QAL in hyperspectral remote sensing, including to solve the limited qubit resources, to mitigate the quantum collapse effect, to design a quantum discriminator with comparable ability, as well as to ensure the quantum expressibility of the generator, to name a few.

Synthesis of high-resolution (HR) FORMOSAT-8 satellite image is a critical task with high economical values, not only for avoiding related issues before launching FORMOSAT-8, but also for predicting and understanding the potential applications like precision agriculture. Nevertheless, there is no existing techniques for this mission, motivating us to reconsider the synthesis problem as a super-resolution problem under the satellite image fusion framework. Specifically, we employ the Sentinel-2 and Pléiades satellite images based on their fundamental properties (e.g., band alignment, and spatial resolution), and trickily fuse them to generate the target image (i.e, the HR FORMOSAT-8 image). Our fusion algorithm adopts the convex/deep (CODE) small-data learning theory, recently invented in the remote sensing area, resulting in a fast (closed-form) and high-quality synthesis 4m product.

Considering that hyperspectral image (HSI) is often of lower spatial resolution when compared to multispectral image (MSI), an economical approach for obtaining a high-spatial-resolution (HSR) HSI is to fuse the acquired HSI and MSI, thereby greatly facilitating the subsequent material identification and classification in satellite remote sensing. As satellite-acquired HSI and MSI are often misaligned, the proposed deep neural network does not require the input HSI/MSI to be spatially co-registered, making the challenging fusion network design even more difficult. In this study, we propose a streamlined and efficient convex model integrated into the sub-network, which obviates the need for complex network structures in learning spatial-spectral relationships, effectively guiding the quasi-residual learning task in our alignment-free fusion network. The convex sub-network is a low-rank model that leverages the convex geometric structure implicitly embedded in the hyperspectral signature space. To address the misalignment between HSI and MSI effectively, we introduce a novel Shifted Window Attention Module (SWAM) that exploits the neighboring correlation in the feature domain, significantly enhancing the performance and stability of the fusion task. Capitalizing on the redundancy among spectrums, we employ grouped convolution to decrease the computational complexity without causing additional performance degradation. The proposed Quasi-residual Convex Deep Network (QRCODE) demonstrates state-of-the-art performance in alignment-free HSI/MSI fusion tasks.

In hyperspectral remote sensing (HRS), signal sub-space identification is a critical step in many widely renowned HRS algorithms, while the accuracy of the subspace identification relies on the complete information of the data pixels. However, as the sensor arrays would be partially damaged after the satellites are launched, hyperspectral pixels are quite often incompletely acquired. Even for those renowned algorithms, they simply remove those incomplete pixels when computing the hyperspectral signal subspace. Nevertheless, even if some spectral bands of a given incomplete pixel are missing, we intuitively believe that the remaining bands of that pixel should still contribute to the accuracy of the subspace identification. We design a computationally efficient algorithm, termed as subspace identification for incomplete signals of hyperspectral image (SISHY), to utilize the information embedded in those incomplete pixels. To this end, we prove a lemma that allows us to reformulate the algebraic identification problem into an affine geometry problem, thereby allowing us to flexibly add suitable regularizer for better identification result as needed. SISHY judiciously associates the regularized subspace identification problem with a denoising operator, thereby allowing an efficient algorithm implementation and yielding a physically interpretable data matrix completion result as a byproduct. Experiments demonstrate that the SISHY algorithm does improve the efficacy of the subsequent tasks of unmixing, inpainting and classification.