HyperKING: Quantum-Classical Generative Adversarial Networks for Hyperspectral Image Restoration

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 <inline-formula> <tex-math notation="LaTeX">$2 \times 2$ </tex-math></inline-formula> 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 <inline-formula> <tex-math notation="LaTeX">$28 \times 28$ </tex-math></inline-formula> (still grayscale), whereas it is still insufficient for SRS. This motivates us to design a radically new hybrid framework, where both the generator and discriminator are hybrid architectures. We demonstrate this feasibility, leading to a breakthrough in processing <inline-formula> <tex-math notation="LaTeX">$128 \times 128$ </tex-math></inline-formula> hyperspectral images (HSIs) 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 (QC) 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 3 dB improvement), and blind source separation (BSS) results.