The hyperspectral image (HSI) has nearly continuous spectral information, thus, the target of interest can be accurately identified by the subtle details of spectral properties. Spectral resolution at different scales can capture different levels of spectral features: small-scale spectral bands are beneficial for extracting global details in vision transformers, while large-scale spectral bands are more effective for local features. Transformer shows advantages in global information extraction with self-attention module and even surpasses CNNs in various tasks. Some works based on the vision transformer have performed surprisingly in HSI classification. However, single-scale vision transformers are insufficient to balance the extraction of local details and redundancy on different scales. The recent work, a multi-scale vision transformer, has provided a solution with spatial patch-wise features in image classification. Inspired by this, we propose the Cross-spectral vision transformer (CSiT) with two branches to extract pixel-wise multi-scale features and further design a multi-scale spectral embedding module to enhance local details between neighboring spectral bands. Moreover, based on the cross-attention operation, a single token for each branch is recognized as a query and used to exchange information with other branches. We evaluate the classification performance of the proposed CSiT in three classic HSI datasets with extensive experiments, showing the multi-scale vision transformer architecture has a promising result for HSI classification with one-dimensional spectral bands.

The Moon-based Synthetic Aperture Radar (Moon-Based SAR), using the Moon as a platform, has a great potential to offer global-scale coverage of the earth’s surface with a high revisit cycle and is able to meet the scientific requirements for climate change study. However, operating in the lunar orbit, Moon-Based SAR imaging is confined within a complex geometry of the Moon-Based SAR, Moon, and Earth, where both rotation and revolution have effects. The extremely long exposure time of Moon-Based SAR presents a curved moving trajectory and the protracted time-delay in propagation makes the “stop-and-go” assumption no longer valid. Consequently, the conventional SAR imaging technique is no longer valid for Moon-Based SAR. This paper develops a Moon-Based SAR theory in which a signal model is derived. The Doppler parameters in the context of lunar revolution with the removal of ‘stop-and-go’ assumption are first estimated, and then characteristics of Moon-Based SAR imaging’s azimuthal resolution are analyzed. In addition, a signal model of Moon-Based SAR and its two-dimensional (2-D) spectrum are further derived. Numerical simulation using point targets validates the signal model and enables Doppler parameter estimation for image focusing.

In this paper, effects of the earth's curvature and lunar revolution on the performance of the moon-based synthetic aperture radar (SAR) are examined by a comprehensive analysis of the motion-induced Doppler frequency and Doppler rate on which azimuthal imaging relies. The motion effects include the earth's self-rotation related to the earth's curvature and lunar revolution around the earth. An extended hyperbolic range equation (EHRE) is proposed in line of the equivalent velocity and equivalent squint angle, and then the signal model based on the EHRE is established to simulate the moon-based SAR image from which the imaging performance is analyzed. Theoretical analyses show that the earth's curvature is a dominant factor in determining the moon-based SAR's Doppler and azimuthal resolution. Furthermore, the earth's curvature distorts the SAR image by way of rotating the azimuth imaging from the cross-range direction within a certain skewed angle. The overall effects of lunar revolution generate a velocity correction factor and a deviate squint angle, which subsequently deteriorate the azimuthal resolution and image focusing. Results also show that effects of the earth's curvature and lunar revolution are in connection with relative positions of the ground target and moon-based SAR. To this end, numerical simulations using point target response is carried out to accentuate the necessary for taking account of the Doppler error induced by the lunar revolution.

This letter examines how the principal component analysis (PCA) affects the performance of the Deep Forest 2021 (DF21) model for the hyperspectral inversion. To this end, the spectra contaminated by eight types of heavy metals are applied and processed by PCA. Subsequently, various retained principal components (PCs) are devoted to establishing the inversion model in line with the DF21. Two typical heavy metal elements, i.e., zinc (Zn) and chromium (Cr), are used for instance; it explores the accuracies of the DF21 model for inverting their concentrations under different PCs. The findings reveal that the DF21 model’s performance fluctuates with varying retained PCs. Furthermore, the fluctuations are influenced by the heavy metal’s type and its concentration distribution. As a result, the optimal performances for inverting the Zn and Cr concentrations appear at the first 9 PCs and first 8 PCs, respectively. Hence, it might not be feasible to improve the accuracy by retaining more PCs in hyperspectral inversion, at least not for the DF21 model.

The spatiotemporal coverage of a Moon-based synthetic aperture radar (SAR) is analyzed based on the imaging geometry, upon which the spatial coverage and image formulation rely. The distance from the Earth to the Moon-based SAR and bounds of the grazing and azimuthal angles jointly determine the coverage area on the Earth's surface. Meanwhile, the ground coverage of the Moon-based SAR is determined by the bounds of the grazing and azimuthal angles and geographic coordinates of the nadir point at a specified time. Moreover, the temporal variation in the spatial coverage is pertinent to the temporally varying nadir point of the Moon-based SAR on the Earth's surface. Furthermore, numerical simulations using the lunar ephemeris data are carried out to complement the analysis and to illustrate the spatiotemporal coverage. Finally, a guideline for the optimal site selection of a Moon-based SAR is proposed. In conclusion, a Moon-based SAR has the potential to perform long-term, continuous Earth observations on a global scale to enhance our capability to understand the planet.

Due to the earth and moon's revolutions, the Doppler centroid of the moon-based synthetic aperture radar (moon-based SAR) varies dramatically along the orbit of the moon when the SAR system is looking broadside (nonsquinted). However, the Doppler centroid should be kept as small as possible to avoid range ambiguity and to alleviate difficulty with focus. This letter presents the Doppler properties along the orbit of the moon in accordance with the antenna coordinate system. Based on the Doppler analysis and the phase scan, we propose a method for Doppler centroid steering to minimize the Doppler centroid frequency without rotating the platform. The new method can accurately compensate the Doppler centroid to zero, because it considers the effects of the lunar orbit and the relative motion between earth's target and moon-based SAR. To validate the proposed method, we also derived the lower and upper bounds of the look angle. Subsequently, we performed simulations in accordance with Jet Propulsion Laboratory Development Ephemeris 430 (JPL DE430). Finally, the performance requirement of the phase scan is analyzed so as to validate the proposed method.