高光谱图像混合噪声去除的稀疏优化模型与算法研究

Due to the limitations of hardware devices and environmental conditions during the imaging process, hyperspectral images are inevitably corrupted by noise, which usually originates from a mix of multiple components, significantly lowering the image visual quality and practical value. Hyperspectral image denoising aims at estimating the true image from the noisy image, which is a fundamental and important inverse problem in remote sensing image processing. In recent years, sparse optimization-based hyperspectral image denoising methods have achieved great success, but still leave many key issues to be tackled, such as inadequate adaptivity of optimization models, low precision of solving algorithms, lack of theoretical support, and so on. This project will develop sparse optimization tools to provide highly effective mathematical models and solving algorithms for mixed noise removal in hyperspectral images, with theoretical support. Specifically, (1) investigate methods and theories for data-driven low-rank tensor modeling of hyperspectral images, by developing characterization and metric for tensor low-rankness; (2) investigate methods and theories for high-accuracy sparse modeling of mixed noise, based on its statistical properties and structural features; (3) design efficient solving algorithms for the proposed models, and establish their theoretical properties. This project will improve the performance of hyperspectral image denoising, and enrich theories and methods in sparse optimization.

受成像过程中硬件设备与环境条件所限，高光谱图像不可避免地被噪声污染，且噪声通常源自多种成份混合，使图像视觉质量与应用价值大为降低。高光谱图像去噪旨在根据带噪图像估计真实图像，是遥感图像处理领域中基础而重要的反问题。近年来，基于稀疏优化的高光谱图像去噪方法取得了巨大成功，然而仍存在诸多关键问题亟待解决，如优化模型普适性不足、求解算法精度偏低、理论支持相对薄弱等。本项目拟通过发展稀疏优化工具，为解决高光谱图像混合噪声去除问题提供高效的数学模型与求解算法，并提供理论支持。具体包括：（1）发展张量低秩性刻画与度量，研究数据驱动的高光谱图像低秩张量建模方法及理论；（2）基于噪声统计性质与结构特征，研究混合噪声的高精度稀疏建模方法及理论；（3）针对所建模型设计高效求解算法，分析算法的理论性质。拟开展的研究将提升高光谱图像去噪的精度与性能，丰富稀疏优化的理论与方法。

高光谱图像去噪的目标是根据受噪声污染的图像估计反映实际场景的真实图像，对提升高光谱图像的视觉质量与应用价值具有重要意义。本项目面向高光谱图像去噪问题，以“先验导向-模型建立-算法设计-实验验证”为研究主线，提出了一系列行之有效的高光谱图像去噪方法。主要研究成果包括：（1）基于Tucker张量低秩逼近与非独立同分布混合Gaussian噪声建模，在变分Bayesian框架下提出高光谱图像去噪模型及求解算法；（2）结合Kronecker基底张量低秩性度量、空间-光谱域卷积神经网络、稳健噪声建模，在最大后验估计框架下提出高光谱图像去噪模型与求解算法；（3）项目组还拓展研究了高维可视化数据复原、张量修补等相关问题。本项目的研究成果有助于提升高光谱图像去噪的求解效果，丰富稀疏优化与机器学习的理论与方法。在项目资助期间，项目组共发表SCI期刊论文12篇。