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Fast Joint Multiband Reconstruction from Wideband Images Based on Low Rank Approximation
IEEE Transactions on Computational Imaging ( IF 5.4 ) Pub Date : 2020-01-01 , DOI: 10.1109/tci.2020.2998170
M. Amine Hadj-Youcef , Francois Orieux , Alain Abergel , Aurelia Fraysse

Multispectral imaging systems are increasingly used in many scientific fields. However multispectral images generally present spectral and spatial limitations: the spectral information within each band is lacking because of spectral integration over the band, and the spatial resolution is limited due to the spatial convolution by spectrally variant Point Spread Functions which introduce a spatial variant blur. To address the ill-posed inverse problem of reconstruction from wideband images, we propose a new approach combining a precise instrument model for the degraded multispectral images together with a spectral approximation on a low-rank subspace of the object. The reconstruction is based on the minimization of a convex objective function composed of a data fidelity and an edge-preserving regularization term. The proposed half-quadratic algorithm alternates between the minimization of a quadratic and a separable problem, and we show that both closed-form solutions are available and tractable. Therefore, even with a non-stationary data model, the algorithm is very fast and results are obtained in a few seconds. Several tests are performed for multispectral data to be taken by MIRI, the mid-infrared imager of the future James Webb Space Telescope (JWST). The reconstruction results show a significant increase in spatial and spectral resolutions compared to state-of-the-art methods. Our proposed algorithm allows us to recover the spectroscopic information contained in the wideband multispectral images and to provide hyperspectral images with a homogenized spatial resolution over the entire spectral range.

中文翻译:

基于低秩逼近的宽带图像快速联合多带重建

多光谱成像系统越来越多地用于许多科学领域。然而,多光谱图像通常存在光谱和空间限制:每个波段内的光谱信息由于波段上的光谱积分而缺乏,并且空间分辨率由于引入空间变体模糊的光谱变化点扩散函数的空间卷积而受到限制。为了解决宽带图像重建的不适定逆问题,我们提出了一种新方法,将退化的多光谱图像的精确仪器模型与对象低秩子空间的光谱近似相结合。重建基于由数据保真度和边缘保留正则化项组成的凸目标函数的最小化。所提出的半二次算法在二次和可分离问题的最小化之间交替,我们表明这两种封闭形式的解决方案都是可用且易于处理的。因此,即使是非平稳的数据模型,该算法也非常快,几秒钟就可以得到结果。未来詹姆斯韦伯太空望远镜 (JWST) 的中红外成像仪 MIRI 对多光谱数据进行了多项测试。重建结果显示,与最先进的方法相比,空间和光谱分辨率显着提高。我们提出的算法使我们能够恢复宽带多光谱图像中包含的光谱信息,并在整个光谱范围内提供具有均匀空间分辨率的高光谱图像。
更新日期:2020-01-01
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