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Fast Fusion of Multi-band Images: A Powerful Tool for Super-resolution

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Hyperspectral (HS) imaging, which consists of acquiring a same scene in several hundreds of contiguous spectral bands (a 3D data cube), has opened a new range of relevant applications, such as target detection [Manolakis and Shaw, 2002], classification [C.I Chang, 2003] and spectral un mixing [Bioucas-Dias et al., 2012]. However, while HS sensors provide abundant spectral informa- tion, their spatial resolution is generally more limited. Thus, fusing the HS image with other highly resolved images of the same scene, such as multispectral (MS) or panchromatic (PAN) images is an interesting problem, also known as multi-resolution image fusion [Amro et al., 2011] (Fig. 1). From an application point of view, this problem is also important as motivated by recent national programs, e.g., the Japanese next-generation space-borne hyperspectral image suite (HISUI), which fuses co-registered MS and HS images acquired over the same scene under the same conditions Bayesian fusion allows for an intuitive interpretation of the fusion process via the posterior distribution. Since the fusion problem is usually ill-posed, the Bayesian methodology offers a convenient way to regularize the problem by defining appropriate prior distribution for the scene of interest.

In this work, a new multi-band image fusion algorithm to enhance the resolution of HS image has been proposed. By exploiting intrinsic properties of the blurring and down-sampling matrices, a much more efficient fusion method has been developed thanks to a closed-form solution for the Sylvester matrix equation associated with maximizing the likelihood. The main contribution of this fusion scheme is that it gets rid of any simulation-based or optimization-based algorithms which are quite time consuming. Coupled with the alternating direction method of multipliers and the block coordinate descent, the proposed algorithm can be easily generalized to incorporate different priors or hyper-priors for the fusion problem, allowing for Bayesian estimators. This method has been applied to both the fusion of MS and HS images and to the fusion of PAN and HS images. We have tested the proposed algorithm in both synthetic data and real data. Results show that the proposed algorithm compares competitively with existing algorithms with the advantage of reducing the computational complexity significantly.

This talk is part of the Machine Learning Reading Group @ CUED series.

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