Fusing a low-resolution hyperspectral image (HSI) and a high-resolution multispectral image (MSI) of the same scene leads to a super-resolution image (SRI), which is information rich spatially and spectrally. In this paper, we super-resolve the HSI using the graph Laplacian defined on the MSI. Unlike many existing works, we don't assume prior knowledge about the spatial degradation from SRI to HSI, nor a perfectly aligned HSI and MSI pair. Our algorithm progressively alternates between finding the blur kernel and fusing HSI with MSI, generating accurate estimations of the blur kernel and the SRI at convergence. Experiments on various datasets demonstrate the advantages of the proposed algorithm in the quality of fusion and its capability in dealing with unknown spatial degradation.
The spectral degradation from the SRI to the MSI can be modeled by a weighted summation of the hyperspectral bands according to the spectral responses of the multispectral sensor. STEREO assumes the availability of such information. HySure provides a way to estimate the spectral response. However, it still needs the spectral coverage information of the multispectral bands. So does dTV, which uses the directional total variation @cite_10 defined on each of the multispectral bands to super-resolve the bands of the HSI within the spectral coverage.
@cite_10
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Magnetic resonance imaging (MRI) is a versatile imaging technique that allows different contrasts depending on the acquisition parameters. Many clinical imaging studies acquire MRI data for more than one of these contrasts---such as, for instance, @math and @math weighted images---which makes the overall scanning procedure very time consuming. As all of these images show the same underlying anatomy, one can try to omit unnecessary measurements by taking the similarity into account during reconstruction. We will discuss two modifications of total variation---based on (i) location and (ii) direction---that take structural a priori knowledge into account and reduce to total variation in the degenerate case when no structural knowledge is available. We solve the resulting convex minimization problem with the alternating direction method of multipliers which separates the forward operator from the prior. For both priors the corresponding proximal operator can be implemented as an extension of the fast gradient...