IEEE Geoscience and Remote Sensing Magazine - June 2017 - 33

Wei et al. developed a Bayesian HS-MS fusion methodology using both a subspace transformation and a regularization in the fusion problem to cope with the ill-posed inverse
problem. The problem formulation is based on the information of the prior distribution in the observed scene, such as
Gaussian or sparsity-promoted Gaussian [38], [57], [58]. Similar to MAP-SMM, the optimization problem was formulated
on a subspace corresponding to the principal components
of the input HS data. Recently, a Sylvester-equation-based
explicit solution was integrated into the Bayesian HS-MS fusion methodology. Called the fast fusion based on Sylvester equation (FUSE) [59], it significantly decreased the computational
complexity while achieving the same performance as the
previous Bayesian HS-MS fusion algorithms. Simões et al.
proposed a method called HS Superresolution (HySure) based
on vector-total-variation-based regularization of the spatial
distribution of subspace coefficients, where the subspace can
be defined either by singular value decomposition (SVD) or
by endmember spectral signatures [39].
SELECTED HYPERSPECTRAL AND MULTISPECTRAL
DATA-FUSION METHODS
In this comparative study, ten HS-MS fusion methods are
selected to represent the state of the art in HS-MS fusion,
including both established methods and recently published
ones. All of the methods under comparison correspond to
at least one of the following four categories: 1) CS, 2) MRA,
3) unmixing, and 4) Bayesian-based approaches. The unmixing and Bayesian-based methods fall into the same
broader category of subspace-based methods. Figure 3(a)
depicts those categories and the correspondence with the
investigated methods. Flowcharts describing the fusion
processes of the CS, MRA (hypersharpening), and subspace-based approaches are illustrated in Figure 3(b)-(d),
respectively. The properties of the ten methods are summarized in Table 1.
Gram-Schmidt adaptive (GSA) [21] is adopted as the
representative CS-based pan-sharpening method. Two
MRA-based pan-sharpening methods, i.e., smoothing filtered-based intensity modulation (SFIM) [22] and generalized Laplacian pyramid (GLP) [23], are adapted to HS-
MS fusion via hypersharpening. CNMF [48], HySure [39],
Akhtar's method [50], and Lanaras's method [54] represent
the unmixing-based approach. [Akhtar's and Lanaras's
methods are referred to as ECCV'14 (for the 2014 European
Conference on Computer Vision) and ICCV'15 (for the 2015
International Convention on Computer Vision), respectively.] MAP-SMM [36] and two versions of FUSE [59] are based
on Bayesian probability. Apart from the Bayesian-based
methods, which use PCA for subspace transformation, the
unmixing-based approaches can also be considered as subspace methods, because the dimension of the space spanned
by the endmembers in these methods is generally smaller
than the dimension spanned by the unknown high-resolution HS image. All ten methods are briefly described in the
following sections.
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GSA
Aiazzi et al. improved CS pan-sharpening methods by taking into account the influence of SRF on the fusion procedure [21]. In the general CS scheme, a low-resolution image
is sharpened by adding spatial details obtained by multiplying the difference between a high-resolution image and a
synthetic intensity component by a band-wise modulation
coefficient. The improvement lies in computing the synthetic intensity component by performing a linear regression between a high-resolution image and lower-resolution
bands to mitigate spectral distortion. GSA integrates this
technique into the Gram-Schmidt algorithm [20]. The
most straightforward way to apply GSA to HS-MS data fusion is to construct multiple image sets for pan-sharpening subproblems, where each set is composed of one MS
band and corresponding HS bands grouped by correlationbased clustering.
SFIM-HS
Based on a simplified model for solar radiation and landsurface reflection, SFIM sharpens the low-resolution image by multiplying an upscaled lower-resolution image by
a ratio between a higher-resolution image and its low-pass
filtered version on a pixel-by-pixel basis [22]. SFIM can be
performed on individual HS bands. A high-resolution image can be either a selected MS band based on correlation
analysis or a synthesized image obtained by a linear regression of MS bands via least squares methods. The latter is
referred to as hypersharpening in [32]. The hypersharpening
technique is adopted in this work. The SFIM hypersharpening method is denoted as SFIM-HS.
GLP-HS
In the GLP fusion scheme [23], spatial details of each lowresolution band are obtained as the difference between
a high-resolution image and its low-pass version multiplied by a gain factor, which can be computed either locally or globally. In this article, a global gain as given
in [32] is adopted. A Gaussian filter, matching the modulation transfer function of a lower-resolution sensor, is used
for low-pass filtering. As with SFIM, hypersharpening is
used here to effectively adapt the GLP fusion scheme
to HS-MS fusion. The GLP hypersharpening method is
referred to as GLP-HS.
CNMF
CNMF [48] alternately unmixes the HS and MS images
by NMF [60] to estimate the spectral signatures of endmembers and the high-resolution abundance maps, respectively. CNMF starts by unmixing the HS image using
VCA [61] to initialize the endmember signatures. Sensor
observation models that relate the two input images with
the relative sensor characteristics (i.e., SRF and PSF) are
built into the initialization of the MS signatures of endmembers and the low-resolution abundance maps to find
better local optima. The final high-resolution HS data are
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Table of Contents for the Digital Edition of IEEE Geoscience and Remote Sensing Magazine - June 2017