IEEE Geoscience and Remote Sensing Magazine - September 2015 - 29

Bayesian one, where the target image is estiTABLE 1. SUMMARY OF THE DIFFERENT CLASSES OF METHODS
mated by maximizing the posterior probabilCONSIDERED IN THIS PAPER. WITHIN PARENTHESES, WE INDICATE
ity density of the full resolution image. The
THE ACRONYM OF EACH METHOD, FOLLOWED BY THE NUMBER OF
works [20], [21], [22] are representative of the
THE SECTION IN WHICH THAT METHOD IS DESCRIBED.
Bayesian and variational classes. As indicated
METHODS ORIGINALLY DESIGNED FOR MS PANSHARPENING
in Table 1, the CS, MRA, and Hybrid classes
Component substitution (CS, II-A)
Multiresolution analysis (MRA, II-B)
of methods are detailed in Sections II-A, IIPrincipal Component Analysis (PCA, II-A-1) Smoothing filter-based intensity
B, and II-C, respectively. Herein, the Bayesian
Gram Schmidt (GS, II-A-2)
modulation (SFIM, II-B-1)
class is not addressed in the MS+PAN context.
Laplacian pyramid (II-B-2)
It is addressed in detail, however, in Section
Bayesian methods
Hybrid methods (II-C)
Not discussed in this paper
Guided Filter PCA (GFPCA)
II-D in the context of HS+PAN fusion.
With the increasing availability of HS sysMETHODS ORIGINALLY DESIGNED FOR HS PANSHARPENING
tems, the pansharpening methods are now exBayesian Methods (II-D)
Matrix Factorization (II-E)
tended to the fusion of HS and panchromatic
Naive Gaussian prior (II-D-1)
Coupled Non-negative Matrix
images [23], [24], [25], [26]. Pansharpening of
Sparsity promoting prior (II-D-2)
Factorization (CNMF)
HS images is still an open issue, and very few
HySure (II-D-3)
methods are presented in the literature to admethods under study, i.e., CS, MRA, hybrid, Bayesian, and
dress it. The main advantage of HS image with respect to MS
matrix decomposition approaches. Section III summarizes
one is the more accurate spectral information they provide,
the quality assessment measures that will be used to assess
which clearly benefits many applications such as unmixing
the image fusion results. Experimental results are presented
[27], change detection [28], object recognition [29], scene
in Section IV. Conclusions are drawn in Section V.
interpretation [30] and classification [31]. Several of the
methods designed for HS pansharpening were originally
II. HYPERSPECTRAL PANSHARPENING TECHNIQUES
designed for the fusion of MS and HS data[32]-[36], the MS
This section presents some of the most relevant methods
data constituting the high spatial resolution image. In this
for HS pansharpening. First, we focus on the adaptation of
case, HS pansharpening can be seen as a particular case,
the popular CS and MRA MS pansharpening methods for
where the MS image is composed of a single band, and thus
HS pansharpening. Later, we consider more recent methods
reduces to a PAN image. In this paper, we divide these methbased on Bayesian and matrix factorization approaches. A
ods into two classes: Bayesian methods and matrix factortoolbox containing MATLAB implementations of these alization based methods. In Section II-D, we briefly present
gorithms can be found online1.
the algorithms of [33], [36], and [35] of the former class and
in Section II-E the algorithm of [32] of the latter class.
Before presenting the different methods, we introduce
As one may expect, performing pansharpening with
notation used along the paper. Bold-face capital letters refer
HS data is more complex than performing it with MS data.
to matrices and bold-face lower-case letters refer to vectors.
Whereas PAN and MS data are usually acquired almost in
The notation X k refers to the kth row of X. The operator () T
the same spectral range, the spectral range of an HS image
denotes the transposition operation. Images are representnormally is much wider than the one of the corresponded by matrices, in which each row corresponds to a specing PAN image. Usually, the PAN spectral range is close to
tral band, containing all the pixels of that band arranged in
the visible spectral range of 0.4−0.8nm (for example, the
lexicographic order. We use the following specific matrices:
advanced land imager-ALI-instrument acquires PAN data
◗ X = 6x 1, f, x n@ ! R m m # n represents the full resolution
in the range 0.48−0.69nm). The HS range often covers the
target image with m m bands and n pixels; W
X represents
visible to the shortwave infrared (SWIR) range (for examan estimate of that image.
ple, Hyperion acquires HS data in the range 0.4−2.5nm, the
◗ YH ! R m m # m, YM ! R n m # n, and P ! R 1 # n represents, rerange 0.8−2.5nm being not covered by the PAN data). The
spectively, the observed HS, MS, and PAN images, nm
difficulty that arises, consists in defining a fusion model
denoting the number of bands of the MS image and m
that yields good results in the part of the HS spectral range
the total number of pixel in the YH image.
that is not covered by PAN data, in which the high resoluY H ! R mm # n represents the HS images YH interpolated at
◗ L
tion spatial information is missing. This difficulty already
the scale of the PAN image.
existed, to some extent, in MS+PAN pansharpening, but it
We denote by d = m/n the down-sampling factor, asis much more severe in the HS+PAN case.
sumed to be the same in both spatial dimensions.
To the best of the authors' knowledge, there is currently
no study comparing different fusion methods for HS data,
A. Component SubStitution
particularly on datasets where the spectral domain of the
CS approaches rely upon the projection of the higher
HS image is larger than the one of the PAN image. This
spectral resolution image into another space, in order to
work aims at addressing this specific issue. The remainder
1http://openremotesensing.net
of the paper is organized as follows. Section II reviews the
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Table of Contents for the Digital Edition of IEEE Geoscience and Remote Sensing Magazine - September 2015