IEEE Geoscience and Remote Sensing Magazine - March 2022 - 16

(a)
(b)
(c)
(d)
(e)
FIGURE 2. The false color images of the denoising results. (a) An original HS, (b) a simulated noise image, (c) an SRROLD, (d) a TensorDL,
and (e) an LRTA.
preserving its spectral information. HS image superresolution
is rooted in pansharpening [179], [180], typically
referred to as PAN/MS fusion. To date, there have been a
number of HS image superresolution algorithms, and the
methods based on sparse and low-rank characteristics
have been attracting ever-increasing attention in recent
years [181]-[187].
OBSERVATION MODEL
Let the desired HRHS image be denoted as ,X an LRHS
image represented as ,Y and Z indicated as the HR MS or
PAN image. The LRHS image can be regarded as the spatialdegradation
version of the HRHS, and the HSMS or PAN is
the spectral-degradation version of the HRHS image. The
observation model is
Y XBS NY
ZC ,XNZ
=+
=+
(8)
(9)
where S denotes the spatial downsampling operation, B is
the spatial blurring operation, and C represents the spectral
downsampling matrix and is generally obtained based on
a spectral response function. NY
and NZ
MATRIX-BASED METHODS
LINEAR SPECTRAL MIXING MODEL-BASED METHODS
The linear mixing model (LMM)-based methods are the
most popular and widely studied HS superresolution
TABLE 2. A QUANTITATIVE EVALUATION OF
THE DENOISING METHODS.
METHODS
SRROLD
LRTA
TensorDL
SAM
2.48
1.35
0.72
ERGAS
3.17
1.42
0.81
RMSE
60
33.34
20.28
CC
0.985
0.996
0.998
TIME (s)
80.65
98.24
156.32
represent noise.
techniques [188]-[195]. It is assumed that mixed pixels can
be represented as a linear combination of endmembers:
XD ,ANX
=+
X , and NX
denotes the noise.
(10)
where D is the endmember matrix, A is the abundance matrix
for each pixel of
Substituting (10) into the observation model defined by
(8) and (9) results in
YDABSN DA
ZCDA ND AZZ
=+ .
=+ .
where AY
and DZ
YY
,
(11)
(12)
are the spatial-degradation abundance
matrix and spectral-degradation endmember matrix,
respectively.
For the LMM-based methods, the idea of using unmixing
for HS fusion was proposed in the early stage. In [51],
LRHS was first unmixed into endmembers and abundances,
and abundance maps were then fused with high-resolution
data. Although this approach did not focus on the
estimation of HRHS data, the idea of using LMM for data
fusion was physically reasonable and effective for MS/HS
fusion. To the best of our knowledge, Kawakami et al. [52]
first recommended HS/MS [red-green-blue (RGB)] fusion
via matrix factorization. The scheme was divided into two
stages: the spectral basis obtained based on the unmixing
of the HS image and the conjunction with the RGB input to
produce the desired HRHS image.
Yokoya et al. [53] advised the popular coupled NMF
(CNMF) fusion method for HS and MS data. It estimated
the endmembers of LRHS and the abundances of high- spatial-resolution
MS (HRMS) images iteratively. Bendoumi
et al. [54] improved the CNMF-based method by dividing
whole images into several subimages. Lin et al. [55] proposed
a convex optimization-based CNMF algorithm for
HS/MS fusion by incorporating sparsity- promoting regularization
and the sum-of-squared-distances regularizer.
16
IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE MARCH 2022
IEEE Geoscience and Remote Sensing Magazine - March 2022

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