IEEE Geoscience and Remote Sensing Magazine - March 2023 - 52

with the assistance of MS images and generate final HS images
with high spatial resolution and original spectral resolution.
High-quality fused HS images benefit the in-depth
recognition of and insight to materials, which contributes
to many RS real applications, such as object classification
and change detection of wetlands and farms [182], [183],
[184], [185], [186], [187], [188].
Figure 20 depicts an HS-MS fusion process to generate
a high-spatial-spectral-resolution HS (HR-HS) image.
Suppose that a desired HR-HS image, low-resolution HS
(LR-HS) image, and high-resolution MS (HR-MS) image
is denoted by ,,
XY
!!
##
Hh Vv Bb&& &
RR and Z RHV b
HV Bh vB
##
!
##
(, ,), respectively. An LR-HS image is seen
as a spatially downsampled and blurred version of X , and
an HR-MS image is the spectrally downsampled version of
X . The two degradation models are expressed as follows:
YX RN() ()
()
33 h
ZGXN()
33 m
=+
=+
(53)
(54)
where the first and second F-norms are data fidelity
terms with respect to models (53) and (54) and ( )f X
represents the prior regularization pertinent to the desired
property on the HR-HS
X . In the following section,
we review currently advanced HS SR methods from two
categories: tensor decomposition and prior-based tensor
decomposition models.
where RB ,K= B denotes a convolution blurring operation,
K is a spatial downsampling matrix, and G represents a
spectral response function of an MS image sensor, which
can be regarded as a spectral downsampling matrix; Nh
and Nm
stand for noise.
According to [189], [190], and [191], R and G are
assumed to be given in advance of solving the HS
SR problem:
min -+ -+ (55)
X
YX RZ GX()
() ()
()
33 FF
2
33 x ()f X
2
PTAPCA-TLRR
1
0.8
0.6
0.4
0.2
AUC: 0.9946
(a)
1
PTA
0.8
0.6
0.4
0.2
AUC: 0.9031
(b)
1
PTA
AUC: 0.9509
(c)
FIGURE 19. Original HS images, ground truth maps, detection maps, and area under the receiver operating characteristic curve (AUC)
curves of PTA on different datasets: (a) San Diego, (b) Airport-1, and (c) Airport-2.
52
IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE MARCH 2023
AUC: 0.9697
0.8
0.6
0.4
0.2
PCA-TLRR
AUC: 0.9478
1E-4 1E-3 0.01
False Alarm Rate
0.1 1
PCA-TLRR
AUC: 0.9957
PTA
PCA-TLRR
1E-4 1E-3 0.01
False Alarm Rate
0.1 1
1E-4 1E-3 0.01 0.1 1
False Alarm Rate
Probability of Detection
Probability of Detection
Probability of Detection

IEEE Geoscience and Remote Sensing Magazine - March 2023

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