IEEE Geoscience and Remote Sensing Magazine - March 2019 - 23

2D wavelet coefficients for the ith fused component. In
[143], the sparse and low-rank component analysis [150],
[151] was used to estimate W and V, given by
1
argmin W,V 2 F - DWV T

2
F

+ m / w (i)
i =1

s.t. V T V = I r . (4)

Note that the estimated fused features are given by
t . The fused features are expected to be sparse
Ftfused = DW
in the 2D wavelet basis. Therefore, in [150], to enforce
the sparsity, an , 1 penalty on the wavelet coefficients W r
was used. As a result, promoting sparsity on the fused
feature improves the SNR and final classification accuracies. The results for this approach can be found in Table 2
as SLRCA.
COMPOSITE KERNEL
Composite kernel-based fusion techniques partially overcome the shortcomings of filtering methods by designing
several kernels to handle spectral, spatial, and elevation
features in feature space [152]. In [139], spectral, spatial
(e.g., EPHSIh, and elevation (e.g., EPlidar h information were
fused using a local-region filter and composite kernels.
The results for this scheme can be found in Table 2 as
FFCK. The main shortcoming here was that the obtained
classification accuracy was dramatically influenced by the
μ parameter, which represents the amount of tradeoff between the spectral and spatial elevation kernels. To solve
this issue, in [140], a fusion approach was introduced

capable of exhibiting substantial flexibility to integrate
different feature sets without requiring any regularization
parameters. That procedure was based on APs and multiple-feature learning using the subspace multinomial logistic regression (MLRsub) classifier. The results are shown as
MLRsub in Table 2.
A joint sparse representation classification technique
was proposed in [141] for multisource data fusion where the
multisource data were weighted to have better sparse representation. The core idea of this scheme was based on sparse
representation classification. Then, the minimum distance
(in the sense of the , 2 norm) between each sample and its
sparse representation using subdictionaries (containing
only training samples for one class) was used to allocate
the class labels. However, in [141] the regularization term
was weighted according to the data sources. Moreover, the
method was translated into the kernel space using kernel
tricks. The results for the composite kernel version can be
found in Table 2 as ALWMJ-KSRC.
DEEP LEARNING
Hyperspectral imaging often exhibits a nonlinear relation
between the captured spectral information and the corresponding material. This nonlinear relation is the result of
several factors, such as undesired scattering from other objects in the acquisition process, different atmospheric and
geometric distortions, and intraclass variability of similar
objects. This nonlinear characteristic is magnified when

HSI
DR2
MPHSI or APHSI or EPHSI

Feature Fusion
DR1
DR2
Filtering

MPLidar or APLidar or EPLidar

Lidar
Filtering

DR2

FiGUrE 9. Low-rank models. The use of DR2 is optional. However, the studies investigated in [136], [138], [142], and [143] recommend the

consideration of this extra step to provide more accurate classification maps.
march 2019

ieee Geoscience and remote sensing magazine

IEEE Geoscience and Remote Sensing Magazine - March 2019

Table of Contents for the Digital Edition of IEEE Geoscience and Remote Sensing Magazine - March 2019