ISPRS Int. J. Geo-Inf. 2020, 9, 242 5 of 21
1
2
3
4
5
0
1
2
3
4
BN-ReLu
-Conv
BN-ReLu
-Conv
BN-ReLu
-Conv
BN-ReLu
-Conv
Transition Layer
Input
Figure 1.
A five-layer dense block with a growth rate of
k =
4. All preceding feature-maps are the
input data of each layer.
In a dense block, the feature map
x
l
of the
l
th
layer can be achieved from the feature maps
x
0
, x
1
, ..., x
l−1
, which is calculated and expressed as follows:
x
l
= H
l
([x
0
, x
1
, ..., x
l−1
]) (1)
where
x
0
, ...,
x
l−1
are the result of tensor stitching of feature maps from the zeroth layer to the
(l −
1
)
th
layer, which are the input data of the
l
th
layer. The standard
H
l
(
.
)
is a compound function consisting of
three successive operations: BN, ReLU, and the convolution kernel with a size of 3
×
3. Each function
H
l
(
.
)
outputs kfeature maps, so there are
k(l −
1
) + k
0
input feature maps in the
l
th
layer, where
k
0
is the channel number of the first input layer. In order to control the width of the network and
improve the efficiency of the parameters,
k
is generally limited to a smaller integer. This control of the
growth rate can not only reduce the parameters of the DenseNet, but also ensure the performance of
the DenseNet.
In addition, although each layer only outputs feature maps, a large amount of feature maps
(
k(l −
1
) + k
0
) is the input data of each layer. To solve this problem, a bottleneck layer is added to
the DenseNet architecture. That is to say, a 1
×
1 convolution operation is introduced before each
3
×
3 convolution operation to reduce the dimension. This network architecture with bottleneck
layers is called DenseNet-B. At the same time, for simplifying the architecture, a compression factor
θ
(0
≤ θ ≤
1) can be added in the transition layer to decrease the output of the feature maps. If the
output of the dense blocks includes feature maps, the subsequent transition layer will output
θ ∗ m
feature maps.
θ =
1 indicates that the number of feature maps passing through the transition layer
remains unchanged. The network architecture containing the compression factor is called DenseNet-C.
The network architecture including the bottleneck layer and compression factor is called DenseNet-BC.
DenseNet-BC uses the bottleneck layer and the compression factor to narrow the network and reduce
the network parameters, effectively suppressing over-fitting. Moreover, the experimental results show
that DenseNet-BC using the bottleneck layer and compression factor can obtain a better fused image
than DenseNet.
3. Methodology
Some studies have demonstrated that deeper CNN architectures can extract more feature
information, but with the deepening of the network architecture, training will become increasingly
difficult. In view of the particularities of pan-sharpening, more feature information needs to be
extracted to ensure the preservation of spectral information and the enhancement of spatial resolution.
Therefore, a new pan-sharpening method is proposed in this paper that employs the advantages of
DenseNet to mitigate gradient disappearance, improve feature propagation, and promote feature reuse.
In this way, the fused image can retain the original image spectrum information and enhance its spatial
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