It is worth mentioning that the self-attention module of each conversion block in the deep learning model M1 may use a multi-head self-attention mechanism, and may include the intra-histogram self-attention module and the inter-histogram self-attention module sequentially connected. It should be noted that the self-attention module SA1 and the multilayer perceptron module CF1 of each encoding block and each decoding block operate in the same manner.

FIG. 5 is a schematic diagram of a self-attention module according to an embodiment of the disclosure. Referring to FIG. 5, the self-attention module SA1 may include the intra-histogram self-attention (Intra-HSA) module SA1_1 and the inter-histogram self-attention (Inter-HSA) module SA1_2. The output of the intra-histogram self-attention module SA1_1 is connected to the input of the inter-histogram self-attention module SA1_2. The multiple histogram features input to the intra-histogram self-attention module SA1_1 are respectively feature matrices of 1*M, and each histogram feature input to the intra-histogram self-attention module SA1_1 includes M feature values. Taking FIG. 4 as an example, the C histogram features input to the intra-histogram self-attention module SA1_1 of the encoding block E1 are respectively feature matrices of 1*N and each includes N feature values. The 2C histogram features input to the intra-histogram self-attention module SA1_1 of the encoding block E2 are respectively feature matrices of 1*N/2 and each includes N/2 feature values.

In FIG. 5, the intra-histogram self-attention module SA1_1 may generate multiple intra-histogram self-attention features Y_intrabased on one feature value corresponding to one position token. That is, the token size used by the self-attention module SA1_1 in the histogram is 1*1. In detail, the intra-histogram self-attention module SA1_1 may firstly perform normalization 51 on the input multiple histogram features X, so as to generate multiple normalized histogram features X^norm. Afterwards, the intra-histogram self-attention module SA1_1 may perform intra-histogram self-attention processing 52 according to the normalized multiple histogram features X^norm. The intra-histogram self-attention module SA1_1 may use a multi-head self-attention mechanism to perform intra-histogram self-attention processing 52. However, the disclosure does not limit the number of heads of the multi-head self-attention mechanism, which may be set according to actual needs. For each histogram feature X^norm, the processor 120 may divide a single histogram feature X^norminto multiple tokens, and these position markers respectively correspond to a feature value.

Thus, the processor 120 may calculate the query matrix, key matrix, and value matrix of each head for each feature value in each histogram feature X^norm, to redistribute the weights of each feature value in each histogram feature X^norm. Specifically, the processor 120 may calculate the correlation between each feature value and other feature values in a certain histogram feature X^norm, to redistribute the weights of each feature value in the histogram feature X^norm. Therefore, the processor 120 may generate multiple attention vectors Y1 respectively corresponding to the normalized histogram features X^normthrough the intra-histogram self-attention processing 52. Afterwards, the intra-histogram self-attention module SA1_1 may perform element-wise addition processing 53 on the input histogram feature X and the attention vector Y1 to obtain multiple intra-histogram self-attention features Y_intra.

Next, the intra-histogram self-attention features Y_intraare input to the inter-histogram self-attention module SA1_2. The multiple histogram self-attention features Y_intrainput to the inter-histogram self-attention module SA1_2 aer respectively feature matrices of 1*M. The inter-histogram self-attention module SA1_2 may generate multiple inter-histogram self-attention features Y_interbased on one intra-histogram self-attention feature Y_intracorresponding to one token. That is, the token size used by the inter-histogram self-attention module SA1_2 is 1*M. In detail, the inter-histogram self-attention module SA1_2 may firstly perform normalization 51 the input multiple intra-histogram self-attention features Y_intrato generate multiple normalized histogram features Y^norm.

Afterwards, the inter-histogram self-attention module SA1_2 may perform inter-histogram self-attention processing 55 according to the normalized multiple histogram features Y^norm. The inter-histogram self-attention module SA1_2 may use a multi-head self-attention mechanism to perform inter-histogram self-attention processing 55. However, the disclosure does not limit the head number of the multi-head self-attention mechanism, which may be set according to actual requirements. Different from the intra-histogram self-attention module SA1_1, the inter-histogram self-attention module SA1_2 respectively uses each histogram feature Y^normas a token to perform inter-histogram self-attention processing 55. These position tokens respectively correspond to a histogram feature Y^normof 1*M.

Thus, the processor 120 may calculate the query matrix, the key matrix, and the value matrix of each head respectively for each histogram feature Y^norm, to redistribute the weights of each histogram feature Y^norm. Specifically, the processor 120 may calculate the correlation between each histogram feature Y^normand other histogram features, to redistribute the weights of each histogram feature Y^norm. Therefore, the processor 120 may generate multiple attention vectors Y2 respectively corresponding to the normalized histogram features Y^normthrough the inter-histogram self-attention processing 55. Afterwards, the inter-histogram self-attention module SA1_2 may perform element-wise addition processing 56 on the inter-histogram self-attention feature Y_intraand the attention vector Y2 to obtain multiple inter-histogram self-attention features Y_inter. These inter-histogram self-attention features Y_interare fed into the multilayer perceptron module CF1.

In some embodiments, the multilayer perceptron module CF1 may be a 2D convolutional feed-forward network (2D-CFF). In addition to convolution processing, the multilayer perceptron module CF1 may also include normalization processing, linear projection processing, and reshape processing, etc.

In some embodiments, the processor 120 may train the deep learning model M1 based on the weighted sum of multiple loss functions. The processor 120 may determine whether the learning of the deep learning model M1 is completed according to the weighted sum of these loss functions. Moreover, the processor 120 may adjust the weight parameters of the deep learning model M1 one by one from the back to the front in a backward transfer manner according to the weighted sum of these loss functions.

In some embodiments, the aforementioned loss functions may include a first loss function, a second loss function, and a third loss function. The first loss function calculates the first loss value [Image Omitted] _hisaccording to the reference histogram of the real reference image and the optimized histogram H_2. The second loss function calculates the second loss value _hmaccording to the target image Img_s and the real reference image through the error calculation method. The third loss function calculates the third loss value [Image Omitted] _h1according to the target image Img_s and the real reference image through another error calculation method.

In some embodiments, during the model training process, after the optimized histogram H_2 is generated, the first loss value [Image Omitted] _hismay be calculated using the following Formula (1) of the first loss function. Referring to Formula (1), it may be seen that the processor 120 may calculate the mean absolute error (MAE) between the optimized histogram H_2 and the reference histogram to generate the first loss value [Image Omitted] _his. In addition, in some embodiments, the processor 120 may calculate the first loss value _hisaccording to respective weight values of multiple color channels.

ℒ
his

=

1
N

⁢

∑

j
=
0

2

w
j

⁢

∑

i
=
0

N
-
1

(

H
ij
out

-

H
ij
ref

)

2

Formula
⁢

(
1
)

Where

H
ij
out

represents the optimized histogram H_2;

H
ij
ref

represents a reference histogram of the real reference image; N represents the number of statistical bins of the histogram; j is the index of multiple color channels; i is the index of multiple statistical bins (also may be regarded as multiple color channel values) in the histogram; w_jrepresents the weight value corresponding to the j^thcolor channel. In some embodiments, the weight value of the red channel among the color channels may be set to be greater than the weight values of other color channels. Here, assuming that j=0 represents the red channel, j=1 represents the green channel, and j=2 represents the blue channel, then the weight value of the red channel may be greater than the weight value of the green channel and the weight value of the blue channel. The reason for setting these weight values in this way is that underwater images often have the highest distortion of the red channel value, so it is expected that the deep learning model M1 may restore the red channel value as much as possible.

In some embodiments, during the model training process, after the target image Img_s is generated, the second loss value [Image Omitted] _hmmay be calculated using the following Formula (2) of the second loss function. Referring to Formula (2), it may be seen that the processor 120 may calculate the mean absolute error (MAE) between the target image Img_s and the real reference image to generate the second loss value [Image Omitted] _hm.

ℒ
hm

=

1
HWC

⁢



S
-
T



1

Formula
⁢

(
2
)

Where S represents the target image Img_s; T represents the real reference image; H represents the image height of the target image Img_s and the real reference image; W represents the image width of the target image Img_s and the real reference image; C represents the number of color channels.

In addition, in this embodiment, during the model training process, after the target image Img_s is generated, the third loss value [Image Omitted] _hlmay be calculated using the following Formula (3) of the third loss function. Here, the third loss value _hlmay be a high-order feature loss based on the VGG-19 network. For details about calculating the high-order feature loss based on the VGG-19 network, reference may be made to relevant technical literature (e.g., as “J. Deng, W. Dong, R. Socher, L. J. Li, K. Li, and L. Fei-Fei, ‘Imagenet: A large-scale hierarchical image database,’ in Proc. Conf. Computer Vision and Pattern Recognition, 2009.”), and are not repeated herein.

ℒ
hl

=