A learning image compression method based on side information autoregression

Abstract

The application discloses a learning image compression method based on side information autoregression, takes a natural image x as input, obtains a compact latent representation y, and directly encodes y when compressing the image x; takes the latent representation y as input, obtains side information z, and the side information z is used to provide prior guidance for entropy coding of the latent representation y; uses a side information autoregression module to estimate a probability distribution of the side information z, and forms a compressed bit stream of the side information z after entropy coding; sends the quantized side information z into a hyper-combination transformation module to obtain hyper-prior information of the latent representation y; estimates a probability distribution of the latent representation y by using a context of the latent representation y and the hyper-prior information, forms a compressed bit stream of the latent representation y after entropy coding; and sends the quantized latent representation y into a combination transformation module to obtain a final reconstructed image. The reconstructed image obtained by the application performs better in structural similarity objective indicators, and the texture details of the reconstructed image obtained in subjective quality are better reconstructed.

Description

Technical Field

[0001] This invention belongs to the fields of computer vision and data compression technology, and is used in industries such as image compression and transmission. Specifically, it is a learning image compression method based on side information autoregression. Background Technology

[0002] The rapid development of the internet and computers has led to a continuous stream of massive amounts of image data. This poses significant challenges to image transmission and storage. Therefore, researchers have been searching for more efficient image compression methods to maintain higher image quality at the lowest possible bit rate. Traditional image coding schemes, such as JPEG, AVC, HEVC, and VVC, while achieving significant performance, suffer from suboptimal module integration; each component relies on manual design. This greatly limits the performance of traditional image compression codecs.

[0003] In recent years, significant progress has been made in learning-based image compression (LIC) models (proposed by Johannes Ballé, Li, Minnen, Hu, and others). In particular, some advanced methods (proposed by Minnen, Cheng, Gao, Zou, Chen, He, Jiang, Li, and others) have surpassed traditional image compression standards such as VVC. The end-to-end optimization capabilities of neural networks enable them to integrate and coordinate internal components under a unified objective, making learning-based image compression techniques a gradually emerging superior choice. Currently, most image compression models are built upon variational autoencoder frameworks and follow a fixed processing flow: transform, quantization, and entropy coding. In the transform stage, the original image is mapped to a latent representation and further quantized into discrete values. The entropy coding model is responsible for estimating the probability distribution of these discrete latent representations, and then using entropy coding tools to losslessly compress them into a bitstream. A major challenge in this process is how to more accurately estimate the conditional probability distribution of the latent representation using the entropy model.

[0004] State-of-the-art learning-based image compression models model redundant information within latent representations by integrating a super-prior module (Johannes Ballé et al.) and a context module (Minnen et al.). These additional modules are able to leverage conditional probabilities to model the correlations between latent representations.

[0005] Specifically, the researchers used a super-prior module to extract edge information from the latent representation, and then used this information as a super-prior in the entropy model to estimate the probability distribution of the latent representation.

[0006] On the other hand, the context module captures the correlation between the spatial and channel dimensions in the latent representation and uses previously decoded features and super-prior to predict the mean and variance of the Gaussian distribution of the currently decoded features.

[0007] In recent years, researchers have proposed various methods (Koyuncu, Liu, He, Qian, Jiang, Li, et al.) to improve the context module, but less attention has been paid to the super-prior module. The original Full Factor Density Model (FFDM), used to model the probability distribution of side information, is still widely used. By visualizing the side information of an FFDM-based model (Figure), we found that the vast majority of channels in the side information are invalid, with only a few channels containing valid information. We believe this is because FFDM relies on a simple assumption that all images share the same distribution within the same side information channels, and the features of different channels are considered independent. This assumption leads to the estimated side information entropy being significantly greater than the actual entropy. During the joint training of end-to-end models, the model tends to allocate more bits to the latent representation using a more accurate Gaussian density model, while allocating very little bit of bitrate to the side information. Figure 1 and 2 The image shows a visualization of Cheng's edge information. Taking Cheng as an example, out of 192 edge information channels, only five channels carry information. It's noteworthy that in the remaining 187 channels, each channel holds the same value across different images (e.g., ...). Figure 1 (As shown). This means that the edge information cannot retain enough useful information and cannot provide effective assistance in estimating the probability distribution of the latent representation. Summary of the Invention

[0008] In this invention, we discovered a common problem in existing learning-based image compression models: the potential of side information is not fully utilized. To overcome this deficiency, this invention provides a learning image compression method based on side information autoregression. During end-to-end learning image compression training, this method encourages the neural network to allocate more bitrate to side information. This allows the side information to retain richer contextual information, better guiding the probability estimation of latent representations and improving the overall performance of the entropy module in the compression model. Experimental results show that our component achieves a significant reduction in the latent representation bitrate with a small increase in the side information bitrate. Our side information autoregression can be used as a plug-and-play module to replace the side information module in existing models. With comparable coding performance, the reconstructed image obtained by this invention performs better in terms of objective structural similarity metrics and, subjectively, shows better reconstruction of texture details.

[0009] The technical solution of this invention is: a learning image compression method based on side information autoregression, comprising the following steps:

[0010] S1 takes a natural image x as input and feeds it into the analysis and transformation module to obtain a more compact latent representation y. This can be used to eliminate redundant information in the image and reduce the number of features that need to be encoded when compressing the image (features are each value in the tensor). In actual image x compression, y can be directly encoded.

[0011] S2, the latent representation y is taken as input and fed into the superanalysis transformation module to obtain the edge information z. The edge information z can be used to provide prior guidance for the entropy encoding of the latent representation y.

[0012] S3, use the side information autoregressive module to estimate the probability distribution of the side information z, which will be used for the entropy encoding of the quantized side information z, and the entropy encoding will form a compressed bit stream of the side information z.

[0013] S4, the quantized edge information z is fed into the supersynthesis transformation module to obtain the super prior information of the latent representation y;

[0014] S5. The probability distribution of the latent representation y is estimated using the context and prior information of the latent representation y. This will be used for entropy encoding of the quantized latent representation y, which forms a compressed bit stream of the latent representation y after entropy encoding.

[0015] S6, the quantized latent representation y is fed into the synthesis transformation module to obtain the final reconstructed image.

[0016] This invention provides a learning image compression method based on side-information autoregression. During end-to-end learning image compression training, it encourages the neural network to allocate more bitrate to side information. This allows the side information to retain richer contextual information, better guiding the probability estimation of latent representations and improving the overall performance of the entropy module in the compression model. Experimental results show that our component achieves a significant reduction in the latent representation bitrate with a small increase in the side information bitrate. Our side-information autoregression can be used as a plug-and-play module to replace the side information module in existing models. With comparable encoding performance, the reconstructed image obtained by this invention performs better in terms of objective structural similarity metrics and, subjectively, shows better reconstruction of texture details. Attached Figure Description

[0017] Figure 1 A visualization of the edge information for the models of Cheng and Cheng+ours (λ = 0.045).

[0018] Figure 2 This is a schematic diagram of the average bitrate per channel of the side information on the Kodak dataset (λ = 0.045).

[0019] Figure 3This is a comparison chart of the original model and our proposed model.

[0020] Figure 4 This is a diagram illustrating the overall framework of the learning image compression based on side information autoregression (SIA) of the present invention.

[0021] Figure 5 A visualization of the latent representation, super-prior, and regularized latent representation of the models for Cheng and Cheng+ours on Kadak8.

[0022] Figure 6 A comparison of performance and bitrate allocation for three baseline models and the model improved by our method on the Kodak dataset, including Cheng, STF-cnn, and MLIC++.

[0023] Figure 7 Rate-distortion plots and ablation experimental results for three baseline models and our improved model.

[0024] Figure 8 Compress and reconstruct the subjective quality map for the image. Detailed Implementation

[0025] The technical solution of this invention is: a learning image compression method based on side information autoregression, such as... Figure 4 As shown, it includes the following steps:

[0026] The natural image x is taken as input and fed into the analysis and transformation module to obtain a more compact latent representation y. This can be used to eliminate redundant information in the image and reduce the number of features that need to be encoded when compressing the image (features are each value in the tensor). In the actual compression of the image x, y can be directly encoded.

[0027] The latent representation y is fed into the superanalysis transformation module to obtain the edge information z, which can be used to provide prior guidance for the entropy encoding of the latent representation y.

[0028] The probability distribution of the side information z is estimated using the side information autoregressive module. This will be used for the entropy encoding of the quantized side information z, which will then form a compressed bitstream of the side information z.

[0029] The quantized edge information z is fed into the supersynthesis transformation module to obtain the super-prior information of the latent representation y;

[0030] The probability distribution of the latent representation y is estimated using the context and prior information of the latent representation y. This will be used for entropy encoding of the quantized latent representation y, which forms a compressed bit stream of the latent representation y after entropy encoding.

[0031] The quantized latent representation y is fed into the synthesis transform module to obtain the final reconstructed image.

[0032] The overall network framework diagram of the network model is as follows: Figure 4 As shown, similar to existing image compression models, it typically includes an analytical transform network (g a A synthetic transform network (g) is used to remove redundant information in an image to obtain a compact latent representation y. s (used to reconstruct the latent representation y back to the original image), a hyperanalysis transform network (h a A hypersynthetic transform network (h) is used to extract edge information from a compact latent representation y, which can be used to help estimate the hyperprior information of y. s The algorithm transforms edge information into prior information of y, and includes a latent representation entropy model (used to estimate the probability distribution of the latent representation) and an edge information entropy model (used to estimate the probability distribution of the edge information).

[0033] In step 3, to encourage the neural network to allocate bit rate (the number of bits occupied by each value of each pixel in the image) more rationally, it is necessary to use a more accurate side information entropy model. Therefore, we propose a plug-and-play side information autoregressive (SIA) module as our side information entropy model. This module can be seamlessly integrated with any side information-based image compression model, replacing the original FFDM. Specifically, to more accurately model the probability distribution of side information, we adopt a channel-wise autoregressive method, dividing the side information z into L (a hyperparameter) slices along the channel dimension (that is, dividing a tensor z into multiple tensors {z0, z1, ..., z...} along the channel). L-1}), each slice {z0,z1,…,z L-1 It contains S (which is a hyperparameter) channels.

[0034] These slices are encoded sequentially, with previously decoded slices serving as the channel context information for the currently decoded slice. Specifically, for the first slice z0, we still use FFDM to model its probability distribution. (Based on the probability distribution, we can determine the entropy of the variables contained in these slices, and accordingly we can use various entropy coding schemes to encode these variables into binary bit streams):

[0035]

[0036] in z0 represents the quantization (that is, quantizing the original continuous value into a discrete value), and Q represents the quantization operation. ψ is the parameter of FFDM (it refers to the weight value in the neural network). The asterisk (*) represents a uniform distribution of units, and the asterisk (*) represents a convolution operation of the function. It is the probability distribution of the edge information obtained, which, as mentioned earlier, will be used to encode the edge information into a binary bit stream. Divided evenly into two halves along the channel dimension. (that is, a tensor) Divide into two tensorz along the channel μ ,z σ ), z μ ,z σ This will be used to compress and encode the remaining slices. When compressing and encoding the remaining L-1 slices {z1,…,z…} L-1 When we use the mean-scale Gaussian probability distribution to model these slices (as mentioned earlier, the probability here is also used to determine the entropy of the variables contained in these slices, based on which we can use various entropy coding schemes to encode these variables into binary bit streams).

[0037] To address this, we designed an L-1 group of edge information mean module and an edge information scaling module (referring to the neural network). To predict the mean and variance (two parameters of a Gaussian probability distribution) of each feature in the current decoded slice.

[0038]

[0039] It refers to the set of all slices with slice numbers from 1 to i-1, that is... μ i This refers to the mean of each characteristic Gaussian distribution mentioned above, σ. i That is, the variance of the Gaussian distribution of each feature. The representative mean is μ i The variance is σ i Gaussian distribution, The values ​​are uniformly distributed, and * represents the convolution operation of the function. To obtain the Gaussian probability distribution of the i-th slice, as mentioned above, this probability distribution can be used in entropy coding to encode feature values ​​into a binary code stream.

[0040] This design leverages rich contextual information from previously decoded slices at the same or nearby locations to adaptively estimate the mean and variance for each feature. This network consists of three convolutional layers and two LeakyReLU activation functions stacked alternately. The input to this network is previously decoded edge information, and the output is the mean and variance of the currently decoded edge information. Using this variance, we can estimate an accurate probability distribution for each currently decoded edge feature.

[0041] In steps 2 and 4, in order to better extract / utilize richer and more compact edge information, h a Modules and h s The modules are no longer simply composed of convolutions, but rather of g from the original model. a Modules and g s It consists of similar modules, such as the window attention layer, residual block and GDN in the original model.

[0042] Furthermore, since we have adjusted the probabilistic modeling method for edge information, the overall loss function of the network needs to be adjusted as follows:

[0043]

[0044] in It is the bitrate of the potential representation of y In other words, it is the average number of bits of y in each of the RGB three channels of each pixel in the original image x. It is the bitrate of the potential representation of y In other words, it is the average number of z bits of each value in the RGB three channels of each pixel in the original image x. Distortion value, that is, the difference between the original image x and the reconstructed image. MES (Metric for Image Dissimilarity, which will be discussed in detail later). λ is the rate-distortion factor, used to measure the balance between bit rate and image distortion. Under end-to-end unified training of the neural network, the larger λ is, the smaller the distortion and the larger the bit rate, and vice versa.

[0045] In summary, the bitrate estimation of the side information is divided into two steps. The first slice of the side information still uses the FFDM method, using a neural network with values ​​increasing from 0 to 1 to fit the probability distribution of each feature. The remaining L-1 slices are fitted using a Gaussian density model.

[0046] Experimental Section

[0047] This invention validates the edge information autoregressive performance of three models—Cheng, STF-cnn, and MLIC++—on the PyTorch 2.2.2 and CompressAI 1.2.6 platforms.

[0048] Following the method of Minnen et al., the hyperparameter S is set to 320, but the number of channels for the side information is set to 224, which means L is set to 7. Considering the non-convex nature of neural networks, we reduce the second term of the loss function during the first 5 epochs of training. Multiply by 0.1. Following the settings in the original papers for each model, we selected a subset of the ImageNet dataset to train Cheng+ours, 300K images from the OpenImage dataset to train STF-cnn+ours, and 100k images larger than 512×512 from ImageNet, COCO 2017, DIV2K, and Flickr2K to train (MLIC++)+ours.

[0049] Experimental dataset:

[0050] The ImageNet dataset is primarily used for computer vision tasks such as image recognition, classification, detection, and segmentation. It contains over 14 million images, divided into 21,841 categories, organized hierarchically based on WordNet. Each category contains hundreds to thousands of high-resolution images. Created in 2009 by Professor Fei-Fei Li's team at Stanford University, it is a key dataset that has enabled deep learning to achieve breakthroughs in image recognition.

[0051] The OpenImages dataset is used for tasks such as image recognition, classification, object detection, and segmentation. It contains approximately 9 million images labeled with 6,000 categories, exhibiting high image diversity and rich annotation information, including image-level labels, bounding boxes, and segmentation masks. Released by the Google team, it is an open-source, diverse, and large-scale image dataset.

[0052] The COCO 2017 dataset is primarily used for tasks such as object detection, segmentation, human keypoint recognition, and caption generation. It contains approximately 120,000 images labeled with over 80 categories. It provides detailed annotation information, including object bounding boxes, segmentation masks, and category labels. Released by Microsoft, it is a significant benchmark dataset in the field of computer vision.

[0053] The DIV2K dataset is primarily used for image super-resolution tasks. It contains 1000 high-resolution images that have been downsampled to low-resolution versions. These images are of high quality and rich in detail, making them suitable for developing and evaluating super-resolution algorithms. Provided by the NTIRE 2017 and 2018 Super Resolution Challenge, it is a standard dataset in the field of super-resolution.

[0054] The Flickr2K dataset, also used for image super-resolution tasks, contains approximately 2,500 high-resolution images. Sourced from Flickr, the images cover a variety of scenes and themes, making them suitable for researching and testing super-resolution algorithms. Used by both academic research and industry, it is a publicly available image dataset.

[0055] Evaluation indicators:

[0056] Mean Squared Error (MSE) is a method for measuring the difference between a reconstructed image and the original image. It calculates the average of the squared errors of each pixel. A smaller MSE value indicates that the reconstructed image is closer to the original image, and the smaller the error. The formula is as follows: Where m and n are the image width and height, and I and K represent the original image and the reconstructed image, respectively.

[0057] PSNR (Peak Signal-to-Noise Ratio): This is an image quality evaluation metric based on MSE (Mean Sequence Size). It measures the ratio of the maximum possible signal strength to the noise strength, expressed in decibels (dB). A higher PSNR value indicates better image quality. Generally, a PSNR value above 30dB indicates acceptable image quality, while a value above 50dB indicates very good image quality. The formula is as follows: Max represents the maximum possible pixel value of the image.

[0058] Experimental setup:

[0059] The models were optimized using Adam, with Mean Squared Error (MSE) as the quality metric. Other hyperparameters, such as λ value, number of iterations, learning rate decay, batch size, and patch size, were consistent with the original papers for each benchmark model and will not be detailed here. Specifically, due to GPU memory limitations, the batch size for training (MLIC++) + ours was set to 4. All models were trained using a single 3080Ti and an AMD A10-7870K Radeon R7, running Ubuntu on a 5TB hard drive.

[0060] Comparative experiment:

[0061] We computed data from widely used Kodak datasets (such as...) Figure 7 We evaluated all models using the average rate-distortion performance (PeakSignal-to-Noise Ratio, λ = 0.03) on the baseline model (as shown in the figure). It can be seen that our method significantly improves the performance of the original model. Specifically, on the Cheng+ours model, the PSNR is improved by 0.65 dB (λ = 0.03) and 0.59 dB (λ = 0.045) compared to the baseline model. Simultaneously, we visualized the latent representation y of Cheng and Cheng+ours, as shown in the figure. Figure 5As shown. In Cheng+ours, since the side information z contains richer information, it can provide a more accurate mean and scale of the Gaussian distribution for the latent representation y. Therefore, the normalized latent representation is closer to uniform noise, and its absolute value is closer to 0. Taking the fifth λ value as an example, our autoregressive side information trades a small increase in the side information bit rate for a significant reduction in the latent bit rate (e.g., Figure 6 (As shown). We are Figure 8 The image shows a comparison of some subjective results between the original model and our improved model. It can be seen that our model has clearer edges and contours compared to the original model. Ablation experiment:

[0062] To demonstrate the performance of our proposed component, the following ablation experiment was conducted.

[0063] We trained a separate hyperanalysis transformation network h with enhancements. a and hypersynthetic transform network h s The rate-distortion curve of the STF-CNN model (denoted as STF-CNN+EN) is as follows: Figure 7 As shown in the right figure, the model's performance is significantly improved at low bit rates, which fully demonstrates the effectiveness of the enhanced hyperanalysis transform network h. a and hypersynthetic transform network h s The effectiveness of the model is demonstrated. Furthermore, it can be observed that at high bit rates, the performance of STF-cnn+EN is close to that of STF-cnn, but far surpasses that of STF-cnn+ours, further proving the effectiveness of SIA.

[0064] Complexity analysis:

[0065] Table 1 shows the complexity and BD-RATE of Cheng, STF-CNN, MLIC++, and our improved model. Complexity includes MACs (multiply-accumulate-add operations), FLOPs (floating-point operations), and the number of parameters (input image size 512×512). It can be seen that the complexity of Cheng+ours and STF-CNN+ours is reduced compared to the baseline model, while (MLIC++)+ours only slightly increases the complexity compared to the original model. In other words, our model improves compression performance while reducing computational cost, or only introduces a slight increase. Furthermore, we also show the complexity of SIA and FFDM (Table 2). Although SIA has a higher complexity than FFDM, it is negligible for the overall model. For example, Cheng's MACs are 282.5G, while SIA's MACs are only 86.7M.

[0066] Table 1. Comparison of complexity and BD-Rate of different models, all models were trained using the maximum λ. Complexity includes MACs (G), FLOPs (G), and Params (M). For the comparison of BD-Rate (%) of PSNR (dB), the baseline is the respective model.

[0067]

[0068] Table 2. Comparison of complexity between FFDM and SIA.

[0069]

Claims

1. A learning-based image compression method based on edge information autoregression, characterized in that, Includes the following steps: S1 takes a natural image x as input and feeds it into the analysis and transformation module to obtain a compact latent representation y, which is used to eliminate redundant information in the image and reduce the number of features that need to be encoded when compressing the image. The feature is each value in the tensor. In actual image x compression, y is directly encoded. S2 takes the latent representation y as input and feeds it into the superanalysis transformation module to obtain the edge information z. The edge information z is used to provide prior guidance for the entropy encoding of the latent representation y. S3 uses the side information autoregressive module to estimate the probability distribution of the side information z, which will be used for the entropy encoding of the quantized side information z, and the entropy encoding will form a compressed bit stream of the side information z. S4 feeds the quantized edge information z into the supersynthesis transformation module to obtain the super-prior information of the latent representation y; S5 uses the context and prior information of the latent representation y to estimate the probability distribution of the latent representation y, which will be used for entropy encoding of the quantized latent representation y, and the entropy encoding will form a compressed bit stream of the latent representation y. S6 feeds the quantized latent representation y into the synthesis transform module to obtain the final reconstructed image. In S3, a plug-and-play autoregressive edge information (SIA) module is proposed as the edge information entropy model. A channel-wise autoregressive method is used to segment the edge information z into L slices along the channel dimension, that is, a tensor z is divided into multiple tensors {z0, z1, ..., z...} along the channel. L-1 }), each slice {z0,z1,…,z L-1 It contains S channels; The slices are encoded sequentially, with previously decoded slices serving as the channel context information for the currently decoded slice; for the first slice z0, FFDM is used to model its probability distribution. The entropy of the variables contained in these slices is determined based on the probability distribution, and various entropy coding schemes are used to encode these variables into a binary bit stream: in z0 represents quantization, Q represents the quantization operation, and ψ is a parameter of FFDM. The asterisk (*) represents a uniform distribution of units, and the asterisk (*) represents a convolution operation of the function. It is the probability distribution of the edge information, which is used to encode the edge information into a binary bit stream; Divided evenly into two halves along the channel dimension. Put one Divide into two tensorz along the channel μ ,z σ ;z μ ,z σ This will be used to compress and encode the remaining slices; when compressing and encoding the remaining L-1 slices {z1,…,z…} L-1 When}, the mean-scale Gaussian probability distribution is used to model the slices.

2. The learning image compression method based on edge information autoregression according to claim 1, characterized in that, The overall network framework of the network model includes an analysis transformation network g. a A synthetic transform network g is used to remove redundant information from the image to obtain a compact latent representation y; s A hyperanalysis transform network h is used to reconstruct the latent representation y back to the original image. a A hypersynthetic transform network h is used to extract edge information from a compact latent representation y, which helps estimate the hyperprior information of y; s The system transforms edge information into prior information of y, and includes a latent representation entropy model to estimate the probability distribution of the latent representation, and an edge information entropy model to estimate the probability distribution of the edge information.

3. The learning image compression method based on edge information autoregression according to claim 1, characterized in that, Design an L-1 group edge information mean module and an edge information scaling module. To predict the mean and variance of each feature in the current decoded slice; This refers to the set of all slices with slice numbers from 1 to i-1, i.e. μ i This refers to the mean of each characteristic Gaussian distribution mentioned above, σ. i That is, the variance of the Gaussian distribution for each feature; The representative mean is μ i The variance is σ i Gaussian distribution, The units are uniformly distributed, and * represents the convolution operation of the function; To obtain the Gaussian probability distribution of the i-th slice.

4. The learning image compression method based on edge information autoregression according to claim 3, characterized in that, By leveraging the rich contextual information of previously decoded slices at the same or nearby locations, the mean and variance of each feature are estimated. It consists of three convolutional layers and two LeakyReLU activation functions stacked alternately; the network input is the previously decoded side information, and the output is the mean and variance of the currently decoded side information; using the variance, an accurate probability distribution is estimated for each currently decoded side information feature.

5. The learning image compression method based on side information autoregression according to claim 4, characterized in that, h a Modules and h s The module consists of g from the original model. a Modules and g s The module consists of similar components, such as the window attention layer, residual block, and GDN in the original model; By adjusting the probabilistic modeling method for edge information, the overall loss function of the network needs to be adjusted as follows: in, It is the bitrate of the potential representation of y The average number of bits for y in each of the three RGB channels of each pixel in the original image x; It is the bitrate of the potential representation y ( and ), the average number of z bits of each value in one of the three RGB channels of each pixel in the original image x; Distortion value, that is, the difference between the original image x and the reconstructed image. MES; λ is the rate-distortion factor, used to measure the balance between bit rate and image distortion. Under the unified end-to-end training of the neural network, the larger λ is, the smaller the distortion and the larger the bit rate, and vice versa; the bit rate estimation of the side information is divided into two steps. The first slice of the side information still uses the FFDM method, using a neural network with values ​​increasing from 0 to 1 to fit the probability distribution of each feature; the remaining L-1 slices are fitted using a Gaussian density model.

Images