End-to-end image lossless compression method based on two-dimensional inseparable wavelet transform

Abstract

The invention discloses an end-to-end image lossless compression method based on two-dimensional inseparable wavelet transform. According to the method, the image is decomposed through multistage wavelet transform, and sub-band coefficients of different sizes are obtained. And inputting the coefficients into an entropy coding model, and using a context model to drive an arithmetic encoder to compress the coefficients into a bit stream. According to the method, two-dimensional inseparable wavelet transformation is adopted, a lifting structure of the wavelet transformation is used, three prediction filters and an updating filter are included, and the filter structure is a convolutional neural network structure. The entropy coding module also uses a neural network structure. Carrying out the overall optimization of all parameters through deep learning, training the network until convergence, and achieving the lossless compression of an image through a trained model. The end-to-end image lossless compression method shows excellent performance in the aspect of lossless compression, is remarkably improved compared with a traditional JPEG2000 lossless compression method, and is also superior to an end-to-end image lossless compression method based on traditional separable wavelet transform.

Description

Technical Field

[0001] The invention belongs to the field of image compression coding and relates to an end-to-end image lossless compression method based on two-dimensional inseparable wavelet transform. Background Art

[0002] Image compression is a key research area in modern digital signal processing and multimedia applications, aiming to improve the efficiency of information transmission and storage. Image compression algorithms include traditional image compression algorithms and end-to-end image compression algorithms based on deep learning. Traditional image compression standards such as JPEG and JPEG2000 are implemented through hand-designed modules with low decoding complexity and strong versatility. However, these standards rely on fixed coding architectures and are difficult to adapt to the diversity and complexity of image content. In contrast, end-to-end image compression algorithms use a large amount of image data for training, and through repeated iterations and optimization of neural networks, they significantly improve coding efficiency and image quality.

[0003] As a classic image coding method, JPEG2000 uses wavelet transform to convert images into coefficients. In JPEG2000, wavelet transform adopts lifting form, that is, wavelet transform is realized through a series of prediction and update operations.

[0004] In order to further improve the performance of image coding, researchers applied wavelet transform to end-to-end image compression methods and proposed an end-to-end image coding method based on learning wavelet transform, namely iWave++. In this method, wavelet transform uses prediction filters and update filters with convolutional neural network structures, and other modules of image coding also use neural network structures, thus forming an overall end-to-end image compression framework. The iWave++ method shows relatively excellent performance in lossless compression, but there is still room for further improvement.

[0005] One of the main reasons for this optimization requirement is that lossless compression must be performed in the integer domain, so rounding operations are required after the filters formed by the convolutional neural network. The traditional wavelet transform method for processing two-dimensional images is to first perform a one-dimensional transform in the horizontal direction and then a one-dimensional transform in the vertical direction, and finally obtain four sub-bands. Each one-dimensional transform contains an update filter and a prediction filter, and each filter needs to be rounded after processing the coefficients, so a total of six rounding operations are required. Since rounding operations will introduce rounding errors, too many rounding operations will lead to the accumulation of errors, which in turn affects the performance of lossless compression.

[0006] Therefore, in order to further improve the performance of this method, reducing the number of rounding operations by changing the structure of the two-dimensional wavelet transform is an important direction. Summary of the invention

[0007] The purpose of the present invention is to address the deficiencies of the prior art and to propose an end-to-end image lossless compression method based on two-dimensional inseparable wavelet transform, comprising the following steps: Step 1: Get an RGB format image and convert it into a grayscale image; Step 2: Use multi-level wavelet transform to perform multi-scale decomposition on the grayscale image to obtain multiple sub-bands; Step 3: Input all sub-band information into the learning-based entropy coding module for compression coding to obtain the coded data of each sub-band coefficient; Step 4: Decode the encoded bitstream and restore the corresponding subband coefficient value according to the probability distribution of each subband coefficient; Step 5: Perform a multi-level wavelet inverse transform corresponding to step 2 on each decoded sub-band coefficient, reconstruct the pixel parameters of the image, and reconstruct the original image; Step 6: Convert the grayscale image obtained after decoding and reconstruction into the original RGB format image.

[0008] Furthermore, in step 2, the grayscale image is decomposed into multiple scales using multi-level wavelet transform as follows: Perform a wavelet transform on the grayscale image to obtain four subband coefficients , , , ; For the low frequency subband coefficients Continue to perform wavelet transform to obtain higher frequency subband coefficients , , , ; And so on, wavelet transformation times, a total of subband coefficients, , Indicates the number of wavelet transforms.

[0009] Furthermore, the wavelet transform adopts a two-dimensional inseparable structure based on learning, including a decomposition step, a prediction step, and an update step; Decomposition step: approximate coefficients of the grayscale image , decomposed into four components according to the parity of the horizontal and vertical directions: , , , ,in represents the number of wavelet decompositions, Indicates the pixel position; Prediction step: use prediction filter to process each component; Update step: Calculate the difference between the output of the prediction filter and each original component to obtain the processed subband component , as well as , input update filter, the result and Combine to generate updated low frequency signal .

[0010] Furthermore, the prediction filter and the update filter are both convolutional neural networks, and rounding operations are performed after filtering. The coefficients of the four output components are obtained by wavelet transformation. , , as well as ; use , , , represents four filters composed of convolutional neural networks, P represents the prediction filter, U Represents the updated filter; the calculation formula for the four coefficient values ​​output by the four decomposed components is as follows: , , , , Among them, [ ] represents rounding operation, and * represents convolution operation; the purpose of rounding operation is to ensure that the encoding is lossless encoding.

[0011] Furthermore, both the prediction filter and the update filter are convolutional neural networks, including convolutional layers and nonlinear activation functions; Extract features from the input image through the first convolutional layer; The features obtained by the first convolutional layer are further processed by two parallel tanh activation functions and the second convolutional layer to output a feature map; The feature map is merged with the extracted features, and the third convolutional layer is used to perform feature fusion on the merged feature map; Add the fused feature map to the input image to get the final output.

[0012] Furthermore, the learning-based entropy coding module includes: The context model uses an autoregressive model to process all sub-band information in turn and outputs a set of entropy parameters as the coefficients of each sub-band , ,……, Parameters of probability distributions; Probabilistic model, predicts the probability distribution of each coefficient based on context information and determines the probability of occurrence of the coefficient for arithmetic coding; Arithmetic encoder, which compresses and encodes each subband coefficient based on the probability obtained by the probability model; Further, the context model includes a long-term context extraction model and a context fusion model; Long-term context extraction model, after encoding sub-bands to extract and obtain long-term context information ; Context fusion model, which integrates long-term context information The information in the current subband The information of the coefficients already encoded in is combined to generate the parameters of the probability distribution of the current coefficients.

[0013] Furthermore, in step 3, the probability model used in the arithmetic encoder is a Gaussian mixture model, which includes three Gaussian distributions.

[0014] Furthermore, in step 4, the encoded bitstream is decoded to restore the probability distribution of each subband coefficient and the corresponding subband coefficient value. , ,……, ; Use the same context model as in the encoding phase to obtain the parameters of the coefficient probability distribution and restore the probability distribution of each coefficient; Using the same probability model as in the encoding stage, the probability distribution of each coefficient is restored for arithmetic decoding according to the parameters generated by the context model; The arithmetic decoder gradually decodes the bit stream according to the output of the probability model and restores the original value of each subband coefficient.

[0015] Furthermore, in step 5, the decoded sub-band coefficients are subjected to a multi-level wavelet inverse transform corresponding to step 2, specifically starting from the highest frequency sub-band and performing inverse transform step by step; The four subbands generated by the last wavelet transform , , , Perform inverse transform to obtain the low-frequency subband of the previous level ; Merge the four sub-bands of the previous level , , , , get the next level of low-frequency sub-band ; Repeat this process until the highest level subband coefficients , , , Values ​​are combined to obtain the complete pixel information of the image.

[0016] Furthermore, the two-dimensional inseparable wavelet inverse transform is a strict inverse process of the two-dimensional inseparable wavelet transform, including the following steps: Inverse update, inverse prediction and merging, the filter parameters used in inverse update and inverse prediction are exactly the same as those used in forward transformation; Similarly, rounding operations are required after each filter to ensure that the results of all operations are integers, thereby achieving lossless image reconstruction; the mathematical expressions corresponding to inverse update and inverse prediction are as follows: , , , , in P , U represents the prediction filter and update filter, [ ] represents the rounding operation, and * represents the convolution operation. , , , Merge to get the inverse result .

[0017] Furthermore, the method also includes step 7: constructing a loss function, and using an optimizer to perform end-to-end training optimization on the overall image compression model to obtain an optimal model.

[0018] Beneficial effects of the present invention: Compared with the prior art, the present invention has the following significant advantages: (1) When performing two-dimensional decomposition, the traditional wavelet transform requires six rounding operations for horizontal and then vertical transformations, while the two-dimensional inseparable wavelet transform only requires four rounding operations. The fewer rounding operations, the smaller the rounding error. Therefore, the image compression method using the two-dimensional inseparable wavelet transform can achieve better lossless compression effect than the existing method using the classic two-dimensional wavelet transform.

[0019] (2) In the end-to-end image compression method, a two-dimensional non-separable wavelet transform is used, and its filter adopts a convolutional neural network structure, and is optimized together with the parameters used in other modules in the image compression method based on deep learning. This process continuously trains and optimizes the model, thereby continuously improving its performance and achieving more excellent lossless compression effects.

[0020] Other features and advantages of the present invention will be described in detail in the following detailed description. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] The above and other objects, features and advantages of the present invention will become more apparent through a more detailed description of exemplary embodiments of the present invention in conjunction with the accompanying drawings, wherein like reference numerals generally represent like components throughout the exemplary embodiments of the present invention.

[0022] Figure 1 It is a diagram of the overall framework structure of the end-to-end image lossless compression based on two-dimensional inseparable wavelet transform of the present invention.

[0023] Figure 2 It is a two-dimensional inseparable wavelet transform structure diagram used in the present invention.

[0024] Figure 3 This is a schematic diagram of the convolutional network structure used by the prediction filter and update filter in the two-dimensional non-separable wavelet transform structure.

[0025] Figure 4 It is a schematic diagram of multi-scale decomposition used in the present invention.

[0026] Figure 5 It is a schematic diagram of a context fusion model in the entropy coding module used in the present invention. DETAILED DESCRIPTION

[0027] The preferred embodiments of the present invention will be described in more detail below with reference to the accompanying drawings. Although the preferred embodiments of the present invention are shown in the accompanying drawings, it should be understood that the present invention can be implemented in various forms and should not be limited to the embodiments set forth herein.

[0028] like Figure 1 As shown, the image lossless compression method based on learning two-dimensional inseparable wavelet transform includes the following steps: Step 1: Input an RGB format image as a training image; first convert the RGB format image to the YCbCr color space, then take the Y channel information and convert the RGB color image to a grayscale image; secondly, extract the 128×128 pixel information at the center of the processed grayscale image as training data; Step 2: Perform the encoding step and perform wavelet transform on each uncoded image; use the learning-based two-dimensional inseparable wavelet structure and the lifting structure of wavelet transform, which consists of three parts: decomposition, update and prediction; like Figure 2 As shown, first the image approximation coefficients Decompose into four components according to the parity of horizontal and vertical directions: , , , ,in represents the number of wavelet decompositions, Indicates the pixel position; each subband signal is processed by the corresponding prediction filter, and the difference between the output of the prediction filter and each original component is calculated to obtain the processed subband component , as well as Input update filter, the result and Combine to generate updated low frequency signal , after filtering, rounding operation is performed, and the coefficients of the four output components are obtained by wavelet transform , , as well as ; Further, using , , , Represents four filters composed of convolutional neural networks, P represents the prediction filter (predict), and U represents the update filter (update). The Z transform calculation formula corresponding to the four coefficient values ​​output is as follows: , , , , Among them, [ ] represents rounding operation, and * represents convolution operation; the purpose of rounding operation is to ensure that the encoding is lossless encoding.

[0029] Furthermore, the prediction filter and update filter in the wavelet transform adopt a convolutional neural network structure, the specific structure is as follows Figure 3 As shown in the figure; the neural network is composed of multiple convolutional layers and nonlinear activation functions. First, the input image layer size is 3×3×1, and then it is extracted through two 3×3×16 convolutional layers; then, after two parallel tanh activation functions and a combination of 3×3×16 convolutional layers, the feature map is output and then merged with the previous features; next, the merged feature map passes through a 3×3×1 convolutional layer for the final feature fusion; finally, this fused feature map is added to the input image to get the final output.

[0030] Step 3: Decompose the image at multiple scales: First, perform a wavelet transform on an image to obtain four sub-bands: , , , , then Continue transforming to obtain higher frequency subbands: , , , , then Continue to transform. This method performs four wavelet transform decompositions in total, and obtains 13 sub-bands in total. The order of placement of the subbands obtained after wavelet transform is arrive , Figure 4 A schematic diagram showing the order in which each subband is placed is shown. In the arithmetic coding stage, the subbands generated above are recorded in reverse order of generation as , ,……, , taking 13 sub-bands as an example, they are expressed as , ,……, , all subbands will follow Figure 4 The wavelet coefficients are compressed one by one in the order shown by the arrows in the middle; within each sub-band, the wavelet coefficients are compressed one by one in the order from left to right and from top to bottom; Furthermore, the multi-level wavelet transforms used in the multi-scale decomposition share the same set of convolutional neural network parameters; by sharing the same convolutional neural network parameters, the transformation process can maintain the same characteristics and effects for images of different resolutions, thereby achieving unified encoding and decoding performance at different scales.

[0031] Step 4: inputting the processed coefficients into a learning-based entropy coding module for processing; the learning-based entropy coding module adopted by the present invention includes: a context model that outputs a set of entropy parameters, a probability model that predicts the probability distribution of each coefficient, and an arithmetic codec; Figure 1 Where AE and AD represent arithmetic encoding and arithmetic decoding respectively; Furthermore, the context model in the entropy coding module is an autoregressive model, which includes a long-term context extraction model and a context extraction model: the long-term context extraction model processes the previously encoded subband , ,……, , derive long-term context information ; The context fusion model will The information in the current subband The information of the coefficients already encoded in is combined to generate the parameters of the probability distribution of the current coefficients.

[0032] Furthermore, the long-term context extraction model uses a recurrent neural network structure and applies three convolution-based long short-term memory layers; After the encoding process, the generated subband Send to the recurrent neural network structure to obtain long-term context information , before encoding the next subband hour, Remain unchanged; after completing the entire subband After the encoding process, Send it to the recurrent neural network to complete the arrive The update will then As the next subband The long-term context information of the sub-band continues to be entropy encoded; this iterative process continues in each subsequent sub-band, enabling the recurrent neural network to capture and maintain the relevant long-term context information between different sub-bands during the encoding process.

[0033] Furthermore, when the subband and When the resolution is different, appropriate adjustments need to be made to handle this; for example, Figure 4 middle, and With different resolutions, when encoding When the output of long-term context is required The upsampling process ensures that the long-term context information and internal state are consistent with the subband and The resolutions of the images are correctly aligned, thus enabling accurate and effective context modeling during encoding.

[0034] Furthermore, the context fusion model utilizes convolutional neural networks, such as Figure 5 As shown in Figure 2, masked convolution is used in the model to ensure that the network only uses the already encoded coefficients, that is, the information of the pixels above and to the left of the current pixel ( Figure 5 middle ); first, and Apply convolutional layers and combine them with residual learning structures. The intermediate results are integrated into The calculation process of the two paths is then passed through a series of convolutional layers to finally generate entropy coding parameters.

[0035] Furthermore, the probability model used in arithmetic coding is a Gaussian mixture model containing three Gaussian distribution components; each Gaussian distribution component has its corresponding mean, variance and mixing coefficient, and these parameters are determined through training.

[0036] Step 5: Decode the encoded bitstream: Use the context model in the decoding process to generate parameters of the current coefficient probability distribution, and restore the probability distribution of each coefficient based on the parameters generated by the context model; use the arithmetic decoder to gradually decode the bitstream according to the output of the probability model and gradually restore the original coefficient value; Step 6: Perform the decoding step and perform four learning-based two-dimensional inseparable wavelet inverse transforms on the coefficients to reconstruct the pixel parameters of the image: First, starting from the highest frequency sub-band, the four sub-bands generated by the last wavelet transform ( , , , ) to perform inverse transform, merge these sub-bands, and reconstruct the low-frequency sub-band of the previous level ; Then reconstruct the low-frequency subband and its corresponding three high-frequency sub-bands ( , , ), perform inverse transformation and merging operations; repeat this process until the original image is reconstructed; Furthermore, the two-dimensional inseparable wavelet inverse transform is the strict inverse process of the two-dimensional inseparable wavelet transform, including the following steps: inverse update, inverse prediction and merging. The filter parameters used in the inverse update and inverse prediction are exactly the same as those used in the forward transform. Similarly, rounding operations are required after each filter to ensure that the results of all operations are integers, thereby achieving lossless image reconstruction. The mathematical expressions corresponding to the inverse update and inverse prediction are as follows: , , , , in P , U represents the prediction filter and update filter, [ ] represents the rounding operation, and * represents the convolution operation. , , , Merge to get the inverse result .

[0037] Step 7: Convert the decoded grayscale image back to a color image in RGB format; Step 8: Construct the loss function as: ,in represents the estimated bit rate, represents the two-dimensional non-separable wavelet forward transform, represents the training set, represents the trainable parameters in the transformation module, Represents all trainable parameters in the entropy coding module; uses the Adam optimizer to perform end-to-end training optimization on the overall image compression model to obtain the optimal model.

[0038] The training set used in this example includes 800 images from the DIV2K dataset, 585 images from the CLIC2020 Professional dataset, and 1048 images from the CLIC2020 Mobile dataset. The training process is implemented using CompressAI. The Adam algorithm and its default settings are used during training, the learning rate is set to 1e-4, and approximately 500 epochs are trained.

[0039] The embodiment tests the comparison between the present invention and the traditional compression method JPEG2000 and the end-to-end image compression method iwave++ based on learning wavelets. The test data sets include the Kodak data set and the Tecnick data set. The Kodak data set contains 24 high-quality lossless color images, and the resolution of each image is 768x512 pixels. The Tecnick data set contains 40 high-resolution images, and the resolution of each image is 1200x1200 pixels. In the test phase, the RGB image is first converted to the YCbCr format, and then the model obtained by training based on the grayscale image in the training phase is used to compress the image on the three channels.

[0040] The embodiment uses bits per pixel (bpp) as an evaluation index. On the Kodak dataset, the average data size of JPEG2000 is 9.58 bpp, the average data size of iwave++ is 8.07 bpp, and the average data size of the present invention is 7.99 bpp, which is 1.59 bpp less than JPEG2000 (a reduction of about 16.6%), and 0.08 bpp less than iwave++ (a reduction of about 0.99%). On the Tecnick dataset, the average data size of JPEG2000 is 7.23 bpp, the average data size of iwave++ is 6.44 bpp, and the average data size of the present invention is 6.38 bpp, which is 0.79 bpp less than iwave++ (a reduction of about 10.9%), and 0.06 bpp less than iwave++ (a reduction of about 0.93%).

[0041] Experimental results show that compared with the traditional image compression algorithm JPEG2000, this method can significantly reduce storage requirements and data volume, demonstrating the great advantages of end-to-end image compression algorithms. In addition, the lossless compression performance of this method on multiple data sets is better than that of the existing end-to-end image compression algorithm iWave++. This shows that this method has stronger lossless compression capabilities, higher compression ratios, and smaller data volumes.

[0042] The embodiments of the present invention have been described above, and the above description is exemplary, not exhaustive, and is not limited to the disclosed embodiments. Many modifications and changes will be apparent to those skilled in the art without departing from the scope and spirit of the described embodiments.

Claims

1. An end-to-end image lossless compression method based on two-dimensional non-separable wavelet transform, It is characterized in that The method comprises the following steps: Step 1: Get an RGB format image and convert it into a grayscale image; Step 2: Use multi-level wavelet transform to perform multi-scale decomposition on the grayscale image to obtain multiple sub-bands; Step 3: Input all sub-band information into the learning-based entropy coding module for compression coding to obtain the coded data of each sub-band coefficient; Step 4: Decode the encoded bitstream and restore the corresponding subband coefficient value according to the probability distribution of each subband coefficient; Step 5: Perform a multi-level wavelet inverse transform corresponding to step 2 on each decoded sub-band coefficient, reconstruct the pixel parameters of the image, and reconstruct the original image; Step 6: Convert the grayscale image obtained after decoding and reconstruction into the original RGB format image.

2. The end-to-end image lossless compression method based on two-dimensional non-separable wavelet transform as claimed in claim 1, Features In step 2, multi-level wavelet transform is used to perform multi-scale decomposition on the grayscale image. Specifically: Perform a wavelet transform on the grayscale image to obtain four subband coefficients , , , ; For the low frequency subband coefficients Continue to perform wavelet transform to obtain higher frequency subband coefficients , , , ; And so on, wavelet transformation j times, a total of t subband coefficients, t =4+3( j -1), j Indicates the number of wavelet transforms.

3. The end-to-end image lossless compression method based on two-dimensional non-separable wavelet transform as claimed in claim 2, Features Wavelet transform adopts a two-dimensional inseparable structure based on learning, including decomposition step, prediction step and update step; Decomposition step: approximate coefficients of the grayscale image , decomposed into four components according to the parity of the horizontal and vertical directions: , , , ,in j represents the number of wavelet decompositions, Indicates the pixel position; Prediction step: use prediction filter to process each component; Update step: Calculate the difference between the output of the prediction filter and each original component to obtain the processed subband component , as well as , input update filter, the result and Combine to generate updated low frequency signal .

4. The end-to-end image lossless compression method based on two-dimensional non-separable wavelet transform as claimed in claim 3, Features The prediction filter and update filter are both convolutional neural networks. After filtering, rounding operations are performed and wavelet transform is used to obtain the coefficients of the four output components. , , as well as ; use , , , represents four filters composed of convolutional neural networks, P represents the prediction filter, U Represents the updated filter; the calculation formula for the four coefficient values ​​output by the four decomposed components is as follows: ; Among them, [ ] represents rounding operation, and * represents convolution operation; the purpose of rounding operation is to ensure that the encoding is lossless encoding.

5. The end-to-end image lossless compression method based on two-dimensional non-separable wavelet transform as claimed in claim 3, Features Both the prediction filter and the update filter are convolutional neural networks, including convolutional layers and nonlinear activation functions; Extract features from the input image through the first convolutional layer; The features obtained by the first convolutional layer are further processed by two parallel tanh activation functions and the second convolutional layer to output a feature map; The feature map is merged with the extracted features, and the third convolutional layer is used to perform feature fusion on the merged feature map; Add the fused feature map to the input image to get the final output.

6. The end-to-end image lossless compression method based on two-dimensional non-separable wavelet transform according to claim 1, It is characterized in that The learning-based entropy coding module includes: The context model uses an autoregressive model to process all sub-band information in turn and outputs a set of entropy parameters as the coefficients of each sub-band Parameters of probability distributions; Probabilistic model, predicts the probability distribution of each coefficient based on context information and determines the probability of occurrence of the coefficient for arithmetic coding; The arithmetic encoder compresses and encodes each subband coefficient based on the probability obtained by the probability model.

7. The end-to-end image lossless compression method based on two-dimensional non-separable wavelet transform according to claim 6, It is characterized in that The context model includes a long-term context extraction model and a context fusion model; Long-term context extraction model, after encoding t sub-bands to extract and obtain long-term context information ; Context fusion model, which integrates long-term context information The information in the current subband The information of the coefficients already encoded in is combined to generate the parameters of the probability distribution of the current coefficients.

8. The end-to-end image lossless compression method based on two-dimensional non-separable wavelet transform as claimed in claim 6, It is characterized in that In step 3, the probability model used in the arithmetic encoder is a Gaussian mixture model, which includes three Gaussian distributions.

9. The end-to-end image lossless compression method based on two-dimensional non-separable wavelet transform according to claim 6, Features In step 4, the encoded bitstream is decoded to restore the probability distribution of each subband coefficient and the corresponding subband coefficient value. ; Use the same context model as in the encoding phase to obtain the parameters of the coefficient probability distribution and restore the probability distribution of each coefficient; Using the same probability model as in the encoding stage, the probability distribution of each coefficient is restored for arithmetic decoding according to the parameters generated by the context model; The arithmetic decoder gradually decodes the bit stream according to the output of the probability model and restores the original value of each subband coefficient.

10. The end-to-end image lossless compression method based on two-dimensional non-separable wavelet transform according to claim 1, Features In step 5, the decoded sub-band coefficients are subjected to a multi-level wavelet inverse transform corresponding to step 2, specifically starting from the highest frequency sub-band and performing inverse transform step by step; The four subbands generated by the last wavelet transform , , , Perform inverse transform to obtain the low-frequency subband of the previous level ; Merge the four sub-bands of the previous level , , , , get the next level of low-frequency sub-band ; Repeat this process until the highest level subband coefficients , , , Values ​​are combined to obtain the complete pixel information of the image.

11. The end-to-end image lossless compression method based on two-dimensional non-separable wavelet transform as claimed in claim 2, Features The inverse two-dimensional inseparable wavelet transform is the strict inverse process of the two-dimensional inseparable wavelet transform, which includes the following steps: Inverse update, inverse prediction and merging, the filter parameters used in inverse update and inverse prediction are exactly the same as those used in forward transformation; Similarly, rounding operations are required after each filter to ensure that the results of all operations are integers, thereby achieving lossless image reconstruction; the mathematical expressions corresponding to inverse update and inverse prediction are as follows: ； in P , U Represents the prediction filter and update filter, [ ] represents the rounding operation, and * represents the convolution operation; the four component values ​​obtained , , , Merge to get the inverse result .

12. The end-to-end image lossless compression method based on two-dimensional non-separable wavelet transform according to claim 1, Features The method also includes step 7: constructing a loss function and using an optimizer to perform end-to-end training optimization on the overall image compression model to obtain an optimal model.

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