A method for optimizing a JPEG quantization table based on decomposition multi-objective optimization
By optimizing the JPEG quantization table using a decomposition-based multi-objective optimization method, we can address the diverse needs of users for images with different bitrates and achieve efficient image compression and quality preservation.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- ANHUI UNIV
- Filing Date
- 2022-05-09
- Publication Date
- 2026-05-15
AI Technical Summary
Existing technologies cannot generate images with different bitrates simultaneously, making it difficult to meet users' diverse needs for high-quality and easy-to-store and transmit low-quality versions.
A decomposition-based multi-objective optimization method is adopted. By randomly listing quality factors, segmenting image blocks and performing discrete cosine transform, the population of the quantization table is optimized using a Gaussian mixture model and the penalized boundary intersection method. An evolutionary operator and a global search strategy for the Gaussian mixture model are designed to optimize the JPEG quantization table.
While improving coding efficiency, it reduces image quality loss, effectively finds the optimal quantization table, and meets the diverse image compression requirements of different users.
Smart Images
Figure CN114898003B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the fields of multi-objective evolutionary algorithms and JPEG encoding optimization technology, specifically to a JPEG quantization table optimization method based on decomposition-based multi-objective optimization. Background Technology
[0002] In today's world, where electronic devices are ubiquitous, people constantly encounter and use digital images in their daily lives and work. This image data has grown exponentially with increasing demand, posing challenges to disk storage and network transmission. Therefore, image compression technology has emerged. The JPEG standard remains dominant in image compression coding applications, making the optimization of JPEG encoding efficiency and the compression of image size while maintaining image quality a crucial requirement with broad application prospects and economic value.
[0003] Currently, JPEG quantization table optimization methods can be mainly classified into the following categories: mathematical statistical methods, which derive suitable quantization tables based on mathematical statistical analysis of the DCT coefficient distribution of an image set; adaptive methods, which not only use unique quantization tables for all images, but also for all blocks of a specific image, utilizing the local frequency content of the image to better control the DCT coefficient quantization process; standard optimization methods, which employ standard optimization techniques such as gradient gradation and simulated annealing; and direct search-based methods, which use a single-objective evolutionary algorithm (SOEA) to search for quantization tables, thereby obtaining the optimal compression and accuracy tradeoff for specific types of images.
[0004] In practical applications, users have diverse needs. For example, when transmitting an image over a network, some people may need a clear, high-quality version, while others may need a low-quality version that is easy to store and transmit. For such application scenarios, it is necessary to reduce the image size while maintaining the image quality as much as possible. To this end, a JPEG quantization table optimization method based on decomposition and multi-objective optimization is proposed. Summary of the Invention
[0005] The purpose of this invention is to provide a JPEG quantization table optimization method based on decomposition and multi-objective optimization, which solves the following technical problems:
[0006] Users have diverse needs. When transmitting an image over the network, some people may need a clear, high-quality version, while others may need a low-quality version that is easy to store and transmit. Current technology cannot generate images with different bitrates at the same time, making it difficult to meet both needs simultaneously.
[0007] The objective of this invention can be achieved through the following technical solutions:
[0008] A JPEG quantization table optimization method based on decomposition and multi-objective optimization includes the following steps:
[0009] A set of quality factors is randomly selected, and the standard quantization table is processed according to the quality factors to obtain an initialized quantization table population. Weight vectors and neighborhoods are assigned to individuals in the quantization table population. The optimization objectives of the quantization table population include bit rate, luminance quality mean square error, and chrominance quality mean square error.
[0010] The chroma components of the image are processed independently, the chroma components are divided into 8x8 image blocks, the image blocks are transformed into discrete cosine blocks for quantization, and the bit rate, luminance quality mean square error and chroma quality mean square error are obtained.
[0011] The subproblems in the quantization table population are sorted based on the distribution sparsity, thereby quickly obtaining the optimal quantization table solution set;
[0012] The population of the quantization table is searched using sampling mutation based on decomposition and Gaussian mixture models or staged multi-method crossover mutation.
[0013] The population of quantization tables is updated using a decomposition-based penalized boundary intersection method. The subproblem with the greatest improvement is selected from the population of quantization tables for updating, thereby obtaining the optimal quantization table.
[0014] As a further aspect of the present invention, the process of processing the chromaticity components of the image is as follows:
[0015] The image's chromaticity components include a luminance chromaticity component Y, a blue chromaticity component Cb, and a red chromaticity component Cr. These chromaticity components are sequentially divided into 8*8 image blocks. The image data within the image is used as the basic processing unit to perform a discrete cosine transform. The resulting image data is the discrete cosine data. The quantization matrix stores the quantization step size for each discrete cosine frequency band. Image compression is achieved by losing some data through division and rounding.
[0016] As a further aspect of the present invention: the process of initializing the quantization table population includes:
[0017] Let N be the population size of the quantization table, obtain the bitrate, luminance quality mean square error, and chrominance quality mean square error for each subproblem, and denote the size of its neighborhood as T. Construct {w 1 w 2 ,…,w N For each subproblem i = 1, 2, ..., N, construct a neighborhood B from the set of weight vectors. i ={i1, i2, ..., i T}, making To be with w iThe j-th nearest weight vector is used to obtain the ideal point. Z * The minimum mean square error of image quality and the minimum bit rate are quantized in the population.
[0018] As a further aspect of the present invention: the process for obtaining the bit rate, the mean square error of luminance quality, and the mean square error of chrominance quality is as follows:
[0019]
[0020] Where (u, v) are the frequency band coordinates, F(u, v) are the discrete cosine coefficients at the frequency band (u, v), Q(u, v) are the quantization step size at the frequency band, and round.integer is the rounding value. The quantization process is shown in the following formula:
[0021]
[0022] Define bitrate:
[0023]
[0024] height and width represent the height and width of the image after segmentation, and count represents the sum of all results with the same quantization coefficient;
[0025] Define the mean square error of luminance quality and the mean square error of chrominance quality:
[0026]
[0027] X and X′ are two M*N pixel matrices, where X represents the original image and X′ represents the compressed image. Substituting the pixel matrices of brightness and chrominance into X and X′ respectively yields the mean square error.
[0028] As a further aspect of the present invention: the process of population sorting based on the quantization table of distribution sparsity is as follows:
[0029] The covariance matrix used in the subproblem sampling is calculated using the neighborhood of the subproblem. For each individual x i Calculate its neighborhood center point:
[0030]
[0031] Obtain the sparsely distributed individuals in the current solution set. If the population distribution in the quantization table is uniform, then the solutions to the subproblems should be close to the center of their neighborhoods. For each individual x... i Calculate its sparsity:
[0032]
[0033] T represents the neighborhood size, N represents the quantization table population size, and sparseness s1 ,s 2 ,…,s N Sort in descending order.
[0034] As a further aspect of the present invention: the process of employing global search and local search includes:
[0035] A neighborhood search probability δ is set. When the random number is greater than δ, sampling using a Gaussian mixture model is used. When the random number is less than δ, crossover and mutation are performed in stages according to the population generation number in the quantization table, using the target estimation method, the difference method, and the Gaussian mixture model respectively. The global search and local search use a maximum of [number missing] times per step. The issue of individual offspring.
[0036] As a further aspect of the present invention, the specific method for hybridization and mutation using a decomposition and Gaussian mixture model is as follows:
[0037] Define a recombination operator based on decomposition and Gaussian mixture model for multi-objective optimization problems, given a set of data x. 1 ,x 2 ,…,x k The mean vector and covariance matrix are estimated as follows:
[0038]
[0039]
[0040] For each subproblem, a Gaussian model is constructed, whose probability density function is expressed as:
[0041]
[0042] Where pi(x) represents the probability density function corresponding to the i-th subproblem, μ i and Σ i Let pi(x) be the mean vector and covariance matrix.
[0043]
[0044] The mean vector is represented by the current best solution to the i-th subproblem, i.e., x i -μ i The covariance matrix ∑ i Obtained through neighborhood subproblems.
[0045] As a further aspect of the present invention, the specific method for updating the quantization table population based on penalized boundary intersections is as follows:
[0046] The subproblem is defined using a decomposition-based penalized boundary intersection method:
[0047] gpbi (x|wz * )=d1+θd2,
[0048]
[0049] d1 represents the convergence of the subproblem, and d2 represents the diversity of the quantized population. Multiplying the value of d2 by θ and d1 makes x have both convergence and diversity. The parameter θ controls the difference between d1 and d2. The penalized boundary intersection method is used to make F(X) approach the boundary.
[0050] As a further aspect of the present invention: the degree of improvement of the obtained offspring quantification table is evaluated, and for each individual x i Calculate the function value g of its subproblem. i (x i ) and g i (x), calculate its degree of improvement d i :
[0051] D i =g i (x i )-g i (x), i = 1, 2, ..., N,
[0052] Sort the improvements from largest to smallest, and then... i Subproblems greater than 0 are updated in the quantization table population, and the current ideal point of the population is updated.
[0053] The beneficial effects of this invention are:
[0054] This invention optimizes the quantization table of JPEG from the perspective of computation based on decomposition and Gaussian mixture model. Addressing the multi-functional requirements of bitrate in image coding, it studies a multi-objective image coding optimization technique that improves coding efficiency while reducing image quality loss. By performing multi-objective optimization on the quantization table, designing an evolutionary operator of Gaussian mixture model, global and local search strategies, and a quantization table population update based on penalized boundary intersections, the optimal quantization table can be effectively found. Attached Figure Description
[0055] The present invention will now be further described with reference to the accompanying drawings.
[0056] Figure 1 This is a schematic diagram of a JPEG quantization table optimization method based on decomposition and multi-objective optimization according to the present invention. Detailed Implementation
[0057] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0058] Please see Figure 1 As shown, this invention is a JPEG quantization table optimization method based on decomposition and multi-objective optimization, comprising the following steps:
[0059] A set of quality factors is randomly selected, and the standard quantization table is processed according to the quality factors to obtain an initialized quantization table population. Weight vectors and neighborhoods are assigned to individuals in the quantization table population. The optimization objectives of the quantization table population include bit rate, luminance quality mean square error, and chrominance quality mean square error.
[0060] The chroma components of the image are processed independently, the chroma components are divided into 8x8 image blocks, the image blocks are transformed into discrete cosine blocks for quantization, and the bit rate, luminance quality mean square error and chroma quality mean square error are obtained.
[0061] The subproblems in the quantization table population are sorted based on the distribution sparsity, thereby quickly obtaining the optimal quantization table solution set;
[0062] The population of the quantization table is searched using sampling mutation based on decomposition and Gaussian mixture models or staged multi-method crossover mutation.
[0063] The population of quantization tables is updated using a decomposition-based penalized boundary intersection method. The subproblem with the greatest improvement is selected from the population of quantization tables for updating, thereby obtaining the optimal quantization table.
[0064] Currently, JPEG quantization table optimization methods can be mainly categorized as follows: mathematical statistical methods, which derive suitable quantization tables through mathematical statistical analysis of the DCT coefficient distribution of an image set; adaptive methods, which not only use unique quantization tables for all images but also for all blocks of a specific image, utilizing the local frequency content of the image to better control the DCT coefficient quantization process; standard optimization methods, which employ standard optimization techniques such as gradient descent and simulated annealing; and direct search-based methods, which use a single-objective evolutionary algorithm (SOEA) to search for quantization tables, thereby obtaining the optimal compression and accuracy tradeoff for a specific type of image. However, in practical applications, user needs are diverse. For example, when transmitting an image over a network, some users may require a clear, high-quality version, while others may require a low-quality version that is easy to store and transmit.
[0065] This invention optimizes the quantization table of JPEG from the perspective of multi-objective evolutionary computation. Addressing the multi-functional requirements of bitrate in image coding, it studies a multi-functional image coding optimization technique based on multi-objective optimization, improving coding efficiency while reducing image quality loss. By performing multi-objective optimization on the quantization table, designing an evolutionary operator based on a Gaussian mixture model, global and local search strategies, and a quantization table population update based on penalized boundary intersections, the optimal quantization table can be effectively found, significantly reducing the data storage of the image quantization table.
[0066] In a preferred embodiment of the present invention, the process of processing the chromaticity components of an image is as follows:
[0067] The image's chromaticity components include a luminance chromaticity component Y, a blue chromaticity component Cb, and a red chromaticity component Cr. These chromaticity components are sequentially divided into 8*8 image blocks. The image data within the image is used as the basic processing unit to perform a discrete cosine transform. The resulting image data is the discrete cosine data. The quantization matrix stores the quantization step size for each discrete cosine frequency band. Image compression is achieved by losing some data through division and rounding.
[0068] Image data can be compressed because it contains redundancy. Common redundancy in image data includes spatial redundancy, temporal redundancy, spectral redundancy, and visual redundancy. Image compression coding aims to remove this redundancy. In some applications, a certain degree of distortion is permissible, thus allowing for lossy compression of images to a certain extent or even a large extent.
[0069] In another preferred embodiment of the present invention, the process of initializing the quantization table population includes:
[0070] Let N be the population size of the quantization table, obtain the bitrate, luminance quality mean square error, and chrominance quality mean square error for each subproblem, and denote the size of its neighborhood as T. Construct {w 1 w 2 ,…,w N A set of weight vectors. For each subproblem i = 1, 2, ..., N, construct a neighborhood B. i ={i1, i2, ..., i T}, making To be with w i Find the ideal point using the j-th nearest weight vector. Z * The minimum mean square error of image quality and the minimum bit rate are quantized in the population.
[0071] In one embodiment of these regulations, the process for obtaining the bitrate, the mean square error of luminance quality, and the mean square error of chrominance quality is as follows:
[0072]
[0073] Where (u, v) are the frequency band coordinates, F(u, v) are the discrete cosine coefficient values at the frequency band (u, v), Q(u, v) are the quantization step size at the frequency band, and round.integer is for rounding to the nearest integer. The quantization process is shown in Equation 3, and the dequantization reconstruction process is as follows:
[0074]
[0075] Define bitrate:
[0076]
[0077] height and width represent the height and width of the image after segmentation, and count represents the sum of all results with the same quantization coefficient;
[0078] Define the mean square error of luminance quality and the mean square error of chrominance quality:
[0079]
[0080] X and X′ are two M*N pixel matrices, where X represents the original image and X′ represents the compressed image. Substituting the pixel matrices of brightness and chrominance into X and X′ respectively yields the mean square error.
[0081] In another preferred embodiment of the present invention, the process of population sorting based on a sparsely distributed quantization table is as follows:
[0082] The covariance matrix used in the subproblem sampling is calculated using the neighborhood of the subproblem. For each individual x i Calculate its neighborhood center point:
[0083]
[0084] Obtain the sparsely distributed individuals in the current solution set. If the population distribution in the quantization table is uniform, then the solutions to the subproblems should be close to the center of their neighborhoods. For each individual x... i Calculate its sparsity:
[0085]
[0086] Where T is the neighborhood size, N is the population size of the quantization table, and for sparsity s 1 ,s 2 ,…,s N Sort in descending order.
[0087] Based on the process strategy of sparsely distributed quantization table population sorting, the obtained bitrate and image quality mean square error are sorted. The sparser the distribution of the subproblems, the higher the ranking will be. Then, the optimal quantization table solution set with uniform distribution can be obtained.
[0088] In one embodiment of this regulation, the process of employing global and local search includes: setting a neighborhood search probability δ; when the random number is greater than δ, sampling using a Gaussian mixture model; when the random number is less than δ, performing crossover and mutation in stages according to the population generation in the quantization table using the target estimation method, the difference method, and the Gaussian mixture model respectively. The global and local search processes use a maximum of [number missing] samples per cycle. The issue of individual offspring.
[0089] To account for the diversity of sampling, at most half of the subproblems are used to generate offspring each time.
[0090] In another instance of this implementing regulation, the specific method for hybridization and mutation based on decomposition and Gaussian mixture models is as follows:
[0091] Define a recombination operator based on decomposition and Gaussian mixture model for multi-objective optimization problems, given a set of data x. 1 ,x 2 ,…,x k The mean vector and covariance matrix are estimated as follows:
[0092]
[0093]
[0094] For each subproblem, a Gaussian model is constructed, whose probability density function is expressed as:
[0095]
[0096] Where pi(x) represents the probability density function corresponding to the i-th subproblem, μ i and Σ i Let pi(x) be the mean vector and covariance matrix, whose values are calculated from the neighborhood subproblems corresponding to the i-th subproblem;
[0097]
[0098] The mean vector is represented by the current best solution to the i-th subproblem, i.e., x i -μ i The covariance matrix Σ i Obtained through neighborhood subproblems.
[0099] Multivariate Gaussian model sampling is used to generate offspring. The parent of the recombination operator mainly comes from the neighborhood. Since the parents are close together, the problem of deviating from the optimal result after recombination can be avoided to a certain extent. The new individual not only updates its parent but also updates its neighborhood individuals, so that good new individuals are retained to the next generation as much as possible. The multinomial mutation operator can enhance the global search capability and accelerate convergence while maintaining diversity in the later stage. Therefore, while using local search based on decomposition and mixture Gaussian model sampling, the multinomial mutation operator is used to optimize the mutation operation.
[0100] In another preferred embodiment of the present invention, the specific method for updating the quantized table population based on penalized boundary intersections is as follows:
[0101] The subproblem is defined using a decomposition-based penalized boundary intersection method:
[0102] g pbi (x|wz * )=d1+θd2,
[0103]
[0104] d1 represents the convergence of the subproblem, and d2 represents the diversity of the quantized population. Multiplying the value of d2 by θ and d1 makes x have both convergence and diversity. The parameter θ controls the difference between d1 and d2. The penalized boundary intersection method is used to make F(X) approach the boundary.
[0105] It is worth noting that the degree of improvement of the obtained offspring quantification table should be evaluated for each individual x. i Calculate the function value g of its subproblem. i (x i ) and g i (x), calculate its degree of improvement d i :
[0106] D i =g i (x i )-g i (x), i = 1, 2, ..., N,
[0107] Sort the improvements from largest to smallest, and then... i Subproblems with values greater than 0 are updated in the quantization table population, and the ideal point of the population at this time is also updated.
[0108] θ is a preset penalty parameter that constrains d1 and d2, thereby obtaining the subproblem with the greatest improvement.
[0109] The foregoing has provided a detailed description of one embodiment of the present invention, but the description is merely a preferred embodiment and should not be construed as limiting the scope of the invention. All equivalent variations and improvements made within the scope of the present invention should still fall within the patent coverage of the present invention.
Claims
1. A JPEG quantization table optimization method based on decomposition and multi-objective optimization, characterized in that, Includes the following steps: A set of quality factors is randomly selected, and the standard quantization table is processed according to the quality factors to obtain an initialized quantization table population. Weight vectors and neighborhoods are assigned to individuals in the quantization table population. The optimization objectives of the quantization table population include bit rate, luminance quality mean square error, and chrominance quality mean square error. The chroma components of the image are processed independently, the chroma components are divided into 8x8 image blocks, the image blocks are transformed into discrete cosine blocks for quantization, and the bit rate, luminance quality mean square error and chroma quality mean square error are obtained. The subproblems in the quantization table population are sorted based on the distribution sparsity, thereby quickly obtaining the optimal quantization table solution set. The population of the quantization table is searched using sampling mutation based on decomposition and Gaussian mixture models or staged multi-method crossover mutation. The population of quantization tables is updated using a decomposition-based penalized boundary intersection method. The subproblem with the greatest improvement is selected from the population of quantization tables for updating, and the optimal quantization table is obtained. The process of population ranking based on the quantization table of distribution sparsity is as follows: The covariance matrix used in the subproblem sampling is calculated using the neighborhood of the subproblem, for each individual. Calculate its neighborhood center point: ， Obtain the sparsely distributed individuals in the current solution set. If the population distribution in the quantization table is uniform, then the solutions to the subproblems should be close to the center of their neighborhoods for each individual. Calculate its sparsity: ， T represents the neighborhood size, N represents the quantization table population size, and sparsity... Sort in descending order; The process of using global search and local search includes: A neighborhood search probability δ is set. When the random number is greater than δ, sampling using a Gaussian mixture model is used. When the random number is less than δ, crossover and mutation are performed in stages according to the population generation number in the quantization table, using the target estimation method, the finite difference method, and the decomposition-based and Gaussian mixture model respectively. The global search and local search use a maximum of [number missing] times per step. The issue of offspring arises from the number of offspring; The specific method for crossover and mutation using the Gaussian mixture model is as follows: Define a recombination operator based on decomposition and Gaussian mixture model for multi-objective optimization problems, given a set of data. The mean vector and covariance matrix are estimated as follows: ， ， For each subproblem, a Gaussian model is constructed, whose probability density function is expressed as: ， Where pi(x) represents the probability density function corresponding to the i-th subproblem. and Let pi(x) be the mean vector and covariance matrix. ， The mean vector is represented by the current best solution to the i-th subproblem, i.e. The covariance matrix Obtained through neighborhood subproblems.
2. The JPEG quantization table optimization method based on decomposition and multi-objective optimization according to claim 1, characterized in that, The process of processing the chromaticity components of an image is as follows: The image's chromaticity components include a luminance chromaticity component Y, a blue chromaticity component Cb, and a red chromaticity component Cr. These chromaticity components are sequentially divided into 8... The image block of 8 uses the image data within the image as the basic processing unit to perform discrete cosine transform. The image data obtained after the transform is discrete cosine data. The quantization matrix stores the quantization step size of each discrete cosine frequency band position. The purpose of image compression is achieved by losing some data through division and rounding.
3. The JPEG quantization table optimization method based on decomposition and multi-objective optimization according to claim 1, characterized in that, The process of initializing the quantization table population includes: Let N be the population size of the quantization table, obtain the bitrate, luminance quality mean square error, and chrominance quality mean square error for each subproblem, and denote the size of its neighborhood as T. Construct... For each subproblem i=1,2,…,N, construct a neighborhood using the set of weight vectors. , making To and The j-th nearest weight vector is used to obtain the ideal point. ,in The minimum mean square error of image quality and the minimum bit rate are quantized in the population.
4. The JPEG quantization table optimization method based on decomposition and multi-objective optimization according to claim 3, characterized in that, The process of obtaining bitrate, mean square error of luminance quality, and mean square error of chrominance quality is as follows: ， in For frequency band coordinates, Located in the frequency band The discrete cosine coefficients at point , The quantization step size is the value within the frequency band, and `round.integer` is the integer value. The quantization process is shown in the following formula: ， Define bitrate: ， height and width represent the height and width of the image after segmentation, and count represents the sum of all results with the same quantization coefficient; Define the mean square error of luminance quality and the mean square error of chrominance quality: ， X and There are two M's. An N-pixel matrix, where X represents the original image. To represent a compressed image, substitute the pixel matrices of luminance and chrominance into X and X respectively. The mean squared error is obtained.
5. The JPEG quantization table optimization method based on decomposition and multi-objective optimization according to claim 1, characterized in that, The specific method for updating the population based on the quantized table using penalized boundary intersections is as follows: The subproblem is defined using a decomposition-based penalized boundary intersection method: ， ， ， The convergence of the subproblem is represented by d2, which represents the population diversity of the quantization table. The value of d2 is multiplied by θ and This makes x possess both convergence and diversity, in and The distance between them is controlled by the parameter θ, and the penalty boundary intersection method is used to make F(X) approach the boundary.
6. The JPEG quantization table optimization method based on decomposition and multi-objective optimization according to claim 5, characterized in that, The degree of improvement of the obtained offspring quantification table was evaluated for each individual. Calculate the function value of its subproblem and Calculate its degree of improvement : ， Sort the improvements from highest to lowest, and then... Subproblems with values greater than 0 are updated in the quantization table population. And update the ideal point of the population at this time. .