Quantization Error Compensation Method and System Based on Real-Time Front-End Detection of Key Points

Abstract

The present invention proposes a quantization error compensation method based on real-time front-end key point detection, belonging to the technical field of error optimization processing. The method includes: Step 1, constructing a key point detection model; Step 2, receiving a target image to be analyzed; Step 3, the key point detection model analyzes the target image and outputs image features; Step 4, integrating the output image features to obtain a coordinate mean value; Step 5, performing a normalization operation on the coordinate mean value using cosine similarity to obtain an expected coordinate mean value; Step 6, constructing a quantization error compensation operator to compensate the expected coordinate mean value; Step 7, outputting the final compensated image data. The present invention, through the quantization error compensation operator, makes up for the integration quantization error caused by softmax, so that without maintaining a high-resolution heat map, the front-end calculation memory overhead and inference time can be greatly reduced, and at the same time, the model detection accuracy is effectively improved.

Description

Technical Field

[0001] The present invention relates to the technical field of error optimization processing, and particularly relates to a quantization error compensation method and system based on real-time detection of key points at the front end. Background Art

[0002] Existing real-time detection algorithms for key points at the front end mostly use the method of regression coordinates for detection. To ensure the front-end inference speed, the model rarely uses the upsampling operation to enrich the receptive field combination. Compared with the Heatmap-based method, the direct regression method does not need to maintain high-resolution features, which can save front-end computing power resources and improve the model running speed.

[0003] The Regression-based method directly regresses coordinates through L1 or L2 loss and does not require the upsampling process, so the inference time is short. However, the fully connected layer in Regression converts the position information into coordinate values, losing the spatial information of the features and having strong non-linearity, so it is not easy to train and converge. Summary of the Invention

[0004] Object of the Invention: To propose a quantization error compensation method and system based on real-time detection of key points at the front end to solve the above problems existing in the prior art. Through the quantization error compensation operator, the integral quantization error caused by softmax is compensated, so that without maintaining a high-resolution heat map, the front-end computing memory overhead and inference time can be greatly reduced. At the same time, the model detection accuracy is effectively improved.

[0005] Technical Solution: In the first aspect, a quantization error compensation method based on real-time detection of key points at the front end is proposed. The method includes the following steps:

[0006] Step 1: Construct a key point detection model; the model includes a downsampling module composed of 3 sampling modules, a Head layer, and a fully connected layer.

[0007] Among them, the downsampling module is composed of a convolution with a stride of 2 and a BN layer. During the data processing, a size compression operation is performed on the received target image; the Head layer is connected to the fully connected layer, and the Head layer includes a 1×1 convolution for changing the dimension of the output feature and using the output feature as the input feature of the fully connected layer.

[0008] Step 2: Receive the target image to be analyzed and input it into the key point detection model;

[0009] Step 3: The key point detection model analyzes the target image and outputs image features;

[0010] Step 4: Integrate the image features output in Step 3 to obtain the coordinate mean value;

[0011] Step 5. Perform a normalization operation on the coordinate mean using cosine similarity to obtain the expected coordinate mean. This further includes the following steps:

[0012] Step 5.1. Receive the output features output by the Head layer;

[0013] Step 5.2. Read the fully connected layer parameters;

[0014] Step 5.3. Perform an operation on the output features in Step 5.1 and the parameters in Step 5.2 using cosine similarity;

[0015] Step 5.4. Perform a normalization operation on the operation result in Step 5.3 in a preset dimension to obtain a discrete probability distribution;

[0016] Step 5.5. Construct a scale factor , and perform a hyperparameter sharpening distribution based on the scale factor ;

[0017]

[0018] In the formula, represents the scale factor; represents the inner product of the input feature and the parameter in the fully connected layer; represents and the cosine similarity between them. Multiply by the scale factor . The scale factor can increase the response amplitude, enabling the input of Softmax to be maintained within an appropriate precision range. At the same time, cosine similarity normalization increases the non-linearity of the features. Therefore, the role of the scale factor will not be diluted by other parameters as the gradient descends.

[0019] Step 5.6. Based on the distribution situation in Step 5.5, in the case of a preset dimension, multiply the grid distance discretization by the discrete probability distribution and then integrate to obtain the expected coordinate mean.

[0020] Step 6. Construct a quantization error compensation operator to compensate the expected coordinate mean. When the key coordinate is , the process of obtaining the final key point coordinate through compensation includes the following steps:

[0021] Step 6.1. Read the output features after the cosine similarity normalization operation ;

[0022] Step 6.2. Perform a dimension conversion on the output features in Step 6.1;

[0023] Step 6.3: Sum the features on dimensions 2 and 3 respectively based on the conversion result in Step 6.2;

[0024] Step 6.4: Based on the processing result of Step 6.3, perform dimensionality reduction on the output feature in Step 6.1 to obtain the output features in two directions of the coordinates, namely and ;

[0025] Step 6.5: Map the output feature in Step 6.4 into a one-dimensional vector;

[0026] Step 6.6: Perform the Softmax operation on the one-dimensional vector in Step 6.5;

[0027] When the processing object is , the operation expression is:

[0028]

[0029] In the formula, represents 's coordinates; represents all possible coordinate points that may appear in the area; represents the total mapping analysis area. Among them, for the convenience of expression, let .

[0030] Step 6.7: According to the Soft-Argmax operation method, perform expression conversion on the expected coordinates of the key points;

[0031]

[0032] In the formula, represents the expected value of the first area plus the expected value of the second area ; represents the feature coordinate index; represents the normalized coordinate value of the current coordinate index; represents the value after performing Softmax;

[0033] Step 6.8: Combine the mapping relationship to perform another conversion on the converted expected coordinates in Step 6.7 to obtain the key point acquisition expression; among them, is equivalent to the weighted sum of two points, and at the same time, the response value in the mapping area is 0. Therefore, after conversion, 's expression is:

[0034]

[0035] Similarly, The expression of

[0036]

[0037] In the formula, .

[0038] Step 6.9: Output the final key point coordinates.

[0039] Step 7: Output the final compensated image data.

[0040] In some implementable ways of the first aspect, the key points are detected by using integral pose regression. No upsampling operation is added to the model backbone network, and the output features maintain a low-resolution size. The coordinate mean is obtained by integrating the output features, and the output features are normalized using cosine similarity to improve the non-linearity of the features before and after the Softmax operation. At the same time, a quantization error compensation operator is designed to make up for the integral quantization error caused by softmax. There is no need to maintain a high-resolution heat map, which greatly reduces the front-end computing memory overhead and inference time, and can effectively improve the model detection accuracy.

[0041] In the second aspect, a quantization error compensation system based on real-time front-end detection of key points is proposed to implement the quantization error compensation method. The system includes: a model construction module, a data transmission module, a feature extraction module, an operation module, a normalization module, a compensation module, and a data output module.

[0042] Among them, the model construction module is used to construct a key point detection model; the data transmission module is used to receive the target image to be analyzed and output it to the constructed key point detection model; the feature extraction module is used to extract the target image features; the operation module is used to integrate the image features output by the feature extraction module to obtain the corresponding coordinate mean; the normalization module is used to perform the operation of normalizing the output features on the coordinate mean obtained by the operation module; the compensation module is used to compensate the coordinate mean according to the preset quantization compensation operator to make up for the integral quantization error; the data output module is used to output the finally compensated image data.

[0043] In the third aspect, a quantization error compensation device based on real-time front-end detection of key points is proposed. The device includes: a processor and a memory storing computer program instructions; wherein, the processor reads and executes the computer program instructions to implement the quantization error compensation method.

[0044] In the fourth aspect, a computer-readable storage medium is proposed. Computer program instructions are stored on the computer-readable storage medium, and when the computer program instructions are executed by a processor, the quantization error compensation method is implemented.

[0045] Beneficial effects: The present invention proposes a quantization error compensation method and system based on real-time keypoint front-end detection. Through the quantization error compensation operator, the integral quantization error caused by softmax is compensated, so that without maintaining a high-resolution heatmap, the front-end computing memory overhead and inference time can be greatly reduced. At the same time, the model detection accuracy is effectively improved. Compared with the analysis models used in the prior art, the model constructed in the present invention does not have an artificial Gaussian distribution and an upsampling operation. Therefore, the inference speed is faster than the existing Heatmap-based methods. At the same time, the quantization error compensation operator can effectively reduce the quantization error caused by downsampling and Softmax, and improve the model detection accuracy. Description of the Drawings

[0046] Figure 1 It is a data processing flow chart in an embodiment of the present invention.

[0047] Figure 2 It is an example diagram of model processing in an embodiment of the present invention.

[0048] Figure 3 In an embodiment of the present invention, It is a schematic diagram of mapping into a one-dimensional vector. Detailed Embodiments

[0049] In the following description, a large number of specific details are given to provide a more thorough understanding of the present invention. However, it is obvious to those skilled in the art that the present invention can be implemented without one or more of these details. In other examples, in order to avoid confusion with the present invention, some well-known technical features in the art are not described.

[0050] The applicant believes that in the process of real-time keypoint front-end detection, in order to ensure the speed of front-end inference, models containing upsampling operations are rarely used, resulting in insufficient receptive fields. In the actual application process, the regression method is directly used without the need to maintain high-resolution features. For example, the output feature size of the Heatmap-based method is 64×64, and the output feature size of the Regression-based method is 8×8. Therefore, the front-end computing power resources can be saved and the model running speed can be improved.

[0051] In actual applications, the Regression-based method directly regresses the coordinates through L1 or L2 loss without an upsampling process and has a short inference time. However, the fully connected layer in Regression converts the position information into coordinate values, losing the spatial information of the features and having strong non-linearity. Therefore, it is not easy to train and converge. Therefore, the detection accuracy of the Regression-based method is lower than that of the Heatmap-based method.

[0052] In view of the problems existing in the actual application process, the present invention proposes a quantization error compensation method and system based on real-time front-end detection of key points. The method uses integral pose regression to detect key points, constructs a detection model that does not perform upsampling operations, so as to output data maintaining low-resolution features. Subsequently, the integral of the output features is calculated to obtain the coordinate mean value, and the output features are normalized using cosine similarity to improve the non-linearity of the features before and after the Softmax operation. Finally, a quantization error compensation operator is designed to achieve the purpose of compensating for the integral quantization error caused by softmax.

[0053] In one embodiment, a quantization error compensation method based on real-time front-end detection of key points is proposed. As Figure 1 shown, the method includes the following steps:

[0054] Step 1: Construct a key point detection model;

[0055] Step 2: Receive the target image to be analyzed and input it into the key point detection model;

[0056] Step 3: The key point detection model analyzes the target image and outputs image features;

[0057] Step 4: Calculate the integral of the image features output in Step 3 to obtain the coordinate mean value;

[0058] Step 5: Perform a normalization operation on the coordinate mean value using cosine similarity to obtain the expected coordinate mean value;

[0059] Step 6: Construct a quantization error compensation operator to compensate the expected coordinate mean value;

[0060] Step 7: Output the final compensated image data.

[0061] In a further embodiment, as Figure 2 shown, during the process of the constructed key point detection model performing key point analysis, the backbone network adopted includes 3 downsampling modules composed of convolutional layers with a stride of 2 and BN layers, which are used to compress the size of the input target image from N×256×256×3 to N×C×8×8. Subsequently, at the Head layer of the key point detection model, through 1×1 convolution, output features with a size of N×J×8×8 are obtained. Then, the cosine similarity between the output features and the full connection layer parameters is calculated, and the obtained cosine similarity features are subjected to Softmax normalization operation in the 8×8 dimension, that is, the WH dimension, to obtain a discrete probability distribution. Based on the obtained discrete probability distribution, a scale factor hyperparameter sharpened distribution is added, and the 8×8 grid distance is discretized and multiplied by the discrete probability distribution and then integrated to obtain the expected coordinate mean value.

[0062] Among them, in the process of using the Softmax function to obtain the discrete probability distribution characteristics, since the Softmax function will increase the values tending to 0 in the characteristics, making the probability distribution too smooth, resulting in the result of Soft-Argmax approaching the center of the distribution and unable to correctly reflect the maximum value position. Therefore, in this embodiment, a quantization error compensation operator is proposed to compensate the mean value of the expected coordinates, which is used to reduce the error caused by Softmax and the quantization error caused by the difference between the input resolution and the output resolution. In a preferred embodiment, in the process of compensating the quantization error of the mean value of the expected coordinates through the constructed quantization error compensation operator, the obtained key point coordinate value size is N×J×2, where N represents the batch-size (the number of samples used for training at one time); C represents the output dimension, preferably 96; J represents the number of key points, As a scale factor, it is preferably 15.

[0063] In a further embodiment, in the process of obtaining the mean value of the expected coordinates by multiplying the discrete probability distribution characteristics of the Head layer by the discrete distance and integrating, the Softmax function is used to obtain the discrete probability distribution characteristics. Therefore, in order to reduce the error caused by Softmax and the quantization error caused by the difference between the input resolution and the output resolution, a quantization error compensation operator is constructed to compensate the quantization error of the mean value of the expected coordinates.

[0064] Specifically, first, the dimension of the Head layer output feature with a size of N×J×8×8 is modified to N×J×64; then, a fully connected layer with an input dimension of 64 and an output dimension of 64 is constructed, and the output feature after the dimension modification of the Head layer is used as the input of the fully connected layer. After being processed by the fully connected layer, the fully connected output feature is obtained, and its corresponding size is N×J×64.

[0065] Based on the 64-layer features in the obtained Head layer output features and the constructed fully connected layer, L2 norm normalization processing is performed to obtain the Head layer L2-normalized feature ||f|| and the fully connected normalization parameter ||w||. Among them, the cosine similarity normalization is used in the Head layer to obtain the feature The expression is:

[0066]

[0067] In the formula, represents the inner product of the input feature and the parameter in the fully connected layer; represents the i-th feature; represents the i-th parameter value; represents and the cosine similarity between them, The output range is compressed to [-1, 1], and the corresponding output expression is:

[0068]

[0069] In the formula, represents the scale factor, which can enlarge the response amplitude and keep the input of Softmax within an appropriate accuracy range. At the same time, the cosine similarity normalization increases the non-linearity of the features. Therefore, the role of the scale factor will not be diluted by other parameters along with the gradient descent.

[0070] Subsequently, the with a size of N×J×64 is re-modified to N×J×8×8 in output dimension, and the features are summed respectively in dimension 2 and dimension 3. After dimensionality reduction, and are obtained, where corresponds to a size of N×J×8, and corresponds to a size of N×J×8.

[0071] In the preferred embodiment, given the key point coordinates , assuming the response values follow a Gaussian distribution, is mapped into a one-dimensional vector, as shown in Figure 3 , where W represents the normalized length of the vector. In this method, the vector length is 8, and after normalization, W equals 1, with each grid interval being 1 / 8. Subsequently, a Softmax operation is performed on , that is:

[0072]

[0073] In the formula, represents 's coordinates; represents all possible coordinate points in the area; represents the total mapping analysis area. Among them, for the convenience of expression, let

[0074] When the response values in the area are all 0, because the numerator part is 1, the result after dividing the area can be expressed as:

[0075]

[0076] According to the calculation formula of Soft-Argmax, the expression of the expected coordinate value is:

[0077]

[0078] In the formula, represents the expected value of the first region plus the expected value of the second region; represents the characteristic coordinate index; represents the normalized coordinate value of the current coordinate index. Additionally, similarly, it can represent the weighted sum of two points, that is:

[0079]

[0080] Meanwhile,

[0081]

[0082] Therefore, can be equivalent to:

[0083]

[0084] Since the sum of the weighted weights is equal to 1, therefore, using to represent , at this time can be equivalent to:

[0085]

[0086] Therefore, can be expressed as:

[0087]

[0088] Meanwhile, in this embodiment, W is normalized, so , at this time the expression of is:

[0089]

[0090] Similarly, the expression of can be obtained as:

[0091]

[0092] During the above data processing, , is obtained by integrating the product of the cosine similarity normalized feature and the coordinate value. Since , is based on conforming to the Gaussian distribution, On the basis that the response values of the regions are all 0, it thus compensates for the integral error caused by the Softmax function increasing the values close to 0 in the features, making the probability distribution too smooth. At the same time, the cosine similarity normalization increases the non-linearity degree of the features, and the scale factor The effect of making the probability distribution sharp will not be diluted by other parameters as the gradient descends.

[0093] The error compensation method proposed in this embodiment compensates for the integral quantization error caused by softmax by quantifying the error compensation operator, so that without maintaining a high-resolution heatmap, the front-end computing memory overhead and inference time can be greatly reduced. At the same time, the model detection accuracy is effectively improved. In addition, since there is no artificial Gaussian distribution and upsampling operation in the model, the inference speed of this method is faster than the Heatmap-based method in the prior art.

[0094] In a preferred embodiment, in the inspection of overhead power lines for UAV network configuration, for the real-time detection technology of key points, since the algorithm is deployed in the front-end device, a low-resolution Gaussian heatmap is generally used for key point regression operations. In the process of this scheme, during inference, because the size of the predicted key point feature map is quite different from the size of the input image (generally, the input image size is 256*256, while the output feature size is 64*64), there is a large quantization error in mapping the index coordinates of the maximum value of the output feature back to the input image. The present invention proposes a quantization error compensation method for the above quantization error, directly regressing the key point coordinates by integrating the output features, thus effectively improving the quantization error caused by mapping. At the same time, the error compensation operator compensates for the integral quantization error caused by softmax, and combines the cosine similarity normalization to improve the key point detection accuracy. In the experiment, the mAP of the original model for detecting insulator key points is 0.71, and using the quantization error compensation method can increase the mAP to 0.73, and the front-end running speed remains unchanged.

[0095] In one embodiment, a quantization error compensation system for real-time front-end detection of key points is proposed to implement the quantization error compensation method for real-time front-end detection of key points. The system includes the following modules: a model construction module, a data transmission module, a feature extraction module, an operation module, a normalization module, a compensation module, and a data output module.

[0096] Among them, the model construction module is used to construct a key point detection model; the data transmission module is used to receive the target image to be analyzed and output it to the constructed key point detection model; the feature extraction module is used to receive the target image to be analyzed and output it to the constructed key point detection model; the operation module is used to integrate the image features output by the feature extraction module to obtain the corresponding coordinate mean value; the normalization module is used to perform the operation of normalizing and outputting features on the mean value obtained by the operation module; the compensation module is used to compensate the coordinate mean value according to the preset quantization compensation operator to make up for the integration quantization error; the data output module is used to output the finally compensated image data.

[0097] In a further embodiment, when the key point detection model constructed by the model construction module performs data processing, ShuffleNetv2 is used as the backbone network, which includes 3 downsampling modules composed of a convolution with a stride of 2 and a BN layer, used to compress image features. For example, an input image with a size of N×256×256×3 is compressed into a feature image with a size of N×C×8×8. And through a 1×1 convolution in the Head layer, an output feature of N×J×8×8 is obtained.

[0098] Subsequently, the operation module calculates the cosine similarity between the output feature and the full connection layer parameters, and the normalization module performs a Softmax normalization operation on the cosine similarity feature in the 8×8 dimension (WH dimension) to obtain a discrete probability distribution, and a scale factor is added Hyperparameter sharpened distribution.

[0099] Finally, the compensation module multiplies the 8×8 grid distance discretization by the discrete probability distribution and then integrates to obtain the expected coordinate mean value, and uses the designed quantization error compensation operator to compensate the quantization error of the expected coordinate mean value to obtain the key point coordinate value, corresponding to a size of N×J×2. And the finally compensated image data is output through the data output module.

[0100] Compared with the analysis model used in the prior art, the model constructed in this embodiment does not have an artificial Gaussian distribution and an upsampling operation. Therefore, the inference speed is faster than the existing Heatmap-based method. At the same time, the quantization error compensation operator can effectively reduce the quantization error caused by downsampling and Softmax, improving the model detection accuracy.

[0101] As described above, although the present invention has been shown and described with reference to specific preferred embodiments, it should not be construed as a limitation of the present invention itself. Various changes can be made in its form and details without departing from the spirit and scope of the present invention defined by the appended claims.

Claims

1. A quantization error compensation method based on real-time front-end detection of key points, characterized in that, It includes the following steps: Step 1: Construct a key point detection model; Step 2: Receive the target image to be analyzed and input it into the key point detection model; Step 3: The key point detection model analyzes the target image and outputs image features; Step 4: Integrate the image features output in Step 3 to obtain the coordinate mean value; Step 5: Use cosine similarity to perform a normalization operation on the coordinate mean value to obtain the expected coordinate mean value; Step 6: Construct a quantization error compensation operator to compensate for the mean of the expected coordinates, which specifically includes the following steps: Step 6.1: Read the output features after the cosine similarity normalization operation ; Step 6.2: Perform dimensional conversion on the output features in Step 6.1; Step 6.3: Based on the conversion result in Step 6.2, sum the features in dimensions 2 and 3 respectively; Step 6.4: Dimension reduction is performed on the output features in Step 6.1 based on the processing result of Step 6.3 to obtain the output features in two directions of coordinates and ; specifically including: Based on the data obtained after dimensionality reduction, the acquisition expression of the expected coordinate value in the x direction is: In the formula, represents the total mapping analysis area, represents the first area plus the expected value of the second area of the expected value; ; represents the normalized coordinate value of the current coordinate index; represents the value after performing Softmax; Based on the data obtained after dimensionality reduction, the acquisition expression of the expected coordinate value in the y direction is: In the formula, represents the expected value of the first region plus the expected value of the second region ; ; represents the normalized coordinate value of the current coordinate index; represents the value after performing Softmax; When the key point coordinates are , after compensation, the acquisition expression of the key point coordinates is: In the formula, , represents all possible coordinate points that can appear in the area; Step 6.5: Map the output features in Step 6.4 into a one-dimensional vector; Step 6.6: Perform a Softmax operation on the one-dimensional vector in Step 6.5; Step 6.7: According to the Soft-Argmax operation method, perform a conversion on the expression of the expected coordinates of the key points; Step 6.8: Combine the mapping relationship to perform a secondary conversion on the expected coordinates converted in Step 6.7 to obtain the key point acquisition expression; Step 6.9: Output the final key point coordinates; Step 7: Output the final compensated image data.

2. The quantization error compensation method based on real-time front-end detection of key points according to claim 1, wherein In the backbone network of the key point detection model, there are 3 downsampling modules, and during the data processing, a size compression operation is performed on the received target image; The downsampling module consists of a convolution with a stride of 2 and a BN layer.

3. A quantization error compensation method based on real-time front-end detection of key points according to claim 1, characterized in that The key point detection model also includes a Head layer and a fully connected layer; the Head layer is connected to the fully connected layer; The Head layer includes a 1×1 convolution, which is used to change the dimension of the output features and use the output features as the input features of the fully connected layer.

4. A quantization error compensation method based on real-time front-end detection of key points according to claim 3, characterized in that, Based on the constructed key point detection module, during the process of obtaining the expected coordinate mean value in Step 5, it includes the following steps: Step 5.1: Receive the output features output by the Head layer; Step 5.2: Read the parameters of the fully connected layer; Step 5.3: Use cosine similarity to perform an operation on the output features in Step 5.1 and the parameters in Step 5.2; Step 5.4: Perform a normalization operation on the operation result in Step 5.3 in a preset dimension to obtain a discrete probability distribution; Step 5.5, construct a scale factor , and based on the scale factor perform hyperparameter sharpening distribution; Step 5.6: Based on the distribution situation in Step 5.5, in the case of a preset dimension, multiply the grid distance discretization by the discrete probability distribution and then integrate to obtain the expected coordinate mean value.

5. A quantization error compensation method based on real-time front-end detection of key points according to claim 1, characterized in that, The output feature expression after the cosine similarity normalization operation is: Wherein, represents a scale factor; represents the inner product of the input feature and the parameter in the fully connected layer; represents and the cosine similarity between; represents the output feature of the Head layer, represents the parameter of the fully connected layer; represents the i-th feature; represents the i-th parameter value.

6. A quantization error compensation system based on real-time front-end key point detection, which is used to implement the quantization error compensation method described in any one of claims 1-5, characterized in that It includes the following modules: A model construction module, which is set to construct a key point detection model; A data transmission module, which is set to receive the target image to be analyzed and output it into the constructed key point detection model; A feature extraction module, which is set to extract target image features; An operation module, which is set to integrate the image features output by the feature extraction module to obtain the corresponding coordinate mean value; A normalization module, which is set to perform an operation of normalizing the output features on the coordinate mean value obtained by the operation module; A compensation module, which is configured to compensate the mean value of the expected coordinates according to a preset quantization compensation operator to make up for the integration quantization error; A data output module, which is configured to output the finally compensated image data.

7. A quantization error compensation device based on real-time front-end detection of key points, characterized in that, The device includes: A processor and a memory storing computer program instructions; The processor reads and executes the computer program instructions to implement the quantization error compensation method according to any one of claims 1-5.

8. A computer-readable storage medium, characterized in that, Computer program instructions are stored on the computer-readable storage medium, and when the computer program instructions are executed by the processor, the quantization error compensation method according to any one of claims 1-5 is implemented.

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