Progressive image compression method based on signal-to-noise ratio features

Abstract

The application discloses a progressive image compression method based on a signal-to-noise ratio feature and belongs to the field of image processing. The method comprises the following steps: determining a hierarchical level of an image thumbnail, expanding the image, performing hierarchical down-sampling, obtaining a thumbnail image, estimating a noise level of the thumbnail image, calculating a signal-to-noise ratio covariance matrix of the thumbnail image, solving a characteristic vector of the signal-to-noise ratio covariance matrix by using a generalized eigenvalue algorithm, performing signal-to-noise ratio maximization projection on the image and retaining compressed image information, and performing image restoration by using the compressed image information. The application is a kind of progressive image compression method, can improve user experience in various systems, has the advantages of high compression ratio and high-quality reconstruction, and has a wide range of application scenarios.

Description

Technical Field

[0001] This invention belongs to the field of image processing technology, specifically relating to a progressive image compression method based on signal-to-noise ratio characteristics. Background Technology

[0002] With the development of image acquisition devices and technologies, increasingly higher quality images can be acquired, but this also brings pressure on image data transmission and storage. In some typical application scenarios, such as web-based human-computer interaction systems, image size is often more sensitive. Image compression technology can significantly reduce the size of image data while losing a small amount of image information. With the widespread use of high-resolution cameras and remote sensing satellites, the demand for processing large-size images is increasing, which places higher demands on compression technology.

[0003] In the image transmission systems of some instant messaging software, a progressive image transmission function is often required to improve the user experience. When a user receives or downloads an image, they will first see a relatively blurry version, and as time goes on, the image becomes clearer and clearer. This "transmit-and-display" progressive transmission method greatly shortens the time users wait for the image to be displayed for the first time, significantly improving the user experience.

[0004] Classic image compression techniques such as JPEG employ block coding based on Discrete Cosine Transform (DCT). While offering high encoding and decoding efficiency, this method produces noticeable "blocking artifacts" at high compression ratios, severely impacting subjective visual quality. To further improve compression efficiency, several machine learning-based or feature extraction-based methods have been proposed. Principal Component Analysis (PCA), a classic dimensionality reduction technique, aims to find the projection direction with the largest data variance and has also been applied to image compression. By dividing the image into blocks and extracting their principal components, data compression can be achieved. However, traditional PCA methods have significant limitations: First, their optimization goal is to maximize the global variance of the data, but the direction with the largest variance may not be the most visually important information and may even contain a large amount of image noise. This leads to noise being treated equally with effective signals during compression and reconstruction, resulting in a poor signal-to-noise ratio in the reconstructed image. Second, conventional PCA compression schemes lack inherent multi-resolution progressive transmission characteristics, making it difficult to achieve a smooth preview experience from blurry to sharp.

[0005] Progressive JPEG or JPEG2000's progressive transmission mode allows the receiver to obtain a rough overview of the entire image by changing the order of image data transmission, and then gradually refine the image as more data is received. This mode greatly improves the user experience in network transmission. Existing progressive compression methods are mostly based on reordering coefficients after frequency domain transformation according to their importance (such as amplitude). However, the metrics for these compression methods fail to comprehensively consider the balance between noise suppression and detail preservation; in low bitrate preview stages, the image is often too blurry or noisy.

[0006] Therefore, there is an unresolved contradiction in the existing technology: how to achieve high compression ratio and progressive transmission while ensuring high signal-to-noise ratio and high quality reconstructed images at each transmission stage (especially the low bit rate preview stage); specifically, there is a lack of a progressive compression mechanism that can actively distinguish and prioritize the preservation of effective image signals while suppressing noise components. Summary of the Invention

[0007] The specific technical problems to be solved by this invention include:

[0008] (1) Improve reconstruction quality under high compression ratio: solve the block effect and noise amplification problem of existing frequency domain compression methods at low bit rate, and ensure that high signal-to-noise ratio and high definition reconstructed images can be obtained in each transmission stage, especially in the preview stage (high compression ratio).

[0009] (2) Achieve a superior progressive transmission experience: Provide a smooth, high-quality progressive transmission mechanism from blurry to clear, from outline to detail.

[0010] (3) Optimize robustness to noise: Provide a compression mechanism that can actively distinguish and suppress noise and effectively preserve the true details of the image, which is especially suitable for fields with high image quality requirements such as medical imaging and remote sensing monitoring.

[0011] Therefore, this invention provides a progressive image compression method based on signal-to-noise ratio characteristics that does not require frequency domain transformation, which can effectively achieve progressive image compression and provide a progressive, high compression ratio, and high-quality reconstructed image compression scheme.

[0012] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0013] By combining multi-resolution image analysis with feature extraction based on maximizing the signal-to-noise ratio, the compression process is constructed and solved as a generalized eigenvalue problem, thereby maximizing the signal-to-noise ratio at each stage of compression.

[0014] The technical solution adopted in this invention is as follows:

[0015] A progressive image compression method based on signal-to-noise ratio features includes the following steps:

[0016] Step 1: Determine the layer level n based on the original image size, and expand both the width and height of the image to [the specified dimensions]. The values ​​are integer multiples of the original values, and the expanded image is layered and downsampled by odd-even multiples of 2. Through multi-level odd-even downsampling, the desired result is obtained. A thumbnail of uniform size;

[0017] Step 2, Calculate The signal covariance matrix of a thumbnail image Simultaneously, the noise covariance matrix is ​​calculated by extracting the noise components of each thumbnail image. And construct the signal-to-noise ratio covariance matrix. ;

[0018] Step 3, calculate the signal-to-noise ratio covariance matrix. eigenvectors The eigenvalues ​​are summed, and the eigenvectors with the largest m eigenvalues ​​are retained. The resulting eigenmatrix is ​​denoted as . Where m is a set value;

[0019] Step 4, using the feature matrix Project each thumbnail image to obtain m projected images;

[0020] Step 5: During image restoration, the feature matrix is ​​used. transpose matrix calculate Reconstructed thumbnails of uniform size are stitched together in the reverse order of downsampling the image from step 1 to restore the original image.

[0021] Furthermore, the specific method of step 1 is as follows:

[0022] Step 1a: Calculate the width and height of the image based on the number of pixels, and set the smaller of the width and height in pixels as the mean. The stratification level n is calculated using the following formula:

[0023] ;

[0024] Step 1b, expand both the width and height of the image to... The values ​​are multiples of the original values, and the expanded image is downsampled by 2 times according to the rows and columns. Then, the odd rows and odd columns, odd rows and even columns, even rows and odd columns, and even rows and even columns of the downsampled image are extracted to obtain 4 thumbnail images.

[0025] Step 1c: Perform a 2x downsampling on each thumbnail image by row and column respectively, and extract the odd rows and odd columns, odd rows and even columns, even rows and odd columns, and even rows and even columns of each downsampled image to obtain the corresponding thumbnail image;

[0026] Step 1d, return to step 1c, until finally obtained A thumbnail image.

[0027] Furthermore, the specific method of step 2 is as follows:

[0028] Step 2a: Perform row and column differencing on each thumbnail image. Calculate noisy images The calculation method is as follows:

[0029] ;

[0030] In the formula, For noisy images The pixel values ​​in the i-th row and j-th column, For thumbnail images The pixel values ​​in the i-th row and j-th column;

[0031] Step 2b, calculate according to the following formulas respectively The signal covariance matrix of a thumbnail image and the corresponding noise image noise covariance matrix :

[0032] ,

[0033] In the formula, L represents the number of thumbnail images. The covariance matrix of the thumbnail image elements For the i-th thumbnail image With the j-th thumbnail image The inner product; the noise covariance matrix of a noisy image. elements For the i-th noisy image With the j-th noisy image The inner product;

[0034] Step 2c: Calculate the signal-to-noise ratio covariance matrix. .

[0035] Furthermore, the specific method of step 3 is as follows:

[0036] Signal-to-noise ratio covariance matrix eigenvectors The calculation can be transformed into a problem of generalized eigenvectors and eigenvalues, as shown in the following formula, and the Lanczos algorithm is used to solve for the set of eigenvectors corresponding to the first m largest eigenvalues. :

[0037] ;in, The eigenvalue corresponding to the i-th eigenvector;

[0038] Furthermore, the specific method of step 4 is as follows:

[0039] Step 4a, let Characteristic matrix The 1 eigenvector;

[0040] Step 4b, using The thumbnail image is projected, resulting in m projected images, where the i-th projected image... The calculation method is as follows:

[0041] , ;

[0042] In the formula, for The element in the j-th row and i-th column of the array.

[0043] Furthermore, the specific method of step 5 is as follows:

[0044] Step 5a, using the feature matrix transpose matrix calculate A reconstructed thumbnail of uniform size, The calculation method for the j-th reconstructed thumbnail is as follows:

[0045] , ;

[0046] In the formula, for The corresponding element;

[0047] Step 5b: Following the reverse order of downsampling in Step 1, reconstruct the image starting from the nth level of sampling, using the reconstructed thumbnail. Restore the original image; if the image was expanded, crop the expanded portion directly after restoration.

[0048] Compared with the prior art, the present invention has the following significant advantages:

[0049] (1) Significantly improved reconstruction quality: Since the core of this invention is to optimize the signal-to-noise ratio rather than simply preserve the variance, the image quality of the reconstructed image is superior to methods based on DCT, wavelet transform, or traditional PCA at the same compression rate. Especially in the low bitrate preview stage, it can effectively suppress block artifacts and noise, presenting a clearer outline.

[0050] (2) Inherent progressive characteristics: The method itself naturally provides progressive transmission capabilities in two dimensions: resolution (through multi-level sampling) and detail quality (through selecting the number of feature vectors m), resulting in a smooth user experience. Taking 4-level compression as an example, it can be implemented according to... The compression ratio can be flexibly set, making it suitable for a wide range of applications.

[0051] (3) Advanced theory and flexible application: This framework is not limited to specific types of images. By adjusting the noise estimation model and feature selection strategy, it can be adapted to the special needs of different application scenarios, such as enhancing the preservation of text image edges or enhancing the weak contrast of medical images. By explicitly constructing the noise covariance matrix and suppressing it, it is more advantageous in applications in noisy environments (such as low-light imaging). Attached Figure Description

[0052] Figure 1 This is an overall flowchart of the progressive image compression method based on signal-to-noise ratio features in an embodiment of the present invention.

[0053] Figure 2 This is a schematic diagram illustrating the process of obtaining a thumbnail image through downsampling in an embodiment of the present invention.

[0054] Figure 3 This is an example diagram illustrating the image compression effect in an embodiment of the present invention; Figure 3 (A) is the original image. Figure 3 (B) is a 20x compressed image. Figure 3 (C) is a classic JPEG compressed image (partially magnified 20 times). Figure 3 (D) is a compressed image of the present invention (local magnification 20 times). Detailed Implementation

[0055] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. The present invention is a progressive image compression method based on signal-to-noise ratio (SNR) characteristics. An example is an 8-bit grayscale standard test image of size 2048×2048 pixels, which details the implementation steps of the method. The present invention combines multi-resolution image analysis with feature extraction based on maximizing the SNR, constructing and solving the compression process as a generalized eigenvalue problem, thereby maximizing the signal-to-noise ratio at each stage of compression. The process is as follows: Figure 1 As shown, it includes the following steps:

[0056] Step 1, Multi-resolution thumbnail generation. Determine the layer level n based on the original image size, and expand both the width and height of the image to [the desired size]. The values ​​are integer multiples of the original values, and the expanded image is layered and downsampled by odd-even multiples of 2. Through multi-level odd-even downsampling, the desired result is obtained. A thumbnail image of uniform size.

[0057] The specific method is as follows:

[0058] Step 1a: Calculate the width and height of the image in pixels, and set the smaller of the width and height in pixels as the mean. In this embodiment, q=2048, and the hierarchical level n is calculated according to the following formula:

[0059] ,but .

[0060] Step 1b, expand both the width and height of the image to... For example, if the image's width and height are both 2048, which is a multiple of 16, then no expansion is needed. For simplicity, let's assume the image width is 1990 and the height is 1000. In this case, the width should be expanded by 10 rows of pixels to 2000 (16*125), and the height by 8 rows of pixels to 1008 (16*63). The nearest neighbor algorithm can be used for this expansion.

[0061] Step 1c: Perform 4 levels of downsampling on the expanded image (2048×2048), as follows: Figure 2 As shown.

[0062] Level 1: Downsample the original image by a factor of 2 according to the parity index of the row and column to obtain 4 thumbnail images of (2048 / 2) × (2048 / 2) = 1024 × 1024.

[0063] Level 2: Perform the same odd-even downsampling on the four thumbnail images obtained in Level 1 to obtain 16 thumbnail images of 512×512.

[0064] Level 3: Perform the same odd-even downsampling on the 16 thumbnail images obtained in Level 2 to obtain 64 thumbnail images of 256×256.

[0065] Level 4: Perform the same odd-even downsampling on the 64 thumbnail images obtained in Level 3 to obtain 256 thumbnail images of 128×128.

[0066] Step 1d results in 256 thumbnails, each 128×128 pixels in size. .

[0067] Step 2, Signal-to-Noise Ratio Covariance Matrix Construction. Calculate the signal covariance matrix of the 256 thumbnail images. Simultaneously, an efficient noise estimation method (such as row and column difference operators) is used to extract the noise components of each thumbnail image, and the noise covariance matrix is ​​calculated. Furthermore, the core signal-to-noise ratio covariance matrix is ​​constructed. .

[0068] The specific method is as follows:

[0069] Step 2a, for each thumbnail image Calculate its noisy image The calculation is performed using row and column differences, as follows:

[0070]

[0071] in, For noisy images The pixel values ​​in the i-th row and j-th column, For thumbnail images The pixel values ​​in the i-th row and j-th column; this algorithm can effectively extract noise components from images, and other noise estimation methods can also be used to calculate... .

[0072] Step 2b: Calculate the signal covariance matrix of each thumbnail image using the following formula. and the noise covariance matrix of the corresponding noisy image :

[0073] ,

[0074] In the formula, L represents the number of thumbnail images, which is 256 in this example, and the covariance matrix of the thumbnail images. elements For the i-th thumbnail image With the j-th thumbnail image The inner product; the covariance matrix of the noisy image. elements For the i-th noisy image With the j-th noisy image The inner product of.

[0075] Step 2c, Signal-to-noise ratio covariance matrix .

[0076] Step 3, Maximum Signal-to-Noise Ratio Feature Extraction. Calculate the signal-to-noise ratio covariance matrix. eigenvectors The eigenvalues ​​are combined, and the eigenvectors with the largest m eigenvalues ​​are retained. The resulting eigenmatrix is ​​denoted as . In this embodiment, m=12.

[0077] To improve computational efficiency and avoid the instability issues of matrix inversion operations, the signal-to-noise ratio covariance matrix... eigenvectors The calculation can be transformed into The problem of defining generalized eigenvectors and eigenvalues, where, Let be the eigenvalue corresponding to the i-th eigenvector; and use the Lanczos algorithm to find the first 12 eigenvectors with the largest eigenvalues, which are . Its size is 256×12.

[0078] Step 4, Feature Projection and Compressed Storage. Utilizing... By projecting the thumbnail image and calculating the projected images, 12 projected images can be obtained; ultimately, only these 12 projected images and the feature matrix need to be stored. This can be achieved. Compression ratio;

[0079] A total of m projected images are generated after projection, where the i-th projected image... The calculation method is as follows:

[0080] , .

[0081] in, for The element in the j-th row and i-th column of the array.

[0082] Step 5, High-Quality Progressive Reconstruction. During image restoration, the feature matrix is ​​utilized. transpose matrix calculate By constructing reconstructed thumbnails of uniform size and stitching them together in the reverse order of downsampling the image from step 1, the original image can be recovered. By controlling the number of feature vectors involved in the reconstruction (12), a smooth and progressive restoration from a low-quality overview to a high-quality original image can be achieved.

[0083] The specific method is as follows:

[0084] Step 5a, using the feature matrix transpose matrix calculate A reconstructed thumbnail of uniform size, The j-th reconstructed thumbnail is calculated as follows:

[0085] , ;

[0086] In the formula, for The corresponding element.

[0087] Step 5b: Following the reverse order of downsampling in Step 1, starting from the 4th level thumbnail, reconstruct the thumbnails. The process gradually restores the thumbnailed images at 128×128, 256×256, 512×512, and 1024×1024, ultimately restoring the original 2048×2048 image. This example does not involve image augmentation; if image augmentation were performed, the augmented portion would simply be cropped.

[0088] Experimental results:

[0089] (1) In this example image, m=12, the image compression ratio is 21.33, and the original image size is 4MB, such as Figure 3 As shown in (A), the compressed size is 192KB. The image compression details are as follows: Figure 3 As shown in (B), it can be seen that the method of the present invention can maintain clear image edges and a smooth background even at a compression ratio of 20.

[0090] (2) Compared with classic JPEG, such as Figure 3 As shown in (C) and (D), at the same compression ratio, JPEG compression exhibits a significant patching effect, with patch sizes of 8×8, primarily because JPEG uses 8×8 block compression. The compression result of this invention does not exhibit patching effects.

[0091] (3) In terms of quantitative evaluation, the peak signal-to-noise ratio (PSNR) is used as a comparison index. The PSNR of JPEG compression is 33.71dB, while that of the method of this invention is 41.29dB, which is significantly better than the JPEG method.

Claims

1. A progressive image compression method based on signal-to-noise ratio characteristics, characterized in that, Includes the following steps: Step 1: Determine the layer level n based on the original image size, and expand both the width and height of the image to [the specified dimensions]. The values ​​are integer multiples of the original values, and the expanded image is layered and downsampled by odd-even multiples of 2. Through multi-level odd-even downsampling, the desired result is obtained. A thumbnail of uniform size; Step 2, Calculate The signal covariance matrix of a thumbnail image Simultaneously, the noise covariance matrix is ​​calculated by extracting the noise components of each thumbnail image. And construct the signal-to-noise ratio covariance matrix. ; Step 3, calculate the signal-to-noise ratio covariance matrix. eigenvectors The eigenvalues ​​are summed, and the eigenvectors with the largest m eigenvalues ​​are retained. The resulting eigenmatrix is ​​denoted as . Where m is a set value; Step 4, using the feature matrix Project each thumbnail image to obtain m projected images; Step 5: During image restoration, the feature matrix is ​​used. transpose matrix calculate Reconstructed thumbnails of uniform size are stitched together in the reverse order of downsampling the image from step 1 to restore the original image.

2. The progressive image compression method based on signal-to-noise ratio features according to claim 1, characterized in that, The specific method of step 1 is as follows: Step 1a: Calculate the width and height of the image based on the number of pixels, and set the smaller of the width and height in pixels as the mean. The stratification level n is calculated using the following formula: ； Step 1b, expand both the width and height of the image to... The values ​​are multiples of the original values, and the expanded image is downsampled by 2 times according to the rows and columns. Then, the odd rows and odd columns, odd rows and even columns, even rows and odd columns, and even rows and even columns of the downsampled image are extracted to obtain 4 thumbnail images. Step 1c: Perform a 2x downsampling on each thumbnail image by row and column respectively, and extract the odd rows and odd columns, odd rows and even columns, even rows and odd columns, and even rows and even columns of each downsampled image to obtain the corresponding thumbnail image; Step 1d, return to step 1c, until finally obtained A thumbnail image.

3. The progressive image compression method based on signal-to-noise ratio features according to claim 1, characterized in that, The specific method for step 2 is as follows: Step 2a: Perform row and column differencing on each thumbnail image. Calculate noisy images The calculation method is as follows: ； In the formula, For noisy images The pixel values ​​in the p-th row and q-th column. For thumbnail images The pixel values ​​in the p-th row and q-th column; Step 2b, calculate according to the following formulas respectively The signal covariance matrix of a thumbnail image and the corresponding noise image noise covariance matrix : ， ； In the formula, L represents the number of thumbnail images. The covariance matrix of the thumbnail image elements For the i-th thumbnail image With the j-th thumbnail image The inner product; the noise covariance matrix of a noisy image. elements For the i-th noisy image With the j-th noisy image The inner product; Step 2c: Calculate the signal-to-noise ratio covariance matrix. .

4. The progressive image compression method based on signal-to-noise ratio features according to claim 3, characterized in that, The specific method for step 3 is as follows: Signal-to-noise ratio covariance matrix eigenvectors The calculation can be transformed into a generalized eigenvector and eigenvalue problem, and the Lanczos algorithm is used to solve for the set of eigenvectors corresponding to the first m largest eigenvalues. : ;in, Let be the eigenvalue corresponding to the i-th eigenvector.

5. The progressive image compression method based on signal-to-noise ratio features according to claim 4, characterized in that, The specific method for step 4 is as follows: Step 4a, let Characteristic matrix The 1 eigenvector; Step 4b, using The thumbnail image is projected, resulting in m projected images, where the i-th projected image... The calculation method is as follows: ， ； In the formula, for The element in the j-th row and i-th column of the array.

6. The progressive image compression method based on signal-to-noise ratio features according to claim 5, characterized in that, The specific method of step 5 is as follows: Step 5a, using the feature matrix transpose matrix calculate A reconstructed thumbnail of uniform size, The calculation method for the j-th reconstructed thumbnail is as follows: ， ； In the formula, for The element in the j-th row and i-th column; Step 5b: Following the reverse order of downsampling in Step 1, reconstruct the image starting from the nth level of sampling, using the reconstructed thumbnail. Restore the original image; if the image was expanded, crop the expanded portion directly after restoration.

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