A Watermarking Optimization Method Based on Matrix Decomposition and DWT for Multi-Size Images
Abstract
:1. Introduction
- (1)
- The algorithm of watermarking can be adapted to multi-size host images and obtain better invisibility and robustness.
- (2)
- To the best of our knowledge, this is the first time that DWT, HMD, SVD, PSO, Arnold transform and logistic mapping combinations are applied to an image watermarking technique.
- (3)
2. Related Work
3. Materials and Methods
3.1. Discrete Wavelet Transform (DWT)
3.2. Matrix Decomposition
3.2.1. Hessenberg Matrix Decomposition
3.2.2. SVD Decomposition
3.3. Watermarking Encryption
3.3.1. Arnold Transform
3.3.2. Logistic Mapping
3.4. Particle Swarm Optimization Algorithm
4. Proposed Scheme
4.1. Scaling Factor
Algorithm 1: Using PSO to calculate the best α |
Input: Number of particles, N = 50, Weights, W = 0.5, Learning factor, C1 = 2, C2 = 2, Maximum number of iterations, T = 100. 1. Randomly initialize the position and velocity of each particle 2. Set and 3. 4. While iter < = T Implement Algorithm 1 using α Perform attacks tests Implement Algorithm 2 Calculate PSNRs using Equation (13), NCs using Equation (14), fitness value using Equation (15) Update and Update the position and velocity of each particle using Equations (10) and (11) end 5. Output: α. |
4.2. Watermark Embedding Algorithm
Algorithm 2: Embedding algorithm |
Input: Host image; watermark image; calculated by PSO. 1. Perform K-level DWT on the host image to obtain , 2. Perform HMD on , using Equation (4) to obtain H 3. Perform SVD on H using Equation (6) to obtain 4. Encrypt watermark using Equations (7) and (9) to obtain 5. Perform SVD on using Equation (6) to obtain 6. Using to embed watermark, 7. Calculate the new Hessenberg matrix 8. Calculate new low-frequency sub-band 9. Using IDWT to obtain the watermarked image Output: watermarked. |
4.3. Watermark Exacting Algorithm
Algorithm 3: Exacting algorithm |
Input: Watermarked image. 1. Perform K-level DWT on watermarked to obtain 2. Perform HMD on to obtain 3. Perform SVD on using Equation (6) to obtain 4. Using to exact into , 5. Calculate the watermark using in step 5 of Algorithm 2, 6. Decrypt Output: exacted watermark image. |
5. Results and Comparisons
5.1. Simulation Results
5.1.1. Invisibility Analysis
5.1.2. Robustness Analysis
5.1.3. Analysis of Attack Test Results
5.2. Algorithm Comparisons
5.2.1. Invisibility Comparison
5.2.2. Robustness Comparison
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Attacks | Parameters |
---|---|
Gaussian filter | 5 × 5 |
Median filter | 3 × 3 |
Average filter | 3 × 3 |
Wiener filter | 3 × 3 |
Gaussian noise | Variance = 0.01 |
Salt and pepper noise | Density = 0.01 |
Speckle noise | Variance = 0.01 |
JPEG compression | Quality factor (QF) = 50 |
Sharpening | 0.7 |
Crop | Left 12% |
Rotate | 90° |
Motion blur | Theta = 4, Len = 7 |
Attacks. | Girl | Park | Man | Lena | Goldhill | Baboon | House | Woman | Pepper |
---|---|---|---|---|---|---|---|---|---|
No | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
Gaussian filter | 0.9999 | 0.9999 | 0.9998 | 0.9999 | 0.9999 | 0.9999 | 0.9996 | 0.9997 | 0.9996 |
Median filter | 0.9999 | 0.9985 | 0.9999 | 0.9999 | 0.9997 | 0.9999 | 0.9993 | 0.9999 | 0.9998 |
Average filter | 0.9999 | 0.9986 | 0.9999 | 0.9999 | 0.9998 | 0.9999 | 0.9966 | 0.9961 | 0.9958 |
Wiener filter | 0.9997 | 0.9987 | 0.9996 | 0.9994 | 0.9993 | 0.9994 | 0.9988 | 0.9984 | 0.9987 |
Gaussian noise | 0.9999 | 0.9998 | 0.9999 | 0.9999 | 0.9999 | 0.9999 | 0.9999 | 0.9999 | 0.9999 |
Salt and pepper noise | 0.9999 | 0.9999 | 0.9999 | 0.9999 | 0.9999 | 0.9999 | 0.9998 | 0.9999 | 0.9999 |
Speckle noise | 0.9999 | 0.9999 | 0.9999 | 0.9999 | 0.9999 | 0.9999 | 0.9999 | 0.9999 | 0.9999 |
JPEG | 0.9999 | 0.9999 | 0.9999 | 0.9998 | 0.9998 | 0.9996 | 0.9992 | 0.999 | 0.9995 |
Crop | 0.9949 | 0.9946 | 0.9923 | 0.9917 | 0.9935 | 0.9919 | 0.9931 | 0.9909 | 0.9852 |
Sharpening | 0.9996 | 0.9988 | 0.9997 | 0.9981 | 0.9988 | 0.9981 | 0.9977 | 0.9968 | 0.9967 |
Rotating | 0.9995 | 0.9998 | 0.9996 | 0.9989 | 0.9984 | 0.9982 | 0.9983 | 0.998 | 0.9978 |
Motion blur | 0.9987 | 0.9986 | 0.9997 | 0.9967 | 0.9969 | 0.9961 | 0.9874 | 0.9899 | 0.9862 |
Attacks | Parameters | Host Image Size | ||
---|---|---|---|---|
1024 × 1024 | 512 × 512 | 256 × 256 | ||
Median Filter | 3 × 3 | 0.9994 | 0.9999 | 0.9985 |
5 × 5 | 0.9985 | 0.9978 | 0.9939 | |
7 × 7 | 0.9967 | 0.9879 | 0.9882 | |
Gaussian Noise | 0.001 | 0.9995 | 0.9998 | 0.9993 |
0.005 | 0.9990 | 0.9997 | 0.9896 | |
0.01 | 0.9984 | 0.9992 | 0.9842 | |
JPEG | 20 | 0.9995 | 0.9993 | 0.9992 |
50 | 0.9997 | 1 | 0.9996 | |
70 | 1 | 1 | 0.9999 | |
Crop | Left6% | 0.9995 | 0.9982 | 0.9875 |
Left 12% | 0.9964 | 0.9970 | 0.9828 | |
Left 25% | 0.9871 | 0.9865 | 0.9738 |
Images | [19] | [21] | [26] | Proposed |
---|---|---|---|---|
Lena | 43.8934 | 44.5125 | 43.9583 | 48.8785 |
Woman | 43.9624 | 44.5182 | 43.9501 | 49.5695 |
Goldhill | 43.9619 | 43.9023 | 43.9687 | 48.9170 |
House | 43.8264 | 44.3835 | 43.9876 | 49.5075 |
Attacks | [19] | [21] | [26] | Proposed |
---|---|---|---|---|
Filter | 25.8663 | 28.8229 | 27.6937 | 35.4073 |
Salt and pepper noise | 28.9628 | 25.3931 | 29.828 | 35.9293 |
JPEG (Q = 10) compression | 27.2172 | 33.8331 | 30.2218 | 37.1349 |
Crop 1/4 left up | 11.4584 | 11.7034 | 11.6027 | 11.7954 |
Sharpening | 28.7682 | 20.1304 | 31.0584 | 34.859 |
Rotating 45° | 10.1527 | 10.4813 | 10.3741 | 10.5114 |
Attacks | [19] | [21] | [26] | Proposed |
---|---|---|---|---|
Gaussian filter | 0.9786 | 0.9998 | 0.9377 | 0.9999 |
Median | 0.9328 | 0.9980 | 0.9872 | 0.9983 |
Average filter | 0.9784 | 0.9969 | 0.9369 | 0.9976 |
Wiener filter | 0.8933 | 0.9981 | 0.9903 | 0.9989 |
Gaussian noise | 0.9546 | 0.9711 | 0.9913 | 0.9999 |
Salt and pepper noise | 0.9921 | 0.9881 | 0.9948 | 0.9999 |
Speckle noise | 0.9917 | 0.9782 | 0.9955 | 0.9999 |
JPEG(Q = 10) compression | 0.9949 | 0.9997 | 0.9982 | 0.9996 |
Crop 1/4 left up | 0.6999 | 0.9702 | 0.9492 | 0.9865 |
Sharpening | 0.8637 | 0.9617 | 0.9923 | 0.9964 |
Rotating 45° | 0.7010 | 0.9805 | 0.9026 | 0.9509 |
Motion blur | 0.9032 | 0.9969 | 0.9921 | 0.9967 |
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Wang, L.; Ji, H. A Watermarking Optimization Method Based on Matrix Decomposition and DWT for Multi-Size Images. Electronics 2022, 11, 2027. https://doi.org/10.3390/electronics11132027
Wang L, Ji H. A Watermarking Optimization Method Based on Matrix Decomposition and DWT for Multi-Size Images. Electronics. 2022; 11(13):2027. https://doi.org/10.3390/electronics11132027
Chicago/Turabian StyleWang, Lei, and Huichao Ji. 2022. "A Watermarking Optimization Method Based on Matrix Decomposition and DWT for Multi-Size Images" Electronics 11, no. 13: 2027. https://doi.org/10.3390/electronics11132027
APA StyleWang, L., & Ji, H. (2022). A Watermarking Optimization Method Based on Matrix Decomposition and DWT for Multi-Size Images. Electronics, 11(13), 2027. https://doi.org/10.3390/electronics11132027