ADAPTIVE DWT-SVD WATERMARKING FRAMEWORK WITH IMAGE-DEPENDENT ALPHA OPTIMIZATION

УДК 004.056:004.932

Abstract

Digital image watermarking is widely used for copyright protection, ownership verification, and multimedia authentication. In this study, an adaptive invisible watermarking framework based on hybrid Discrete Wavelet Transform and Singular Value Decomposition (DWT-SVD) with image-dependent alpha optimization is proposed. Initially, traditional watermarking methods including DCT, DWT, Block-SVD, and hybrid DWT-SVD were experimentally compared under JPEG compression, Gaussian noise, and Gaussian blur attacks. The comparison was performed using Peak Signal-to-Noise Ratio (PSNR), Structural Similarity Index (SSIM), Bit Error Rate (BER), and correlation coefficient metrics. Experimental results demonstrated that the DWT-SVD framework achieved superior robustness and imperceptibility compared with the other methods. Therefore, DWT-SVD was selected as the primary embedding framework for adaptive optimization experiments. Multiple alpha values were evaluated independently for different test images using a weighted optimization function based on PSNR, SSIM, BER, and correlation values. The experimental results showed that while several images achieved optimal performance with alpha = 20, some images required different embedding strengths to achieve a better balance between watermark robustness and image quality. In addition, EfficientNet-B0 deep image features were preliminarily investigated for intelligent alpha prediction. The proposed framework demonstrates the potential of adaptive and context-aware watermarking systems for improving invisible watermarking performance under common image processing attacks.

Аннотация

Цифровое водяное маркирование изображений широко используется для защиты авторских прав, подтверждения владения и аутентификации мультимедийного контента. В данной работе предлагается адаптивная система невидимого водяного маркирования на основе гибридного метода Discrete Wavelet Transform и Singular Value Decomposition (DWT-SVD) с оптимизацией параметра alpha в зависимости от изображения. На первом этапе были экспериментально сравнены традиционные методы водяного маркирования, включая DCT, DWT, Block-SVD и гибридный DWT-SVD, при воздействии JPEG-сжатия, гауссовского шума и гауссовского размытия. Сравнение выполнялось с использованием метрик Peak Signal-to-Noise Ratio (PSNR), Structural Similarity Index (SSIM), Bit Error Rate (BER) и коэффициента корреляции. Экспериментальные результаты показали, что метод DWT-SVD обеспечивает лучшую устойчивость и незаметность по сравнению с другими подходами. Поэтому DWT-SVD был выбран в качестве основного алгоритма внедрения для этапа адаптивной оптимизации. Для различных тестовых изображений независимо оценивались несколько значений alpha с использованием взвешенной функции оптимизации на основе значений PSNR, SSIM, BER и корреляции. Результаты показали, что, хотя для многих изображений оптимальное качество достигалось при alpha = 20, некоторые изображения требовали других значений embedding strength для достижения лучшего баланса между устойчивостью водяного знака и качеством изображения. Кроме того, были предварительно исследованы глубокие признаки EfficientNet-B0 для интеллектуального прогнозирования параметра alpha. Предложенная система демонстрирует потенциал адаптивных и контекстно-зависимых систем водяного маркирования для повышения эффективности невидимого водяного маркирования при распространённых атаках обработки изображений.

Keywords: Digital watermarking, DWT-SVD, adaptive watermarking, alpha optimization, EfficientNet-B0, robustness, imperceptibility.

Ключевые слова: Цифровое водяное маркирование, DWT-SVD, адаптивное водяное маркирование, оптимизация alpha, EfficientNet-B0, защита авторских прав, невидимое водяное маркирование.

1. Introduction

Invisible watermarking is an important technique for protecting digital images against unauthorized copying and distribution.Watermarking systems are widely used for copyright protection, authentication, and ownership verification by embedding hidden information into multimedia content [1].

A watermarking method must satisfy two important requirements: imperceptibility and robustness. Imperceptibility means that the watermark should not noticeably reduce the visual quality of the host image. Robustness means that the watermark should remain detectable after common image processing operations and attacks.

Transform-domain watermarking methods generally provide better robustness than spatial-domain approaches. Discrete Cosine Transform (DCT), Discrete Wavelet Transform (DWT), and Singular Value Decomposition (SVD) are commonly used in invisible watermarking systems because they provide better resistance to compression and noise [3].

Hybrid watermarking approaches that combine multiple transforms have recently attracted attention because they can improve both robustness and image quality. In particular, the DWT-SVD combination provides a stable embedding environment while maintaining high imperceptibility [2].

Another important problem in watermarking systems is the selection of embedding strength. Most traditional methods use a fixed alpha value for all images. However, different image structures may require different embedding strengths to achieve the best balance between robustness and imperceptibility.

Motivated by these problems, this study compares DCT, DWT, SVD, and DWT-SVD watermarking methods under several attacks. After identifying DWT-SVD as the best-performing method, adaptive alpha optimization experiments were conducted using multiple test images. The study also preliminarily investigates EfficientNet-B0 deep features for intelligent alpha prediction. The objective of this study is to develop and evaluate an adaptive DWT-SVD watermarking framework with image-dependent alpha optimization for invisible image watermarking. The study aims to compare traditional watermarking methods including DCT, DWT, Block-SVD, and hybrid DWT-SVD under common image processing attacks and to investigate whether adaptive alpha selection can improve the balance between watermark robustness and image imperceptibility. In addition, preliminary experiments using EfficientNet-B0 deep image features are conducted for intelligent alpha prediction.

2. Materials and Methods

2.1. DWT-SVD Watermarking Framework

The proposed method combines DWT and SVD transforms for invisible watermark embedding. First, the host image is converted into grayscale and decomposed using one-level DWT. The LL sub-band is selected for watermark embedding because it provides higher robustness against attacks.

After DWT decomposition, Singular Value Decomposition is applied to the selected sub-band:

The watermark information is embedded into the singular values using the embedding strength parameter alpha:

where:

Σ represents original singular values,

W represents the watermark matrix,

α is the embedding strength.

Finally, inverse SVD and inverse DWT are applied to reconstruct the watermarked image [4].

2.2. Experimental Setup

Experiments were conducted using grayscale images selected from the Oxford-IIIT Pet Dataset. Since the original dataset contains RGB images, all images were converted into grayscale format prior to watermark embedding and evaluation. The watermark image was transformed into a 32×32 binary watermark matrix before the embedding process.

Four watermarking approaches including DCT, DWT, Block-SVD, and hybrid DWT-SVD were experimentally evaluated under common image processing attacks. The robustness evaluation included JPEG compression, Gaussian noise, and Gaussian blur attacks applied at different intensity levels. JPEG compression experiments were conducted using quality factors between 50 and 90. Gaussian noise attacks were applied using multiple variance levels, while Gaussian blur attacks were performed using different kernel sizes in order to evaluate watermark robustness under varying distortion conditions.

For adaptive optimization experiments, multiple embedding strength values were independently tested for each image:

α= {10,15,20,25,30,40}

For each alpha value, watermark embedding and extraction were performed, and the resulting PSNR, SSIM, BER, and correlation values were recorded [6]. In addition to average metric values, statistical analysis was performed using mean-based comparative evaluation across multiple experimental samples in order to reduce the influence of image-specific variability and attack-dependent fluctuations.

Figure 1. Examples of Oxford-IIIT Pet Dataset images

2.3. Adaptive Alpha Optimization

Traditional watermarking systems commonly use a fixed embedding strength parameter for all images. However, different image structures may respond differently to watermark embedding depending on texture complexity, edge distribution, and frequency-domain characteristics. Therefore, this study introduces an adaptive alpha optimization framework for selecting suitable embedding strengths individually for different images.

For each test image, multiple alpha values were experimentally evaluated. The optimal alpha value was selected using a weighted optimization function based on both imperceptibility and robustness metrics:

Score = w₁·PSNR + w₂·SSIM + w₃·Correlation – w₄·BER

where:

• PSNR and SSIM evaluate image imperceptibility,
• correlation evaluates watermark recovery similarity,
• BER evaluates watermark extraction errors.

In the experiments, the weighting coefficients were empirically selected as:

w₁ = 0.25

w₂ = 0.25

w₃ = 0.30

w₄ = 0.20

Higher PSNR, SSIM, and correlation values increase the optimization score, while higher BER values reduce the score. The alpha value producing the highest optimization score was selected as the optimal embedding strength for the corresponding image.

Experimental results demonstrated that although several images achieved optimal performance with alpha = 20, some images achieved better robustness-imperceptibility balance with alternative alpha values, indicating the usefulness of adaptive optimization strategies. [5]

2.4. Deep Feature-Based Alpha Prediction

In addition to statistical optimization, preliminary experiments were conducted using EfficientNet-B0 deep image features for intelligent alpha prediction. EfficientNet-B0 was used as a deep feature extractor to obtain representative image features related to texture distribution, structural complexity, and visual characteristics.

The extracted deep features were combined with experimentally determined optimal alpha values and used for preliminary machine learning-based alpha estimation experiments. The objective of this stage was not to develop a fully trained prediction model, but rather to investigate whether deep image representations could support adaptive watermarking optimization.

Recent studies have demonstrated the increasing importance of deep learning techniques for intelligent and adaptive watermarking systems [7]. EfficientNet-B0 was selected because of its efficient feature extraction capability and strong image representation performance [9].

3. Results

3.1. Comparison of Watermarking Methods

Initially, all watermark embedding methods including DCT, DWT, SVD, and DWT-SVD were experimentally evaluated. Table 1 presents the statistical comparison of DCT, DWT, Block-SVD, and hybrid DWT-SVD watermarking methods using average PSNR, SSIM, BER, and correlation values obtained from experimental evaluations under multiple attacks. The experimental results demonstrate that the hybrid DWT-SVD framework achieved the best overall balance between imperceptibility and robustness. In particular, DWT-SVD produced the highest PSNR and correlation values together with very low BER values, indicating strong watermark recovery performance while preserving image quality. Therefore, DWT-SVD was selected as the primary embedding framework

Table 1. Comparative Statistical Analysis of Watermarking Methods

3.2. Adaptive Alpha Optimization Results

After selecting DWT-SVD as the best-performing watermarking method, adaptive alpha optimization experiments were conducted using multiple test images. Different images were evaluated independently in order to investigate whether different image structures may benefit from different embedding strengths. The results shown in Table 2 indicate that some images selected different alpha values during the optimization process. Experimental results demonstrated that fixed alpha values do not always provide optimal performance across all image structures.

For multiple test images, the framework automatically selected alpha values such as:

α = 15

α = 20

α = 25

depending on image characteristics and attack performance. Several test images achieved optimal performance with alpha = 20, while some images achieved better robustness-imperceptibility balance using alternative embedding strengths. High PSNR and SSIM values together with low BER and high watermark correlation were maintained during the optimization process.

Table 2. Adaptive Alpha Optimization Results for the DWT-SVD Framework

To improve the visual interpretability of the experimental results and avoid unnecessary numerical precision, PSNR values were rounded to two decimal places, whereas SSIM, BER, correlation, and optimization score values were rounded to four decimal places.

3.3. Deep Feature-Based Prediction Results

A preliminary deep feature-based alpha prediction experiment was conducted using EfficientNet-B0 feature extraction together with a Random Forest classifier. The experiment aimed to investigate whether deep image features contain sufficient information for predicting the optimal embedding strength selected during the adaptive optimization process. Grayscale images selected from the Oxford-IIIT Pet Dataset were used for the experiment, and the optimal alpha values obtained from Table 2 were used as classification labels.

Due to the limited number of experimentally optimized image samples, Leave-One-Out Cross Validation (LOOCV) was used for evaluation. Experimental results demonstrated that the preliminary EfficientNet-B0-based classifier achieved an accuracy of 70% for adaptive alpha prediction.

Figure 2 presents the resulting confusion matrix for alpha prediction. The results indicate that the classifier successfully identified the dominant alpha = 20 class, while prediction performance for minority classes remained more limited because of dataset imbalance and the small number of available training samples. Nevertheless, the experimental observations suggest that deep image features may provide useful information for adaptive watermarking optimization and intelligent embedding parameter selection in future studies.

Figure 2. Confusion matrix for preliminary EfficientNet-B0-based adaptive alpha prediction using Leave-One-Out Cross Validation

4. Discussion

The experimental results show that DWT-SVD provides better robustness and imperceptibility compared with standalone DCT, DWT, and SVD methods. The hybrid method maintained low BER and high correlation under several attacks while preserving image quality.

The experiments also show that fixed alpha values may not provide the best performance for all images. Different images selected different alpha values during the optimization process. This indicates that adaptive alpha selection can improve the balance between robustness and imperceptibility.

The preliminary EfficientNet-B0 experiments also show that deep image features may be useful for intelligent alpha prediction in future adaptive watermarking systems.

5. Conclusion

This study presented an adaptive invisible watermarking framework based on hybrid DWT-SVD watermark embedding with image-dependent alpha optimization. Initially, DCT, DWT, Block-SVD, and DWT-SVD watermarking methods were experimentally compared under JPEG compression, Gaussian noise, and Gaussian blur attacks using PSNR, SSIM, BER, and correlation metrics. Experimental results demonstrated that the hybrid DWT-SVD method achieved the best overall balance between robustness and imperceptibility.

An adaptive optimization strategy was then introduced to evaluate multiple embedding strength values independently for different images. The experimental results indicated that although several images achieved optimal performance with alpha = 20, some images benefited from alternative embedding strengths, demonstrating the usefulness of adaptive optimization strategies for invisible watermarking systems.

In addition, preliminary EfficientNet-B0 experiments suggested that deep image features may support intelligent embedding parameter prediction in future context-aware watermarking systems. Future research may focus on fully automated deep learning-based alpha prediction and evaluation under additional geometric and adversarial attacks [8].

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