Enhanced Adaptive Discrete Wavelet Transform and Quantization Index Modulation Steganography Using Artificial Bee Colony

The unprecedented expansion of internet connectivity has revolutionized global communications, enabling the seamless transmission of data across long distances [1]. However, this digital convenience comes at a high cost, as cybercriminals are increasingly able to misuse sensitive information on networks. To address these security challenges, two complementary approaches have been developed: cryptography [2] and steganography [3]. Recent developments have even encouraged the evolution towards public-key steganography that can be proven secure for identity verification mechanisms [4], while, on the other hand, the endless competition between data hiding and detection (steganalysis) is driving innovation in data security architecture [5]. While cryptography converts messages into unreadable ciphertext, steganography develops a more subtle approach by hiding the existence of the message or secret image. This technique involves invisibly embedding secret data into a harmless cover object, such as a digital image, to produce a stego-image that remains visually indistinguishable from the original.

The effectiveness of image steganography depends on achieving an optimal balance between three conflicting performance metrics. The first is imperceptibility: the stego-image must look exactly like the cover image so that the embedded data leaves no visible artifacts [6]. The second is capacity, which is the sensitive data that can be embedded without worsening security. Optimization methods such as Ant Colony Optimization (ACO) have been shown to significantly increase embedding capacity compared to older methods [7]. The last performance metric is robustness, which is the ability of the embedded data to withstand common manipulations and attacks, such as JPEG compression, on social media [8], while maintaining its extractability and integrity [5].

Steganography techniques are classified into spatial-domain and frequency-domain methodologies. The spatial domain approach, exemplified by the Least Significant Bit (LSB) process [9], offers simplicity and high embedding capacity but is vulnerable because it is susceptible to statistical analysis attacks and shows weak resistance to image processing operations. To overcome these limitations, frequency domain techniques have become increasingly popular due to their superior imperceptibility and enhanced robustness. These methods embed secret data into image transformation coefficients using mathematical transforms such as the Discrete Wavelet Transform (DWT) [10]. This DWT decomposes images into several frequency sub-bands, namely LL (approximation), LH (horizontal details), HL (vertical details), and HH (diagonal details), which offer a multi-resolution representation of image content. Research that embeds data into the middle-frequency sub-bands (LH and HL) achieves balanced evaluation metrics between imperceptibility and robustness because these sub-bands capture important edge information but are more difficult for the human eye to perceive as embedded compared to the low-frequency components [11, 12].

In the DWT domain, Quantization Index Modulation (QIM) stands out as a powerful embedding technique known for its exceptional robustness, especially when combined with a metaheuristic optimization approach [13]. However, QIM performance is highly dependent on a single parameter, namely the quantization step, denoted as delta (Δ). This parameter governs a fundamental trade-off: a smaller delta value enhances imperceptibility but weakens robustness, while a larger value improves robustness at the expense of visual quality [14]. Recent studies also show that optimizing wavelet transformation coefficients, such as using Particle Swarm Optimization (PSO), is critical for preserving high image quality [15]. Consequently, manually selecting a fixed delta value is suboptimal because it fails to adapt to the coefficient characteristics of different cover images and payloads. Therefore, the main challenge is how to automatically determine the optimal delta value that maximizes imperceptibility and robustness for each combination of cover image and secret message.

This proposed method addresses these critical challenges by proposing an adaptive steganography framework that combines DWT and QIM with adaptive parameter optimization. The main contributions of this work are as follows:

1. Multi-Objective Fitness Function: Design of a weighted fitness function that automatically evaluates imperceptibility and robustness, enabling intelligent trade-off optimization.
2. Performance Improvement: The visual quality and capacity achieved in the research is better than existing methods.
3. Adaptive embedding: Implementation of a dynamic approach in each image-message pair receives customized embedding parameters, rather than using static parameter selection.

This paper is organized into five main sections. Section I outlines the background and defines the core research problem. Section II reviews previous methods and current approaches to data hiding. Section III provides a detailed description of the proposed method. Section IV reports experimental findings and includes a comparative assessment with current techniques. Finally, Section V summarizes the study's contributions and suggests potential research for future experiments.

This study introduces a steganography method that combines DWT with the ABC algorithm to optimize the Delta parameter in the QIM embedding process. Firstly, experiments used 512 × 512 grayscale images from SIPI dataset [27], followed by another dataset for validation. This section provides a detailed explanation of the proposed method, divided into two main parts, namely the embedding process and the extraction process.

3.1 Embedding process

This section explains the complete proposed embedding workflow used in the proposed method shown in Figure 1. The process begins by loading the cover image and the secret message that has been converted into a binary bit stream. If the image is still in RGB format, it is converted to grayscale to simplify signal processing. Next, a level 1 DWT transformation is performed on the grayscale image. This transformation breaks the image into different frequencies using low-pass and high-pass filters, which produce the LL, LH, HL, and HH sub-bands. The focus of this algorithm is on the HL (horizontal) and LH (vertical) detail coefficients, which are combined to form the embedding area. The selection of this area is crucial because it guarantees imperceptibility. Once the area is ready, the ABC algorithm begins by randomly initializing the solution population. In this step, the solution is the value of (Δ (Delta)), which is the quantization step parameter that determines how strongly the data is embedded. The algorithm generates several $(N_E)$ initial solutions randomly within a specified range $(\Delta_{\min }-\Delta_{\max })$ using Eq. (1).

$\Delta_i \sim U\left(\Delta_{\min }, \Delta_{\max }\right)$ for $i=1, \ldots, N_E$          (1)

Figure 1. Embedding process workflow

After a set of random (Δ) values is generated, each value must be tested for quality. This test is performed by embedding a message into a temporary image using the $\left(\Delta_i\right)$ value, with the aim of seeing how well the image's visual quality and data robustness are balanced. Therefore, the next step is to calculate the fitness value $\left(f_i\right)$ for each $\left(\Delta_i\right)$. This evaluation function serves as the primary benchmark for determining whether a (Δ) solution is worth keeping or should be discarded using Eq. (2).

$f_i=f_{\text {eval}}\left(\Delta_i\right)$           (2)

In group-based optimization algorithms such as ABC, it is essential to detect if a solution has stagnated (not improved after several attempts). To facilitate this mechanism, a trial counter array named $\left(T_i\right)$ is created. In the initial stage, since no improvement or neighbor search process has been performed, all values in this array are set to 0 for each solution (i) using Eq. (3). Later, this value increases each time the solution fails to improve until the limit is reached, at which point the scout bees reset the value to 0 again.

$T_i=0$, for $i=1, \ldots, N_E$           (3)

Next, to determine the quality of a solution (Δ), the first parameter measured is imperceptibility, or how invisible the embedded message. This parameter is calculated using PSNR. The higher PSNR more similar the stego image is to the original image. However, for this PSNR value to be combined with other metrics in the objective function, it needs to be normalized using Eq. (4) to normalize the PSNR value $\left(f_{p s n r}\right)$ that the visual quality target is in the range of 30 dB (poor) to 70 dB (good). If the PSNR is above 70, the value is considered maximum (0), and division by 40 is used to scale the value into the range of 0 to 1.

$f_{p s n r}(\Delta)=\max \left(0, \frac{70-P S N R}{40}\right)$          (4)

The second important parameter is robustness. A successful steganography system must be able to preserve the secret message even if the image is attacked (such as with noise or compression). This robustness is measured using BER, which is the ratio of bit errors that occur when the message is extracted. A series of experiments was conducted by varying the weights assigned to PSNR and BER across different configurations, and it was observed that unbalanced weighting consistently led to an imbalance increasing the PSNR weight caused the optimizer to sacrifice robustness, resulting in a low BER score, while increasing the BER weight reduced the inaudibility level below the threshold. The selected weights (0.7 for PSNR and 0.3 for BER) represent the configuration that yields the most balanced result between imperceptibility and robustness, which is consistent with the inherent characteristics of the DWT domain where frequency-domain modifications have a relatively stronger perceptual impact than bit-level errors. This BER test is conducted to obtain an accurate evaluation, with the attack simulation being performed repeatedly $(N_{\text {trials}})$. The following uses Eq. (5) to calculate the average BER $(f_{\text {ber}})$ of the original bitstream compared to the bitstream extracted from the attacked stego image.

$f_{\text {ber}}(\Delta)=\frac{1}{N_{\text {trials}}} \sum_{t=1}^{N_{\text {trials}}} \mathrm{BER}_{\text {trial}}(t)$           (5)

After obtaining the normalized values for visual quality $\left(f_{p s n r}\right)$ and robustness $\left(f_{b e r}\right)$, the next step is to combine them into a single total fitness value ($f_{\text {eval}}$) using Eq. (6). This combination uses a weighted sum method, where $\left(W_{p s n r}\right)$ is the weight for PSNR (0.3) and ($W_{b e r}$) is the weight for BER (0.7). This weighting indicates that in this scenario, data resilience $(\mathrm{BER})$ is considered more important than visual quality.

$f_{\text {eval}}(\Delta)=\left(W_{p s n r} \cdot f_{p s n r}(\Delta)\right)+\left(W_{\text {ber}} \cdot f_{\text {ber}}(\Delta)\right)$            (6)

In the core iteration of the ABC algorithm, the first phase is called Employed Bee. In this phase, each worker bee attempts to improve the current solution by searching for new food sources in its vicinity (searching for new deltas from surrounding deltas $\left(\Delta_i\right)$ using Eq. (7)). This procedure is done by modifying the current value of $\left(\Delta_i\right)$ using information from the random neighbor solution ($\Delta_k$). The variable ($\phi$) is a random number between -1 and 1 , which indicates the direction and length of the search step. If this new candidate solution $\left(v_i\right)$ has a better fitness value $\left(f_{\text {eval}}\left(\Delta_i\right)>f_{\text {eval}}\left(v_i\right)\right)$, then the old solution is replaced by $\left(v_i \rightarrow \Delta_i\right)$, and if not, the old solution $\left(f_{\text {eval}}\left(\Delta_i\right)<f_{\text {eval}}\left(v_i\right)\right.$) is kept $\left(\Delta_i\right)$ (greedy selection).

$v_i=\Delta_i+\phi\left(\Delta_i-\Delta_k\right)$           (7)

After the worker bee phase is complete, information about food source quality is shared with the onlooker bee. Before the observer bee chooses which solution to explore further, the previously calculated fitness value $\left(f_i\right)$ must be converted into a non-negative fitness score $\left(S_i\right)$ using Eq. (8). This equation ensures that the smaller the error, the greater the fitness score. This is necessary because the probability selection process requires increasingly larger positive values for increasingly better solutions.

$S_i=\frac{1}{1+f_i}$, where $f_i \geq 0$          (8)

Based on the calculated fitness score $\left(S_i\right)$, the ABC algorithm then determines the probability $\left(P_i\right)$ for each solution. This probability establishes the likelihood of the observer bee choosing a solution for further enhancement through roulette wheel selection using Eq. (9). Solutions with higher fitness exhibit a greater probability of being selected. This algorithm imitates the natural behavior of bees, which tend to swarm around food sources that are richer in nectar.

$P_i=\frac{S_i}{\sum_{j=1}^{N_E} S_j}$         (9)

During the search process, solutions sometimes become stuck in local optima and progress further. Scout bees play a crucial role in this situation, if a solution $\left(\Delta_i\right)$ does not improve within a specific limit, marked by the counter value $\left(T_i\right)$ reaching 20 iterations, then that solution is considered stuck. The scout bee then discards that solution and randomly generates an entirely new solution within the delta range using Eq. (10). This random value generation refreshes the population and maintains solution variety.

$\Delta_i=\operatorname{random}\left(\Delta_{\min }, \Delta_{\max }\right)$           (10)

Once the maximum number of iterations (100) is reached and all phases (Employed, Onlooker, and Scout) are completed, the algorithm produces a final population of solutions. The process terminates by selecting the best (Δ) value from the global population using Eq. (11). The best value is defined as the value that produces the minimum objective function $\left(f_i\right)$ because $\left(f_i\right)$ is the fitness that combines BER and PSNR. This value is called $\left(\Delta_{\text {optimal}}\right)$ and is utilized for the final embedding process.

$\Delta_{\text {optimal}}=\arg \min _{\Delta_i}\left(f_i\right)$           (11)

After $\left(\Delta_{\text {optimal}}\right)$ is found, this value is used to embed all message bits into the original coefficients $\left(c_i\right)$ using the QIM method, resulting in modified coefficients $\left(c_i^{\prime}\right)$. The last step is to restore the image so it can be seen. The modified frequency coefficients are reinserted into the DWT structure, then an Inverse Discrete Wavelet Transform (IDWT) is performed. This inverse process converts the data from the frequency domain back to the spatial domain, generating the final stego image.

3.2 Extraction process

This section describes the complete extraction workflow used in the proposed method shown in Figure 2. The extraction process begins by loading two main components, namely the stego image (an image that has been embedded with a message) and the secret key. At this stage, the stego image appears visually identical to the original image but contains hidden data in its frequency domain. The key plays a crucial role because it includes all the optimal parameters generated by ABC during the embedding process, including information about the DWT decomposition level used, the exact coordinate position of the coefficients, and the specific HL and LH sub-band areas where the data is hidden. Without this key, the receiver cannot find the valid data extraction location.

Figure 2. Extraction process workflow

Like the embedding process, the next step is to convert the stego image from the spatial domain back to the frequency domain. The image is changed using the DWT based on the level set in the key. After the transformation is complete, the system uses the index information from the key to map and retrace the embedding area in the one-dimensional array of the HL and LH subbands. The algorithm then isolates specific coefficients in the selected subband that contain message bits, separating the data signal from other coefficients that do not contain secret messages.

After the coefficient location is found, the system reads the index list (I) from the secret key to process each modified coefficient $\left(c_i^{\prime}\right)$. At this step, extraction is performed using the inverse of QIM. The distance of each coefficient value is analyzed relative to the 0-bit quantization point $\left(\Delta_{\text {optimal}} \times n\right.$, where $\left.n \in\{0,2,4,6, \ldots\}\right)$ and bit 1 $\left(\Delta_{\text {optimal}} \times n\right.$, where $\left.n \in\{1,3,5,7, \ldots\}\right)$. The message bits (0 or 1) are determined based on the proximity of the coefficient value to the nearest quantization point. This process ensures that even if there is a bit of distortion in the image, the most possible bit value can still be recovered.

The binary bits successfully extracted from each coefficient are then collected and combined in sequence. This process puts the message's original data structure back together. Each bit taken from the nearest point will then be arranged in length until it reaches the total length of the specified message, forming a complete single-bit stream and restoring the structure of the secret message. The final step is to convert the bitstream to represent the secret message, using the reconstructed bitstream into byte units (8 bits). This collection of bytes is then converted or translated back into plain text format. The result is a secret message that can be read and understood by the receiver.

The proposed method proposes a steganography method based on DWT with QIM whose delta parameter is optimized by ABC algorithm. The method achieves higher PSNR values and robustness against additive noise attacks, maintaining low BER under Gaussian noise in several cover images. The proposed approach results in the stego image with better visual quality and less distortion as compared with existing methods. Additionally, the steganalysis evaluation with SiaStegNet and ZhuNet attained the detection accuracy of 45.02% and 42.64% respectively, which is close to the random guessing baseline, confirming the resistance of the method to modern learning-based steganalysis.

However, the method is sensitive to geometric and structural attacks with BER values higher than 0.42 for the resizing, median filtering and average filtering conditions, which indicates that spatial transformations and frequency-smoothing operations are still a challenge for the current QIM-ABC scheme. Future work should address these limitations by exploring geometric correction mechanisms, expanding the embedding to the LL and HH subbands, and exploring different delta parameters for each bit to further improve the imperceptibility-robustness trade-off.