Gradient-Adaptive LSB Steganography with Hamming Matrix Encoding for Enhanced Imperceptibility

Gradient-Adaptive LSB Steganography with Hamming Matrix Encoding for Enhanced Imperceptibility

Ashish Rangra (1*) and Kumari Archana (1)

(1*)Department of Computer Science and Engineering, Himachal Pradesh Technical University, Hamirpur, India.

Abstract

Image steganography enables secure communication by embedding condential information within digital images while maintaining visual quality. However, con-ventional Least Signicant Bit (LSB) steganography methods often suer from high pixel modication rates and vulnerability to statistical detection attacks. To address these limitations, this paper proposes a gradient-adaptive LSB steganog-raphy framework integrated with Hamming (7,4) matrix encoding. The proposed method utilizes Sobel-based gradient analysis to identify high-texture regions suitable for data embedding, thereby reducing perceptual distortion. In addition, Hamming matrix encoding minimizes the number of pixel modications required during the embedding process. Unlike conventional adaptive LSB techniques that mainly focus on embedding location selection, the proposed framework jointly improves embedding region selection and modication eciency. The proposed method was evaluated on the BOSSBase 1.01 dataset using payload capacities of 0.05, 0.10, and 0.20 bits per pixel (bpp). Experimental results demonstrated improved image quality with PSNR values of 70.75 dB, 67.74 dB, and 64.73 dB, respectively. Furthermore, chi-square analysis conrmed reduced statistical detectability compared to conventional LSB-based methods. Overall, the proposed framework provides an eective balance between imperceptibility, embedding eciency, and computational simplicity, making it a practical solution for secure image communication.

Keywords: Steganography, LSB, Gradient-Based Embedding, Hamming Code, BOSSBase, PSNR

1. Introduction

   As digital communication continues to expand, multimedia data transmission over open networks has increased signicantly. Consequently, maintaining the conden-tiality and integrity of sensitive information has become an important concern. Conventional security techniques such as cryptography eectively protect the content of data, but they do not conceal the existence of communication. In contrast, steganog-raphy provides an additional layer of security by embedding secret information within digital media in such a way that the hidden data remains imperceptible to the human visual system, including images, audio, and video [1, 18].

   Among dierent steganographic approaches, image steganography is widely used because digital images contain a large amount of redundant information suitable for data hiding. Spatial-domain techniques, particularly Least Signicant Bit (LSB) sub-stitution, are commonly adopted due to their simplicity, high embedding capacity, and ease of implementation [2, 3]. In LSB-based methods, secret data is embedded by modifying the least signicant bits of pixel values, resulting in minimal visual dis-tortion. However, despite these advantages, conventional LSB algorithms suer from several limitations, including high pixel modication rates, limited robustness, and vulnerability to statistical and structural steganalysis attacks [4, 5].

   To overcome these limitations, researchers have proposed adaptive and content-aware steganography techniques that utilize image characteristics such as edges, textures, and gradients to identify suitable embedding regions. Embedding data within edge or high-texture regions reduces perceptual distortion because modications in these regions are less noticeable to the human visual system [24]. In addition, optimiza-tion techniques such as Genetic Algorithms have been employed to improve embedding eciency by selecting optimal embedding locations [33]. More recently, deep learning-based steganography methods have attracted attention because of their ability to automatically learn embedding patterns and improve resistance against steganalysis attacks [12]. However, such approaches generally require complex training procedures and high computational resources.

   Despite these advancements, achieving an eective balance between impercepti-bility, embedding capacity, security, and computational eciency remains a major challenge. Many existing methods improve image quality at the cost of increased computational complexity, while others focus mainly on security without eectively reducing pixel modications. Therefore, there is still a need for a lightweight and ecient steganography framework capable of minimizing embedding distortion while maintaining high embedding performance.

   To address this research gap, this paper proposes a gradient-adaptive LSB steganography framework integrated with Hamming (7,4) matrix encoding. The pro-posed method utilizes Sobel-based gradient analysis to identify high-texture regions suitable for embedding, thereby reducing perceptual distortion. Furthermore, Ham-ming matrix encoding minimizes the number of pixel modications required during data embedding, which helps preserve image quality and reduce embedding artifacts. Experimental results demonstrate that the proposed framework achieves signi-cantly higher Peak Signal-to-Noise Ratio (PSNR) values compared to conventional LSB and adaptive LSB-based approaches, indicating improved imperceptibility and

   embedding eciency. In addition, statistical validation conrms the consistency and eectiveness of the proposed method. Unlike many existing approaches that indepen-dently focus on either adaptive embedding location selection or modication reduction, the proposed framework jointly optimizes both objectives within a unied lightweight spatial-domain architecture.

   1. Novelty and Research Contributions

      Unlike conventional adaptive LSB steganography methods that mainly focus on embedding location selection, and matrix encoding approaches that independently reduce modication rates, the proposed framework simultaneously optimizes both embedding region selection and pixel modication eciency within a lightweight spatial-domain steganography architecture.

      The proposed framework introduces a joint optimization strategy that com-bines gradient-adaptive embedding with Hamming (7,4) matrix encoding to achieve improved imperceptibility and reduced embedding distortion. The Sobel gradient oper-ator is employed to identify perceptually insensitive high-texture regions for secure data embedding, while Hamming matrix encoding minimizes the number of pixel modications required during the embedding process.

      In contrast to many optimization-based and deep learning-based steganography techniques, the proposed method maintains low computational complexity while achieving high PSNR values and reduced modication rates across dierent payload capacities. Therefore, the proposed framework provides an eective balance between embedding capacity, imperceptibility, and computational simplicity.

      The key contributions of this work are summarized as follows:

      • A gradient-based adaptive embedding strategy for selecting perceptually suitable embedding regions.

      • Integration of Hamming (7,4) matrix encoding to reduce pixel modication rates

        during embedding.

      • Signicant improvement in PSNR values across multiple payload capacities.

      • A lightweight and computationally ecient steganography framework suitable for practical applications.

      • Improved resistance against statistical detectability throughreduced embedding

      distortion.

2. Related Work

   Image steganography has been extensively studied, and numerous techniques have been proposed to improve security, imperceptibility, and embedding capacity. Existing approaches can generally be categorized into spatial-domain, adaptive and edge-based, optimization-based, hybrid cryptographic, and deep learning-based steganography techniques.

   1. Spatial-Domain Steganography

      Spatial-domain techniques are among the most widely used steganography approaches, particularly Least Signicant Bit (LSB) substitution due to its simplicity, high embed-ding capacity, and ease of implementation [2, 3, 6]. In these methods, secret information is directly embedded by modifying pixel values within the image. As a result, the computational complexity remains relatively low. However, conventional LSB-based techniques often suer from high pixel modication rates and are vulnerable to statistical steganalysis attacks [4, 5].

   2. Adaptive and Edge-Based Steganography

      To improve imperceptibility, adaptive steganography techniques utilize image charac-teristics such as edges and textured regions for data embedding. These approaches commonly employ edge detection operators, including Sobel and Kirsch operators, to identify high-frequency regions suitable for embedding [20, 32]. Since modications within edge and textured regions are less noticeable to the human visual system, perceptual distortion can be signicantly reduced [24]. Nevertheless, many adaptive approaches primarily focus on embedding location selection and do not eectively minimize pixel modication rates.

   3. Optimization-Based Steganography

      Optimization techniques such as Genetic Algorithms (GA) have also been applied in steganography to improve embedding eciency and select optimal embedding locations. These methods aim to enhance imperceptibility and embedding perfor-mance by intelligently selecting suitable pixels for data hiding [9, 33]. Although optimization-based approaches improve embedding quality, they generally introduce higher computational complexity, making them less suitable for lightweight and real-time applications.

   4. Hybrid Cryptography and Steganography

      Several researchers have combined cryptography with steganography to improve data condentiality. In such approaches, secret information is rst encrypted using algo-rithms such as AES or chaotic encryption methods before being embedded into images [6, 23]. While these methods enhance security, they mainly focus on condentiality and do not specically address embedding eciency or reduction of pixel modications.

   5. Deep Learning-Based Steganography

      Recent developments in deep learning have led to the emergence of CNN-based and reinforcement learning-based steganography techniques. These methods can automat-ically learn ecient embedding strategies and improve resistance against steganalysis attacks [8, 12, 27, 31]. However, deep learning-based approaches typically require large training datasets, complex model architectures, and high computational resources, lim-iting their applicability in lightweight and resource-constrained environments. Recent

      studies have also explored hybrid frameworks that combine traditional LSB embed-ding with encoder-decoder architectures to improve imperceptibility and robustness [35].

   6. Research Gap

      Despite the progress achieved in existing steganography methods, several challenges still remain. Conventional spatial-domain techniques are computationally simple but provide limited security. Adaptive methods improve imperceptibility by selecting suitable embedding regions, but they often fail to reduce pixel modication rates eectively. Similarly, optimization-based and deep learning-based techniques improve embedding performance at the cost of increased computational complexity.

      Furthermore, many existing approaches independently focus on either adaptive embedding region selection or modication minimization, which limits the overall e-ciency of the steganography framework. Therefore, there is still a need for a lightweight and ecient method capable of simultaneously reducing embedding distortion while maintaining high imperceptibility and embedding eciency [24].

      Unlike existing steganography methods that separately address adaptive region selection and modication reduction, the proposed framework jointly optimizes both objectives within a unied lightweight spatial-domain steganography architecture.

      To address this research gap, the proposed method integrates gradient-based adap-tive embedding with Hamming (7,4) matrix encoding to achieve improved image quality with reduced embedding distortion and lower pixel modication rates.

      Table 1 Comparison of Existing Steganography Approaches with Proposed Method

      Method	Adaptive Region Selection	Matrix Encoding	Modication Reduction	Complexity
      Traditional LSB	No	No	Low	Low
      Edge-based LSB	Yes	No	Medium	Medium
      Hamming-based LSB	No	Yes	High	Low
      Optimization-based Methods	Yes	No	High	High
      Deep Learning-based Methods	Yes	No	High	Very High
      Proposed Method	Yes	Yes	High	Low

3. Proposed Method

   1. Overview

      The proposed framework aims to jointly optimize embedding location selection and modication eciency in order to achieve high imperceptibility with reduced embed-ding distortion. The framework combines gradient-based adaptive embedding with

      Hamming (7,4) matrix encoding to improve image quality while minimizing pixel alterations during the embedding process. The main objective is to embed secret infor-mation within high-texture regions of the image while reducing the number of modied pixels required for data hiding.

      The overall architecture of the proposed method consists of three major stages: gradient-based region selection, Hamming matrix encoding, and LSB embedding.

   2. Gradient-Based Region Selection

      In the proposed method, the gradient magnitude of the cover image is computed using the Sobel operator. Gradient information represents variations in pixel intensity and is commonly used to identify edges and textured regions within an image.

      x

      y

      G = G2 + G2

      (1)

      where Gx and Gy represent the horizontal and vertical gradient components, respectively.

      Pixels with higher gradient values generally correspond to edge or textured regions [24]. Therefore, these regions are selected for secret data embedding, while smooth regions are avoided in order to reduce perceptual distortion and improve imperceptibility.

   3. Hamming (7,4) Matrix Encoding

      The proposed framework utilizes Hamming (7,4) matrix encoding to minimize the number of pixel modications during data embedding. In this encoding scheme, 4 bits of secret information are represented using 7-bit codewords with parity relationships. This approach improves embedding eciency by reducing the number of mod-ications required during embedding. In most cases, only a single bit modication is sucient to encode 4 bits of secret data, which signicantly educes embedding

      distortion and preserves image quality.

   4. LSB Embedding Process

      After selecting suitable embedding locations and encoding the secret data, LSB substitution is performed to generate the stego image.

      1. Input a grayscale cover image from the BOSSBase dataset.

      2. Compute the gradient magnitude using the Sobel operator.

      3. Select high-gradient pixels based on a predened threshold.

      4. Encode secret data using Hamming (7,4) matrix encoding.

      5. Embed the encoded bits into the least signicant bits of selected pixels.

      6. Generate the nal stego image.

   5. Extraction Process

      The extraction process is performed by reversing the embedding procedure as follows:

      1. Extract LSB bits from the stego image.

      2. Identify embedding locations using the same gradient calculation process.

      3. Decode the extracted bits using Hamming (7,4) decoding.

      4. Recover the original secret message.

   6. System Flow Diagram

      Compute Gradient (Sobel)

      Select High-Texture Regions

      Hamming (7,4) Encoding

      LSB Embedding

      Input Cover Image

Stego Image

Fig. 1 Flow diagram of the proposed steganography method

1. Pseudo-Code of Proposed Method

   Input: Cover Image I, Secret Data S Output: Stego Image I

   1. Compute gradient G using Sobel operator

   2. Identify high-gradient pixel positions P

   3. Convert secret data S into binary form

   4. Apply Hamming (7,4) encoding on S

   5. For each position p in P:

      Embed encoded bits into LSB of I(p)

   6. Generate stego image I

   7. Return I

2. Advantages of Proposed Method

   • Reduced pixel modication through Hamming matrix encoding.

   • Improved imperceptibility using gradient-based adaptive embedding.

   • Lower computational complexity compared to optimization and deep learning-based methods.

   • Better balance between embedding capacity, image quality, and embedding e-

   ciency.

1. Experimental Setup

   1. Dataset

      The experiments were conducted using the BOSSBase 1.01 dataset, which is widely used as a benchmark dataset in image steganography research [18]. The dataset con-sists of 10,000 grayscale images in PGM format with a resolution of 512 × 512 pixels. All experiments were performed on the complete dataset to ensure unbiased evaluation and statistically reliable results.

   2. Preprocessing

      All images were used in their original form without resizing or compression in order to preserve their inherent image characteristics. The secret data was converted into binary form prior to embedding. No additional preprocessing or ltering operations were applied to maintain consistency with standard steganography evaluation practices.

   3. Payload Conguration

      To evaluate the performance of the proposed framework under dierent embedding capacities, xed payload levels were dened as follows:

      • 0.05 bits per pixel (bpp) Low payload

      • 0.10 bits per pixel (bpp) Medium payload

      • 0.20 bits per pixel (bpp) High payload

      The total number of embedded bits for each image was computed using:

      Total Bits = bpp × (M × N ) where M × N represents the image resolution.

      (2)

   4. Evaluation Metrics

      The performance of the proposed method was evaluated using the following metrics:

      1. Peak Signal-to-Noise Ratio (PSNR)

         PSNR was used to evaluate the visual quality of the stego images. Higher PSNR values indicate lower distortion and better imperceptibility.

      2. Mean Squared Error (MSE)

         M N

         MSE = 1 (I(i, j) It(i, j))2 (3)

         MN

         i=1 j=1

         where I and It represent the original and stego images, respectively.

      3. Structural Similarity Index (SSIM)

         SSIM measures the perceptual similarity between the original and stego images by considering luminance, contrast, and structural information.

      4. Modied Pixel Percentage

         Modied Pixel Percentage represents the proportion of pixels altered during the embedding process and is computed as:

         Number of Modied Pixels

         Modication Rate =

         Total Pixels

         × 100 (4)

         Lower modication rates indicate fewer embedding changes and improved imper-

         ceptibility.

      5. Chi-Square Analysis

         Chi-square analysis was performed to evaluate the statistical similarity between the histogram distributions of original and stego images. Lower chi-square values indicate reduced statistical detectability and better preservation of histogram characteristics. The analysis was conducted at 0.20 bpp payload to evaluate the robustness of the proposed method under maximum embedding distortion conditions.

   5. Statistical Validation

      To verify the consistency and reliability of the experimental results, statistical validation was performed on all 10,000 images using the following measures:

      • Mean and standard deviation were computed for all evaluation metrics.

      • A paired t-test was conducted to evaluate the statistical signicance of performance improvements.

      • Eect size analysis using Cohens d was performed to measure the magnitude of

      improvement achieved by the proposed method.

   6. Distortion Localization Analysis

      Gradient-based distortion localization analysis was conducted to examine the spatial distribution of embedding modications. The average gradient values of modied pixel locations were compared with the global average gradient values of the images.

      The analysis revealed that most embedding modications were concentrated within high-gradient and textured regions. This conrms the eectiveness of the proposed gradient-adaptive embedding strategy in minimizing perceptual distortion.

   7. Implementation Details

      The proposed framework was implemented and evaluated using MATLAB in a stan-dard computing environment. Gradient computation was performed using the Sobel

      operator, while Hamming (7,4) matrix encoding was applied to minimize pixel modi-cations during embedding. All experiments were conducted under identical conditions on the complete BOSSBase dataset to ensure fair and reproducible evaluation.

   8. Baseline Methods for Comparison

      To validate the eectiveness of the proposed method, the following baseline steganog-raphy techniques were implemented for comparison:

      • Simple LSB steganography (sequential embedding)

      • Random LSB steganography

      • Gradient-based LSB steganography

2. Results and Discussion

   1. Quantitative Evaluation

      The proposed framework was evaluated on the BOSSBase dataset under dierent payload capacities. The obtained results were compared with Simple LSB, Random LSB, and Gradient-based LSB steganography methods.

      1. Results at 0.05 bpp

         Table 2 Performance Comparison at 0.05 bpp

         Method	PSNR (dB)	MSE	SSIM	Modied (%)
         Simple LSB	64.1416	0.025072	0.999778	2.50178
         Random LSB	64.1371	0.025089	0.999769	2.508937
         Gradient LSB	64.1470	0.025026	0.999962	2.502634
         Proposed (Gradient + Hamming)	70.7544	0.005467	0.999988	0.546665

      2. Results at 0.10 bpp

         Table 3 Performance Comparison at 0.10 bpp

         Method	PSNR (dB)	MSE	SSIM	Modied (%)
         Simple LSB	61.1300	0.050154	0.999560	5.015418
         Random LSB	61.1271	0.050174	0.999540	5.017438
         Gradient LSB	61.1374	0.050045	0.999890	5.004452
         Proposed (Gradient + Hamming)	67.7411	0.010940	0.999965	1.093980

         Table 4 Performance Comparison at 0.20 bpp

         Method	PSNR (dB)	MSE	SSIM	Modied (%)
         Simple LSB	58.1178	0.100342	0.999137	10.034169
         Random LSB	58.1159	0.100371	0.999088	10.037092
         Gradient LSB	58.1277	0.100074	0.999669	10.007360
         Proposed (Gradient + Hamming)	64.7313	0.021876	0.999893	2.187626

      3. Results at 0.20 bpp

   2. PSNR vs Payload Analysis

      Fig. 2 PSNR vs Payload comparison for dierent steganography methods on BOSSBase dataset

   3. PSNR Analysis

      As illustrated in Fig. 2, the proposed Gradient + Hamming framework consistently achieves higher PSNR values across all payload capacities compared to the base-line methods. Although PSNR values decrease with increasing payload due to higher embedding distortion, the proposed method maintains a signicant performance advantage.

      At 0.05 bpp, the proposed method achieved a PSNR value of 70.75 dB, which is approximately 6 dB higher than conventional LSB-based approaches. Similar improve-ments were observed at 0.10 bpp and 0.20 bpp, demonstrating the stability and eectiveness of the proposed framework across dierent embedding capacities.

      The improvement in PSNR is primarily achieved due to two important factors:

      (i) gradient-based adaptive embedding selects perceptually less sensitive regions for data hiding, and (ii) Hamming (7,4) matrix encoding signicantly reduces the number

      of modied pixels during embedding. These factors collectively minimize embedding distortion and improve imperceptibility [24, 28].

   4. Modication Rate Analysis

      The proposed framework signicantly reduces the pixel modication rate compared to conventional LSB-based approaches. At 0.20 bpp payload, traditional LSB methods modify approximately 10% of the image pixels, whereas the proposed method reduces the modication rate to nearly 2.18%.

      Similarly, at 0.05 bpp, the modication rate decreases from approximately 2.5% to 0.54%, demonstrating the eciency of the proposed embedding framework.

      This improvement is mainly achieved through the use of Hamming (7,4) matrix encoding, which enables ecient embedding with fewer pixel alterations. Similar ben-ets of matrix encoding techniques have also been reported in earlier studies [7]. The reduction in pixel modications directly contributes to improved image quality and lower visual detectability.

   5. Statistical Validation

      To verify the reliability and consistency of the proposed method, statistical validation was performed across all 10,000 images in the BOSSBase dataset. Mean and stan-dard deviation values for the evaluation metrics demonstrated consistent performance throughout the dataset.

      A paired t-test was conducted to evaluate the statistical signicance of PSNR improvements, and the obtained p-values were found to be below 0.05, indicating statistically signicant improvements. In addition, eect size analysis using Cohens

      d demonstrated substantial performance improvements achieved by the proposed framework.

      These statistical results further conrm the eectiveness and reliability of the proposed steganography method [18].

   6. Distortion Localization Analysis

      Distortion localization analysis was conducted to examine the spatial distribution of embedding modications. The results indicate that modied pixels are primarily concentrated within high-gradient and textured regions of the image.

      A comparison between global average gradient values and gradient values at modied pixel locations revealed signicantly higher gradient values at embedding positions. This conrms that the proposed framework eectively avoids smooth regions and performs embedding mainly within textured areas.

      Embedding modications within high-gradient regions improve imperceptibility because changes in textured areas are less noticeable to the human visual system [24].

   7. Chi-Square Analysis

      Table 5 presents the average chi-square values obtained for dierent steganography methods on the BOSSBase dataset at 0.20 bpp payload.

      Table 5 Average Chi-Square Comparison on BOSSBase Dataset

      Method	Average Chi-Square	Standard Deviation
      Simple LSB	19160.8054	379433.9571
      Gradient LSB	149.2024	488.3313
      Proposed Method	21.4333	338.1425

      The proposed method achieved substantially lower chi-square values compared to Simple LSB and Gradient-based LSB methods, indicating improved preservation of histogram characteristics and reduced statistical detectability. These results further conrm that the integration of gradient-adaptive embedding with Hamming matrix encoding eectively minimizes embedding distortion and statistical artifacts even at higher payload capacities.

   8. Discussion

      The experimental results demonstrate that the proposed Gradient-adaptive Hamming-encoded LSB framework achieves an eective balance between embedding capacity, image quality, and modication eciency.

      Unlike conventional LSB methods that uniformly modify image pixels, the pro-posed framework selectively embeds data within high-gradient regions and employs matrix encoding to reduce pixel modications. This combined optimization strategy leads to signicant improvements in PSNR and modication rate performance.

      Compared to conventional adaptive embedding methods, the proposed approach achieves lower embeding redundancy due to the use of Hamming matrix encod-ing. Furthermore, the framework maintains low computational complexity because it does not rely on computationally expensive optimization algorithms or deep learning architectures, making it suitable for real-time and resource-constrained applications.

      Compared with recent deep learning-based hybrid steganography approaches [35], the proposed framework achieves higher PSNR values with signicantly lower computational complexity.

   9. Comparison with Existing Research Papers

      Table 6 Performance Comparison with Existing Methods on BOSSBase Dataset

      Method	Domain	Payload (bpp)	Dataset	PSNR (dB)
      Content-Adaptive LSB [1]	Spatial	0.20	BOSSBase	58.22
      Multi-image ISS [3]	Spatial	0.20	BOSSBase	55.30
      Edge-Guided Adaptive [4]	Spatial	0.10	BOSSBase	61.20
      DRL-based DCT [2]	Transform	0.20	BOSSBase	51.40
      Proposed (Gradient +	Spatial	0.20	BOSSBase	64.73
      Hamming)

      The comparison results presented in Table 6 indicate that the proposed frame-work outperforms several existing steganography methods under similar experimental conditions on the BOSSBase dataset.

      Compared to the edge-guided adaptive method in [4], which achieved a PSNR value of 61.20 dB at 0.10 bpp, the proposed method achieved 64.73 dB at a higher payload of 0.20 bpp. This demonstrates the ability of the proposed framework to maintain high image quality even at larger embedding capacities.

      Similarly, the content-adaptive LSB technique in [1] achieved a PSNR value of

      58.22 dB at 0.20 bpp, which is considerably lower than the proposed method. The improvement mainly results from the integration of gradient-adaptive embedding and Hamming matrix encoding.

      The multi-image steganography method in [3] achieved a PSNR value of 55.30 dB at 0.20 bpp by distributing payloads across multiple images using optimization techniques. Although the method improves security, it introduces greater embedding distortion compared to the proposed framework.

      In addition, transform-domain approaches based on deep reinforcement learning

      [2] achieved lower PSNR values while requiring signicantly higher computational complexity. This comparison highlights the eciency of the proposed lightweight spatial-domain framework.

      Overall, the comparison results demonstrate that the proposed method achieves an eective balance between imperceptibility, embedding eciency, and computational simplicity.

   10. Overall Performance Summary

       The experimental evaluation conrms that the proposed Gradient-adaptive Hamming-encoded LSB framework consistently outperforms conventional and adaptive steganog-raphy techniques across dierent payload capacities.

       The major improvements achieved by the proposed framework are summarized as follows:

       • Improved PSNR: The proposed framework achieves approximately 6 dB higher PSNR values compared to conventional LSB-based methods at similar payload capacities.

       • Reduced Modication Rate: Pixel modication rates are signicantly reduced

         compared to baseline methods, resulting in lower embedding distortion.

       • High Structural Similarity: SSIM values remain close to 1, indicating minimal perceptual degradation.

       • Consistent Performance: Experimental results remain stable across multiple

         payload levels and throughout the complete dataset.

       • Reliable Evaluation: The use of the complete BOSSBase dataset ensures reliable and statistically meaningful evaluation results.

       These ndings conrm that integrating gradient-adaptive embedding with Ham-ming matrix encoding provides an eective and lightweight solution for high-quality and low-distortion image steganography.

3. Conclusion

   In this paper, a gradient-adaptive LSB steganography method combined with Ham-ming (7,4) matrix encoding was proposed to improve imperceptibility and reduce embedding distortion. The proposed framework utilizes gradient information to iden-tify high-texture regions for secure embedding, while Hamming matrix encoding minimizes pixel modications during data hiding.

   The proposed method was evaluated on the BOSSBase 1.01 dataset at payload lev-els of 0.05, 0.10, and 0.20 bpp. Experimental results demonstrated higher PSNR values, lower modication rates, and improved imperceptibility compared to conventional LSB and gradient-based methods. Statistical validation and distortion localization analysis further conrmed the eectiveness and consistency of the proposed framework.

   Additionally, chi-square analysis demonstrated reduced statistical detectability and improved preservation of histogram characteristics compared to existing LSB-based approaches. The major novelty of the proposed work lies in the joint integration of gradient-adaptive embedding and Hamming (7,4) matrix encoding for simultaneous distortion localization and pixel modication reduction within a lightweight spatial-domain framework.

   Overall, the proposed method provides an ecient and practical solution for secure image communication, digital watermarking, medical image protection, and privacy-preserving multimedia applications.

4. Limitations

The proposed framework is currently limited to grayscale images and has not been evaluated on color images or video data. In addition, although the method improves imperceptibility and reduces pixel modication rates, resistance against advanced ste-ganalysis techniques has not been extensively investigated. Furthermore, the use of a xed gradient threshold may not provide optimal performance for all image categories and texture distributions.

Future Work

Future research may focus on extending the proposed framework to color image and video steganography applications. In addition, lightweight optimization techniques or deep learning-based approaches may be incorporated to further improve security and resistance against advanced steganalysis attacks.

Another important direction for future work is the evaluation of the proposed method under practical conditions such as image compression, noise addition, and transmission distortions. Furthermore, adaptive gradient threshold selection tech-niques may be explored to improve embedding performance across dierent image characteristics and texture variations.

Declarations

Funding

This research did not receive any specic grant from funding agencies in the public, commercial, or not-for-prot sectors.

Data Availability

The data used in this study is based on the publicly available BOSSBase 1.01 dataset. Processed data and implementation details are available from the corresponding author upon reasonable request.

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