Robustness of Modified Non-Separable HaarWavelet Transform and Singular Value Decomposition for Non-blind Digital Image Watermarking

Razak, Muhammad Khairi A; Abdullah, Kamilah; Halim, Suhaila Abd

doi:10.47836/mjms.16.2.08

Cited by 3 publications

(2 citation statements)

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“…Following that, numerous scholars investigated the subject of wavelet expansion convergence. For example, [10] modified non-separable Haar wavelet expansion as a wavelet transform to embed a binary watermark image into a color cover image. In another works, [4] and [3] used the radial decreasing as well as partial continuous wavelet functions to describe the convergence expansions of L p (R n ) functions with respect to (1 p < ∞) corresponding to every Lebesgue point of f .…”

Section: Related Workmentioning

confidence: 99%

The Convergence of Operator With Rapidly Decreasing Wavelet Functions

Shamsah¹,

Ahmedov²,

Kılıçman³

et al. 2022

MJMS

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The expansion of (2D) wavelet functions with respect to Lp(R2) space converging almost everywhere for 1<p<∞ throughout the length of the Lebesgue set points of space functions is investigated in this research. The convergence is established by assuming some wavelet function minimal regularity ψj1,j2,k1,k2 under the current description of the wavelet projection operator known as 2D Hard Sampling Operator. Note that the feature of fast decline in 2D is derived here. Another condition is used, for instance, the wavelet expansion's boundedness under the Hard Sampling Operator. The bound (limit) is governed in magnitude with respect to the maximal equality of the Hardy-Littlewood maximal operator. Some ideas presented in this work are to find a new method to prove the convergence theory for a new type of conditional wavelet operator. Propose some conditions for wavelets functions and their expansion can support the operator to be convergence. It also performs a comparison with the identity convergent operator is our method for achieving this convergence.

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Section: Related Workmentioning

confidence: 99%

The Convergence of Operator With Rapidly Decreasing Wavelet Functions

Shamsah¹,

Ahmedov²,

Kılıçman³

et al. 2022

MJMS

View full text Add to dashboard Cite

show abstract

“…In addition, the algorithm is evaluated in term of accuracy using peak signal to noise ratio (PSNR), structural similarity index measure (SSIM) and normalized correlation (NC). The algorithm is robust and imperceptible with high efficiency and embedding capacity [7].…”

Section: Introductionmentioning

confidence: 99%

Non-blind Image Watermarking Algorithm based on Non-Separable Haar Wavelet Transform against Image Processing and Geometric Attacks

Razak

Abdullah

Halim

2023

ARASET

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The protection of digital media become crucial and needs to be developed as technology continues to become more advanced. This is to cater to the problems in copyright protection and data security. This paper presents a new non-blind image watermarking algorithm applying modified non-separable Haar wavelet transform (NSHWT), singular value decomposition (SVD), Arnold’s cat map and Rabin-p cryptosystem. The traditional transform domain watermarking (DWT) is resource-consuming, especially when performed on large image data. In order to improve on this issue, the proposed algorithm applied the modified NSHWT, a much more efficient alternative to the DWT. Another concern of digital watermarking algorithms is it is often publicly known, so encryptions are important to keep the image secure. The embedded watermark image is protected by scrambling the image using Arnold’s cat map, and the scrambling parameters are encrypted with the Rabin-p cryptosystem to keep the algorithm secure. In general, the application of modified NSHWT and SVD makes the watermark highly robust against image processing and geometric processing attacks, and its security is ensured with the protection by Arnold’s cat map and Rabin-p cryptosystem. There are already many algorithms with high imperceptibility and robustness, but in finding the perfect balance, authors often forsake other metrics such as efficiency, security, and flexibility. These are also essential when the algorithm is considered in real applications. Thus, the proposed algorithm is evaluated in terms of imperceptibility, robustness, and efficiency. The algorithm achieved imperceptibility results of 51.5157 average PSNR and 0.9991 average SSIM, and robustness results from 0.9710 to 0.9966 NC values. The algorithm is also around 40% faster to execute with modified NSHWT compared to the traditional DWT. Finally, it has a high embedding capacity of 6 bits per pixel. Overall, results show that the algorithm is highly imperceptible and robust against image processing and geometric attacks, while additionally being secure and flexible.

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