Image watermarking based on the space/spatial-frequency analysis and Hermite functions expansion

The purpose of this paper is to study coefficient multipliers of the Hardy spaces \(H^p({\mathbb R})\) associated with Hermite expansions. The main results are that, if a sequence \(\{\lambda _n\}_{n=0}^{\infty }\) satisfies the condition \(\sum _{k=n}^{2n}|\lambda _k|^q=O\left( n^{\frac{q}{2}\left( \frac{7}{6}-\frac{1}{p}\right) }\right) \), then \(\{\lambda _n\}\) is a multiplier of \(H^p({\mathbb R})\) into the sequence space \(\ell ^q\) associated with Hermite expansions for (i) \(p=1\), \(2\le q 1\) and for \(f\in H^p({\mathbb R})\), \(0<p\le 1\), the coefficients \(a_n(f)\) of its Hermite expansion satisfy \(\sum _{k=1}^{\infty }n_k^{\frac{7}{6}-\frac{1}{p}}|a_{n_k}(f)|^2<\infty \). The results in the paper are proved in a more general case, that is, for the generalized Hermite functions which are defined by \({\mathcal {H}}_{2k}^{(\lambda )}(x)=c_kL_k^{(\lambda -1/2)}(x^2)e^{-\frac{x^2}{2}}|x|^{\lambda }\), \({\mathcal {H}}_{2k-1}^{(\lambda )}(x)=c_k k^{-1/2}xL_{k-1}^{(\lambda +1/2)}(x^2)e^{-\frac{x^2}{2}}|x|^{\lambda }\), where \(c_k=\left( 2k!/\Gamma (k+\lambda +1/2)\right) ^{1/2}\). Note that \({\mathcal {H}}_n(x)={\mathcal {H}}_n^{(0)}(x)\) (\(n\ge 0\)) are the usual Hermite functions.

Decomposition systems with rapidly decaying elements (needlets) based on Hermite functions are introduced and explored. It is proved that the Triebel-Lizorkin and Besov spaces on ℝ d induced by Hermite expansions can be characterized in terms of the needlet coefficients. It is also shown that the Hermite-Triebel-Lizorkin and Besov spaces are, in general, different from the respective classical spaces.

In genetic testing of non-tuberculous mycobacteria, false positives due to cross-reactions and differences in detection performance among strains are problematic. A rapid genetic testing method with high specificity to distinguish only Mycobacterium avium and Mycobacterium intracellulare and high detection performance against genetic diversity among strains is desirable. We identified completely novel genes (MAA44156_02837 for M. avium and KN251_15665 for M. intracellulare) showing strong identity with M. avium and M. intracellulare respectively. We then developed a new M. avium/M. intracellulare simultaneous detection assay targeting these genes and evaluated their specificity and sensitivity. To evaluate cross-reactivity, the newly developed assay correctly identified all Mycobacterium spp. type strains, except for one examination of a duplicated evaluation with a Mycobacterium kyorinense type strain as a false positive at McFarland 1.0. All M. avium-positive and M. intracellulare-positive clinical isolates used in this study were accurately detected using the newly developed assay. The limits of detection for the newly developed assay were estimated to be 100CFU/mL for M. avium and 30CFU/mL for M. intracellulare. In addition, the detection performance was maintained even in samples containing both M. avium and M. intracellulare. The M. avium/M. intracellulare simultaneous detection assay developed in this study demonstrated high specificity, detection performance, and sensitivity for detecting M. avium and M. intracellulare.

A feature-based robust digital image watermarking scheme using bandelet transform

Propagating waves in a binary gas mixture from a boundary of variable temperatures and velocities are discussed on the basis of two Boltzmann equations. Variable temperatures on the boundary could be gotten by using a thin thermal absorbent with fine holes heated by laser lights of variable powers, and variable velocities on a boundary could be gotten by moving gases through a porous media. In this paper, the Hermite expansion method (Grad [1]) of the distribution function would be extended to a binary gas-mixture, i.e. the Herimite expansion method is used to solve two distribution functions for both gases. We have two Boltzmann equations expanded by Hermite functions. The Galerkin method is applied to solve two Boltzmann equations, i.e. the scalar products of Hermite functions and two expanded Boltzmann equations are executed. Thus, a system of partial differential equations for the expansion coefficients, which are functions of position and time, is obtained. The Hermite expansion is taken up to the third order, so that we have twenty coefficients and a system of twenty partial differential equations. Here, the one dimensional flow in space is considered, so that the number of expansion coefficients and differential equations would reduce from twenty to eight. The intermolecular force consisting of an inverse fifth- and inverse third- order power of intermolecular distance. We have applied this method to the relaxation phenomena of the binary gas mixture with different temperatures and velocities, which are both uniform in space ([2]and [3]). In this paper, we are going to discuss propagating waves in the gas mixture. Temperatures, number densities and velocities at x = 0 could be given. We calculate numerically the time developments of velocity, temperature and number density. The initial conditions of \( v_1^{(i)}(x,0), T^{(i)}(x,0), n^{(i)}(x,0) \) etc. are taken as uniform in 0 ≤ x ≤ ∞ . The boundary conditions at x = 0 are taken as \( T^{(i)}(0,t)=T_b^{(i)}(t),\> v_1^{(i)}(0,t)=u_b^{(i)}(t), \> n^{(i)}(0,t)=n_b^{(i)}(t) \). Time developments of temperatures, mass velocities and number densities etc. have been calculated.

Prior research studies have shown that the peak signal to noise ratio (PSNR) is the most frequent watermarked image quality metric that is used for determining the levels of strength and weakness of watermarking algorithms. Conversely, normalised cross correlation (NCC) is the most common metric used after attacks were applied to a watermarked image to verify the strength of the algorithm used. Many researchers have used these approaches to evaluate their algorithms. These strategies have been used for a long time, however, which unfortunately limits the value of PSNR and NCC in reflecting the strength and weakness of the watermarking algorithms. This paper considers this issue to determine the threshold values of these two parameters in reflecting the amount of strength and weakness of the watermarking algorithms. We used our novel watermarking technique for embedding four watermarks in intermediate significant bits (ISB) of six image files one-by-one through replacing the image pixels with new pixels and, at the same time, keeping the new pixels very close to the original pixels. This approach gains an improved robustness based on the PSNR and NCC values that were gathered. A neural network model was built that uses the image quality metrics (PSNR and NCC) values obtained from the watermarking of six grey-scale images that use ISB as the desired output and that are trained for each watermarked image’s PSNR and NCC. The neural network predicts the watermarked image’s PSNR together with NCC after the attacks when a portion of the output of the same or different types of image quality metrics (PSNR and NCC) are obtained. The results indicate that the NCC metric fluctuates before the PSNR values deteriorate.

Today, the Internet is a worldwide broadcasting capability, a mechanism for information dissemination and a medium for collaboration and interaction between individuals and their computers without regard for geographic location. With the rapid evolution of digital networks, digital libraries and World Wide Web (WWW) services, the convenient broadcasting or exposition of digital products on the global network leads easily to illegal copying, modifying and retransmission. The Internet has spawned many copyright issues involving multimedia content distribution. Let’s say an owner would like to sell or distribute a work to legal/registered users only. If the work were subsequently copied/redistributed illegally, how could the owner find who was responsible? Cryptographic techniques provide an effective solution for securing the delivery process and controlling the use of the contents that an user has obtained. However, with flawless transmission through the network, the contents after decryption are exactly the same as the original data. The contents can be copied perfectly infinite times. A user can also manipulate the contents. Digital watermarking (Arnold, Schmucker, &amp; Wolthusen, 2003; Katzenbeisser &amp; Petitcolas, 2000) offers a way to counter copyright piracy on global networks that are not solvable by cryptography. It provides proof and tracking capabilities to illegal copying and distribution of multimedia information. Most existing digital watermarking schemes are based on some assumptions for watermark detection and extraction. Some schemes require the previous knowledge of watermark locations, strengths or some thresholds. In some algorithms, the watermark is estimated with the help of the original watermark information. To ensure the robustness and invisibility of the watermark, the optimum embedding locations are usually different for different images. For a large image database, it could be a disadvantage to require watermark location and strength information for watermark detection and extraction. A large amount of information then needs to be stored. On the Internet, an owner would like to distribute multimedia data by signing different watermarks to different users in order to prevent illegal redistribution of the data by a legal user. In this scenario, watermark detection and extraction algorithms requiring information of either watermark embedding locations and strengths or the original watermark should fail, since one does not know exactly which watermark is embedded in a particular copy of the watermarked image. To this end, we present a new blind watermarking scheme (Yu, Sattar, &amp; Ma, 2002; Yu &amp; Sattar, 2003, 2005) based on Independent Component Analysis (ICA) (Hyvarinen, 1999; Hyvärinen &amp; Oja, 1999; Lee, 1998) for color images, which can overcome existing problems of watermark detection and extraction as described above. The new ICA-based scheme is found to be efficient in the application of data tracking/tracing for multimedia distribution through the Internet against other digital watermarking schemes. By adopting this ICA-based watermarking scheme, an efficient multimedia distribution framework/protocol for copyright protection can be accomplished. This article is organized as follows: The watermark embedding and extraction algorithms for color image watermarking using the new ICA-based scheme are presented next, followed by a discussion and comments on the results, security issues, summary and future works.

A procedure for combined image watermarking and compression, based on the Hermite projection method is proposed. The Hermite coefficients obtained by using the Hermite expansion are used for watermark embedding. The image can be efficiently reconstructed by using a set of Hermite coefficients that is quite smaller than the number of original ones. Hence, the watermark embedding is actually done in the compressed domain, while maintaining still high image quality (measured by high PSNR). The efficiency of the proposed procedure is proven experimentally, showing high robustness even for very strong standard attacks. Moreover, the method is robust not only to the standard attacks, but to the geometrical attacks, as well. The proposed approach can be suitable for different copyright and ownership protection purposes, especially in real-applications that require image compression, such as multimedia and Internet applications, remote sensing and satellite imaging.

In this paper, Digital Watermarking is carried out in the frequency domain and the technique proposed uses single level Stationary Wavelet Transform (SWT) along with Singular Value Decomposition (SVD). SWT is used over other transformations because of its non-decimation and shift invariance property. The singular values of SWT transformed watermark image is embedded into the singularly decomposed HH sub-band (sub-image) of R, G or B channel of a Host color image. The experimental results of watermarked images shows increase in Peak Signal to Noise Ratio (PSNR) and the extracted watermark image is highly correlated with the original watermark for various types attacks.

This article proposes a stereo vision based digital watermarking scheme that uses regularized feature-based disparity estimation for copyright protection of stereo content. The watermark data are embedded into the right image of a stereo image using the discrete wavelet transform algorithm, and a disparity vector is extracted from the left and watermarked right images. The disparity vector and the left image are then transmitted to the recipient through a communication channel. At the receiver, the watermarked right image is reconstructed from the received left image and disparity vector by employing regularized feature-based disparity estimation. From the difference between the watermarked and original right images, the embedded watermark image can then be extracted. From experiments using the stereo image pair of "Fichier," "Tunnel," and watermark data of "3D," it was found that the peak signal to noise ratio (PSNR) of the reconstructed right image through the proposed algorithm can be improved by an average of 3.61 dB compared to those of a conventional algorithm. At the same time, the PSNR of the watermark image extracted from this reconstructed right image can also be improved by an average of 2.36 dB when the Quantizer Scale is given as 20.

This work presents the design and implementation of a digital watermarking system used for the copyright protection of digital images. This watermarking system involves both the visible and invisible watermarking or bitmap images. In the instance where invisible watermarking takes place, it is important to maintain the integrity or image quality of the image being watermarked. This implies that the image should not be subjected to more than the acceptable degradation level which is specified in terms of the peak signal to noise ratio (PSNR). An acceptable degradation level was defined to be a PSNR value greater than 35 dB. Running the secure hash algorithm (SHA-1) hash function over the encrypted watermark ensures the integrity of the watermark. Secrecy is provided by means of symmetric key encryption. This is achieved by the utilization of the AES-Rijndael algorithm. Embedding and reconstruction of the watermark is based on the discrete cosine transform (DCT). This method ensures that the watermark is cryptographically secure when embedded in an image. Watermark detection, reconstruction and tamper indication are features of this design.

Security and authentication of the people information is effectively provided through various watermarking algorithms. Most of the conventional watermarking algorithms have their own drawbacks in maintaining the quality and security of the image against various attacks. In order to overcome the above stated issues, a watermarking technique based on optimization is required for preserving image quality. In this paper, singular value decomposition (SVD) based digital image watermarking (DIW) scheme is proposed in hybrid discrete cosine transform (DCT) and discrete wavelet transform (DWT) using optimization algorithms like particle swarm optimization (PSO) and Jaya algorithm. The watermark image (WI) is embedded into low frequency DWT sub-band of DCT of cover image. PSO and Jaya algorithms are applied to improve the security threats and quality by assessing the fitness function. The work involves in utilizing the feature points in embedding of watermarks and analyzing the impact of various types of attacks with respect to image quality. The performance parameters like peak signal to noise ratio (PSNR), Structural Similarity Index (SSIM) and correlation coefficient of fitness function given by PSO and Jaya algorithm.

For copyright protection, a watermark signal is embedded in host images with a secret key, and a correlation is applied to judge the presence of watermark signal in the watermark detection. This paper treats a discrete wavelet transform (DWT)-based image watermarking method under specified false positive probability. We propose a new watermarking method to improve the detection performance by using not only positive correlation but also negative correlation. Also we present a statistical analysis for the detection performance with taking into account the false positive probability and prove the effectiveness of the proposed method. By using some experimental results, we verify the statistical analysis and show this method serves to improve the robustness against some attacks.

The success of internet technology transform the world of technology and fashioned our life such a lot easier. The matter of duplication and unauthorized use of information become a great threat within the field of technology. To beat these problems, techniques like digital watermarking, steganography and cryptography were introduced. The approach of embedding a secret data associated with the digital signal inside the signal itself is digital watermarking. For embedding and detecting the watermark different techniques are used; spatial domain techniques like Least Significant Bit (LSB) and Patch Work Algorithm, then the frequency domain techniques such as Discrete Cosine Transform (DCT), Discrete Wavelet Transform (DWT) and Discrete Fourier Transform (DFT) are some of them. Combination of DCT & DWT technique for digital watermarking is proposed here. The proposed methodology is implemented in MATLAB 2017a simulator and result is analysed using evaluation parameters like Peak Signal to Noise Ratio (PSNR) & Mean Square Error (MSE). PSNR value obtained for the case of watermarking using DWT is 27.46 and MSE value is 17.45. The value of PSNR for watermarking using DCT is 41.4 and for MSE the value is 0.67. The PSNR and MSE values obtained for watermarking using LSB technique is 50.55 and 0.58. The proposed method improves the watermarked image quality and the MSE & PSNR value obtained is 0.52 and 51.017 respectively.

Digital watermarking is a growing paradigm in information science and communication systems that can be applied in the medical field. In general, a digital watermark is a mechanism for protecting digital information's copyright. Various algorithms have been developed till date to implement watermarking in order to safeguard data. The Discrete Cosine Transform is one such well-known algorithm (DCT). This algorithm is a frequency domain technique that provides security against attacks. ECG signals can also be compressed using DCT in electrocardiography. The proposed method primarily focuses on the application of digital watermarking techniques on patient medical records. The solution's goal is to preserve patients' medical records by integrating them in their MRI scan reports. As a result, the attacker will only be able to see the MRI scan report, while the health information will be buried. Singular value decomposition is used to compress the MRI scan report in this case (SVD). The medical health record, on the other hand, is encrypted using Advanced Encryption Standard (AES) algorithm, and the cipher picture obtained is employed in the embedding procedure. The DCT technique is used to embed the compressed MRI scan (cover image) and cipher image (watermark image). The embedded medical health record can be extracted by reverse application of DCT. The extracted cipher image is then decrypted using AES decryption algorithm. The produced watermark image’s (health record) quality is then assessed using a set of standards referred to as the Peak Signal to Noise Ratio (PSNR) and Mean Square Error (MSE).