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Secure and Robust ECG Steganography Using Fractional Fourier Transform
Published in S. Ramakrishnan, Cryptographic and Information Security, 2018
Gajanan K. Birajdar, Vishwesh A. Vyawahare, Mukesh D. Patil
Robustness is another critical and significant characteristic of the steganography technique, as it is important to recover the patient’s information at the receiver side with zero bit error rate. Different methods including [16,20,23] recovers the secret data with zero bit error rate at the receiver. Reconstruction of the ECG signal without any loss (reversible approach) is proposed in [14,16,22,23]. Fractional Fourier transform is a generalization of the classical Fourier transform and used in various signal and image processing applications. This chapter presents fractional Fourier transform based secure and robust ECG data hiding techniques with zero bit error rate. Secret information of the patient is encrypted using XOR encryption to increase the security. Additionally, Hamming code is applied to enhance the robustness of the proposed approach and lowering the bit error rate at the receiver (extraction side). Table 19.1 summarizes different ECG steganography techniques.
FrWT-PPCA-Based R-peak Detection for Improved Management of Healthcare System
Published in IETE Journal of Research, 2021
Varun Gupta, Monika Mittal, Vikas Mittal
Conventional Fourier transform (FT) has been widely used to observe the important attributes of a signal from its frequency spectrum. Unfortunately, it is suitable only for stationary signal analysis with limited frequency resolution. This limitation can be overcome by analysing the signal simultaneously in both time and frequency domains using time–frequency techniques such as Hilbert Huang transform, short-time Fourier transform, Stockwell transform (S-transform), Gabor Wigner transform, etc. Later, the signal analysis is improved further due to the advent of time-fractional frequency domain techniques. One of the most popular among them was fractional Fourier transform (FrFT) due to its capabilities such as low computational cost, preservance of important signal attributes, and flexibility. Since it is based on a global kernel, it can highlight only corresponding spectral components without any associated time information. Moreover, it is not able to provide time–frequency description of raw ECG datasets with multiresolution capability [11,12]. Multiresolution analysis can provide finer resolution to handle variability present within the ECG signal. Hence, it can cover varieties of patient’s heart conditions such as coronary artery heart disease, valvular heart disease, cardiomyopathy, etc.
Fractional biorthogonal wavelets in L 2(ℝ)
Published in Applicable Analysis, 2023
Owais Ahmad, N. A. Sheikh, Firdous A. Shah
In 1980, Victor Namias [3] introduced the concept of fractional Fourier transform (FrFT) as a generalization of the conventional Fourier transform to solve certain problems arising in quantum mechanics. It is also referred as rotational Fourier transform or angular Fourier transform since it depends on a parameter α which is interpreted as a rotation by an angle α in the time-frequency plane. Like the ordinary Fourier transform corresponds to a rotation in the time–frequency plane over an angle , the FrFT corresponds to a rotation over an arbitrary angle with .
Image encryption algorithm based on the fractional Hermite transform
Published in Journal of Modern Optics, 2021
Li-Hua Gong, Jing Zeng, Xiao-Zhen Li
The interference of various noises during the process of channel transmission may seriously affect the quality of decryption images [20]. Compared with the traditional Fourier transform, the Hermite transform has better image recognition ability and better noise tolerance [21]. The Hermite transform is a peculiar case of polynomial transform, whose core content is Hermite polynomial [22]. Because of its outstanding performance in noise reduction and image retrieval, Hermite transform has been widely employed in image processing [23]. In 2020, Shinde et al. devised a new flexible directional filter by adjusting the order of Hermite transform, which enhances the performance of the image retrieval system [24]. To make the image encryption system more robust to noise, Neto et al. constructed a number-theoretic transform based on generating matrix [25]. Joshi demonstrated how to construct the orthogonal basis of the eigenvector of Hermite-Gaussian-like with a special generating matrix [26]. The introduction of generating matrix not only promotes the image encryption scheme to be extended from time domain to frequency domain mathematically, but also helps better understand the fractional order transform, such as the discrete fractional Fourier transform (DFrFT) [27]. Similarly, the generating matrix was utilized to analyse the convergence of the feature vectors and the corresponding continuous Hermite-Gaussian function samples [28], so as to better understand the properties of the fractional Fourier transform [29]. The fractional Fourier transform has the characteristic of time–frequency rotation [30]. As the transform order increases from 0 to 1, the fractional Fourier transform shows all the characteristics of the signal from time domain to frequency domain [31]. In other words, the fractional Fourier transform can present the frequency plane of the function, which makes the correlation between the functions intuitive [32]. With the help of the properties of the fractional Fourier transform, the concept of fractional order can be applied to Hermite transform [33]. The input non-stationary signal can be better processed via the fractional Hermite transform (FHT), and the angle with the most concentrated information in the signal can be reasonably selected. The FHT could be regarded as a signal decomposition technique and is a convolution process of an input function and a window function as an analysis filter [34]. This window function can sample the input signal equally. To facilitate the analysis of important parts of the input signal, a weighting function was also deliberately introduced in the window function [35]. The optimal order of the FHT was achieved by selecting the result with the largest amplitude among different fractional orders. Through the centralized protection of the important information, the noise impacting on the input signal was minimized [36].