Dual Image Cryptosystem Using Henon Map and Discrete Fourier Transform

This paper introduces an efficient image cryptography system.The pro-posed image cryptography system is based on employing the two-dimensional(2D)chaotic henon map(CHM)in the Discrete Fourier Transform(DFT).The proposed DFT-based CHM image cryptography has two procedures which are the encryption and decryption procedures.In the proposed DFT-based CHM image cryptography,the confusion is employed using the CHM while the diffu-sion is realized using the DFT.So,the proposed DFT-based CHM image crypto-graphy achieves both confusion and diffusion characteristics.The encryption procedure starts by applying the DFT on the image then the DFT transformed image is scrambled using the CHM and the inverse DFT is applied to get the final-ly encrypted image.The decryption procedure follows the inverse procedure of encryption.The proposed DFT-based CHM image cryptography system is exam-ined using a set of security tests like statistical tests,entropy tests,differential tests,and sensitivity tests.The obtained results confirm and ensure the superiority of the proposed DFT-based CHM image cryptography system.These outcomes encourage the employment of the proposed DFT-based CHM image cryptography system in real-time image and video applications.

Anomaly Detection Based on Discrete Wavelet Transformation for Insider Threat Classification

Unlike external attacks,insider threats arise from legitimate users who belong to the organization.These individuals may be a potential threat for hostile behavior depending on their motives.For insider detection,many intrusion detection systems learn and prevent known scenarios,but because malicious behavior has similar patterns to normal behavior,in reality,these systems can be evaded.Furthermore,because insider threats share a feature space similar to normal behavior,identifying them by detecting anomalies has limitations.This study proposes an improved anomaly detection methodology for insider threats that occur in cybersecurity in which a discrete wavelet transformation technique is applied to classify normal vs.malicious users.The discrete wavelet transformation technique easily discovers new patterns or decomposes synthesized data,making it possible to distinguish between shared characteristics.To verify the efficacy of the proposed methodology,experiments were conducted in which normal users and malicious users were classified based on insider threat scenarios provided in Carnegie Mellon University’s Computer Emergency Response Team(CERT)dataset.The experimental results indicate that the proposed methodology with discrete wavelet transformation reduced the false-positive rate by 82%to 98%compared to the case with no wavelet applied.Thus,the proposed methodology has high potential for application to similar feature spaces.

ASTER Data Processing by Discrete Wavelets Transform and Band Ratio Techniques for the Identification of Lineaments and Hydrothermal Alteration Zones in Poli, North Cameroon

The aim of this study is to carry out hydrothermal alteration mapping and structural mapping using ASTER images in order to identify indices that could guide mining exploration work in the Poli area and its surroundings. To achieve this, the ASTER images were first preprocessed to correct atmospheric effects and remove vegetation influence. Secondly, a lineament mapping was conducted by applying Discrete Wavelet Transform (DWT) algorithms to the First Principal Component Analysis (PCA1) of Visible Near-Infrared (VNIR) and Shortwave Infrared (SWIR) bands. Lastly, band ratio methods were applied to the VNIR, SWIR, and Thermal Infrared (TIR) bands to determine indices of iron oxides/hydroxides (hematite and limonite), hydroxyl-bearing minerals (chlorite, epidote, and muscovite), and the quartz index. The results obtained showed that the lineaments were mainly oriented NE-SW, ENE-WSW, and E-W, with NE-SW being the most predominant direction. Concerning hydrothermal alteration, the identified indices covered almost the entire study area and showed a strong correlation with lithological data. Overlaying the obtained lineaments with the hydrothermal alteration indices revealed a significant correlation between existing mining indices and those observed in the field. Mineralized zones generally coincided with areas of high lineament density exhibiting significant hydrothermal alteration. Based on the correlation between existing mining indices and the results of hydrothermal and structural mapping, the results obtained can then be used as a reference document for any mining exploration in the study area.

A New Image Watermarking Scheme Using Genetic Algorithm and Residual Numbers with Discrete Wavelet Transform

Transmission of data over the internet has become a critical issue as a result of the advancement in technology, since it is possible for pirates to steal the intellectual property of content owners. This paper presents a new digital watermarking scheme that combines some operators of the Genetic Algorithm (GA) and the Residue Number (RN) System (RNS) to perform encryption on an image, which is embedded into a cover image for the purposes of watermarking. Thus, an image watermarking scheme uses an encrypted image. The secret image is embedded in decomposed frames of the cover image achieved by applying a three-level Discrete Wavelet Transform (DWT). This is to ensure that the secret information is not exposed even when there is a successful attack on the cover information. Content creators can prove ownership of the multimedia content by unveiling the secret information in a court of law. The proposed scheme was tested with sample data using MATLAB2022 and the results of the simulation show a great deal of imperceptibility and robustness as compared to similar existing schemes.

Interpolation of Images Using Discrete Wavelet Transform to Simulate Image Resizing as in Human Vision

This paper presents discrete wavelet transform （DWT） and its inverse （IDWT） with Haar wavelets as tools to compute the variable size interpolated versions of an image at optimum computational load. As a human observer moves closer to or farther from a scene, the retinal image of the scene zooms in or out, respectively. This zooming in or out can be modeled using variable scale interpolation. The paper proposes a novel way of applying DWT and IDWT in a piecewise manner by non-uniform down- or up-sampling of the images to achieve partially sampled versions of the images. The partially sampled versions are then aggregated to achieve the final variable scale interpolated images. The non-uniform down- or up-sampling here is a function of the required scale of interpolation. Appropriate zero padding is used to make the images suitable for the required non-uniform sampling and the subsequent interpolation to the required scale. The concept of zeroeth level DWT is introduced here, which works as the basis for interpolating the images to achieve bigger size than the original one. The main emphasis here is on the computation of variable size images at less computational load, without compromise of quality of images. The interpolated images to different sizes and the reconstructed images are benchmarked using the statistical parameters and visual comparison. It has been found that the proposed approach performs better as compared to bilinear and bicubic interpolation techniques.

Fractal Surface Synthesis Based on Two Dimensional Discrete Fourier Transform

The discrete Fourier transform（DFT） is used for fractional Brownian motion（FBM） surface synthesis in tribology（i.e., contact, sliding, and sealing, etc）. However, the relationship between fractal parameters（fractal dimension and scale factor） and traditional parameters, the influence of fractal parameters on surface appearance, have not been deeply discussed yet. These lead to some kind of difficulty to ensure the synthesized surfaces with ideal fractal characteristic, required traditional parameters and geometric appearance. A quantitative relationship between fractal parameters and the root mean square deviation of surface （Sq） is derived based on the energy conservation property between the space and frequency domain of DFT. Under the stability assumption, the power spectrum of a FBM surface is composed of concentric circles strictly, a series of FBM surfaces with prescribed Sq could be synthesized with given fractal dimension, scale factor, and sampling numbers, but the ten-point height（Sz）, the skewness（Ssk） and the kurtosis（Sku） are still in random, where the probability distributions of Sz and Ssk are approximately normal distribution. Furthermore, by iterative searching, a surface with desired Abbott-Firestone curve could be obtained among those surfaces. An intuitive explanation for the influence of fractal dimension and scale factor on surface appearance is obtained by discussing the effects on the ratio of energy between high and low frequency components. Based on the relationship between Sq and surface energy, a filtering method of surface with controllable Sq is proposed. The proposed research ensures the synthesized surfaces possess ideal FBM properties with prescribed Sq, offers a method for selecting desired Abbott-Firestone curve of synthesized fractal surfaces, and makes it possible to control the Sq of surfaces after filtering.

Digital watermarking for still image based on discrete fractional fourier transform

Presents a digital watermarking technique based on discrete fractional Fourier transform (DFRFT), discusses the transformation of the original image by DFRFT, and the modification of DFRFT coefficients of the original image by the information of watermark, and concludes from experimental results that the proposed technique is robust to lossy compression attack.

Theory and algorithms for two-dimensional warped discrete Fourier transform

In this paper, the two-dimensional Warped Discrete Fourier Transform （2-D WDFT） is developed based on the concept of the 1-D WDFT. An exact computation algorithm is developed for 2-D WDFT based on matrix factorizing with special structure. A fast algorithm is then proposed to reduce greatly the computational complexity of the inverse 2-D WDFT. Finally, numerical examples are given to show the efficiency of the proposed approach.

A Matrix Formulation of Discrete Chirp Fourier Transform Algorithms

This work presents a computational matrix framework in terms of tensor signal algebra for the formulation of discrete chirp Fourier transform algorithms. These algorithms are used in this work to estimate the point target functions （impulse response functions） of multiple-input multiple-output （MIMO） synthetic aperture radar （SAR） systems. This estimation technique is being studied as an alternative to the estimation of point target functions using the discrete cross-ambiguity function for certain types of environmental surveillance applications. The tensor signal algebra is presented as a mathematics environment composed of signal spaces, finite dimensional linear operators, and special matrices where algebraic methods are used to generate these signal transforms as computational estimators. Also, the tensor signal algebra contributes to analysis, design, and implementation of parallel algorithms. An instantiation of the framework was performed by using the MATLAB Parallel Computing Toolbox, where all the algorithms presented in this paper were implemented.

AN EFFICIENT 3-DIMENSIONAL DISCRETE WAVELET TRANSFORM ARCHITECTURE FOR VIDEO PROCESSING APPLICATION

This paper presents an optimized 3-D Discrete Wavelet Transform (3-DDWT) architecture. 1-DDWT employed for the design of 3-DDWT architecture uses reduced lifting scheme approach. Further the architecture is optimized by applying block enabling technique, scaling, and rounding of the filter coefficients. The proposed architecture uses biorthogonal (9/7) wavelet filter. The architecture is modeled using Verilog HDL, simulated using ModelSim, synthesized using Xilinx ISE and finally implemented on Virtex-5 FPGA. The proposed 3-DDWT architecture has slice register utilization of 5%, operating frequency of 396 MHz and a power consumption of 0.45 W.

Peak-to-Average Power Ratio Performance Analysis for Orthogonal Chirp Division Multiplexing Multicarrier Systems Based on Discrete Fractional Cosine Transform

In doubly selective fading channels, the orthogonal frequency division multiplexing (OFDM) multicarrier system may fail. Chirp like basis (fractional Fourier transform-fractional cosine transform) may be used instead of complex exponential basis in this case to improve the system performance. However, in multicarrier transmission, the high peak to average power ratio (PAPR) of the transmitted signal is one of the difficult problems that face both the chirp and the exponential basis. In this paper, an evaluation for the PAPR performance of a multicarrier system based on the fractional cosine transform (FrCT) is introduced and then compared with DFrFT and FFT. Moreover, applying the SLAM technique over these systems is provided to understand the behaviour of these systems when applying SLAM. Simulations verify that this system obtains a better PAPR performance. Moreover, further PAPR reduction can be gained using the well-known PAPR reduction methods. Moreover, applying SLAM technique improves the performance of (dB) by 4 dB to 5 dB and all systems become as competitive to each other when SLAM is applied. Finally, BER performance comparison among OFDM, Discrete Cosine Transform MCM (DCT- MCM), Discrete Hartley Transform MCM (DHT-MCM), DFrFT-OCDM and DFrCT- OCDM MCM systems was done by means of simulation over 100,000 multicarrier blocks for each one and showed that our proposed scenario gave the best performance.

Multiple Image Watermarking with Discrete Cosine Transform

Multiple image watermarking is an advanced concept of singular watermarking techniques. The existing singular digital image watermarking techniques cannot obtain all the design goals, such as imperceptibility, robustness, security, and capacity simultaneously with perfection. Hence, the multiple image watermarking technique is designed that embeds several watermarks into the same host image for conveying multiple information. This paper proposed a multiple image watermarking technique with Discrete Cosine Transform (DCT) for ensuring the low computational time for embedding, encryption, decryption as well as extraction of the watermark images. Here, DCT is used to ensure the visual quality of the host image, and a random binary matrix is used to improve the security of the digital image. We have given a basic framework for multiple image watermarking. Our experimental results show satisfactory performance.

Low complexity reconfigurable architecture for the 5/3 and 9/7 discrete wavelet transform

Efficient reconfigurable VLSI architecture for 1-D 5/3 and 9/7 wavelet transforms adopted in JPEG2000 proposal, based on lifting scheme is proposed. The embedded decimation technique based on fold and time multiplexing, as well as embedded boundary data extension technique, is adopted to optimize the design of the architecture. These reduce significantly the required numbers of the multipliers, adders and registers, as well as the amount of accessing external memory, and lead to decrease efficiently the hardware cost and power consumption of the design. The architecture is designed to generate an output per clock cycle, and the detailed component and the approximation of the input signal are available alternately. Experimental simulation and comparison results are presented, which demonstrate that the proposed architecture has lower hardware complexity, thus it is adapted for embedded applications. The presented architecture is simple, regular and scalable, and well suited for VLSI implementation.

Adaptive Biorthogonal Local Discrete Cosine Transform for Interference Excision in Direct Sequence Spread Spectrum Communications

A novel time-frequency domain interference excision technique is proposed. The technique is based on adaptive biorthogonal local discrete cosine trans form (BLDCT). It uses a redundant library of biorthogonal local discrete cosine bases and an efficient concave cost function to match the transform basis to the interfering signal. The main advantage of the algorithm over conventional trans form domain excision algorithms is that the basis functions are not fixed but ca n be adapted to the time-frequency structure of the interfering signal. It is w e ll suited to transform domain compression and suppression of various types of in terference. Compared to the discrete wavelet transform (DWT) that provides logar ithmic division of the frequency bands, the adaptive BLDCT can provide more flex ible frequency resolution. Thus it is more insensitive to variations of jamming frequency. Simulation results demonstrate the improved bit error rate (BER) perf ormance and the increased robustness of the receiver.

A Robust Digital Watermarking Algorithm Based on Finite-Set Discrete Radon Transform Tight Frame

Digital watermarking technology plays a powerful role in the effective protection of digital media copyright, image authentication, image sharing, image information transmission and other fields. Driven by strong demand, digital image watermarking technology has aroused widespread research interest and has gradually developed into one of the most active research directions in information science. In this paper, we present a novel robust digital watermarking algorithm based on discrete radon transform tight frame in finite-set (FDRT). FDRT of the zero mean image is a tight frame, the frame boundary A = B = 1, the dual of the frame is itself. The decomposition and reconstruction of the FDRT tight frame will not cause the phenomenon of image distortion. The embedding of hidden watermark is to add a weak signal to the strong background of the original image. Watermark extraction is to effectively identify the embedded weak signal. The feasibility of the watermarking algorithm is analyzed from two aspects of information hiding and robustness. We select the independent Gaussian random vector as the watermark series, and the peak signal-to-noise ratio (PSNR) as the visual degradation criterion of the watermark image. Basing the FDRT compact stand dual operator, we derived the relationship among the strength parameter, square sum of watermark series, the PSNR. Using Checkmark system, the simulation results show that the algorithm is robust enough to some very important image processing attacks such as lossy compression, MAP, filtering, segmentation, edge enhancement, jitter, quadratic modulation and general geometric attack (scaling, rotation, shearing), etc.

Medical Image Compression Using Wrapping Based Fast Discrete Curvelet Transform and Arithmetic Coding

Due to the development of CT (Computed Tomography), MRI (Magnetic Resonance Imaging), PET (Positron Emission Tomography), EBCT (Electron Beam Computed Tomography), SMRI (Stereotactic Magnetic Resonance Imaging), etc. has enhanced the distinguishing rate and scanning rate of the imaging equipments. The diagnosis and the process of getting useful information from the image are got by processing the medical images using the wavelet technique. Wavelet transform has increased the compression rate. Increasing the compression performance by minimizing the amount of image data in the medical images is a critical task. Crucial medical information like diagnosing diseases and their treatments is obtained by modern radiology techniques. Medical Imaging (MI) process is used to acquire that information. For lossy and lossless image compression, several techniques were developed. Image edges have limitations in capturing them if we make use of the extension of 1-D wavelet transform. This is because wavelet transform cannot effectively transform straight line discontinuities, as well geographic lines in natural images cannot be reconstructed in a proper manner if 1-D transform is used. Differently oriented image textures are coded well using Curvelet Transform. The Curvelet Transform is suitable for compressing medical images, which has more curvy portions. This paper describes a method for compression of various medical images using Fast Discrete Curvelet Transform based on wrapping technique. After transformation, the coefficients are quantized using vector quantization and coded using arithmetic encoding technique. The proposed method is tested on various medical images and the result demonstrates significant improvement in performance parameters like Peak Signal to Noise Ratio (PSNR) and Compression Ratio (CR).

FPGA Implementation of Approximate 2D Discrete Cosine Transforms

Discrete cosine transform (DCT) is frequently used in image and video signal processing due to its high energy compaction property. Humans are able to perceive and identify the information from slightly erroneous images. It is enough to produce approximate outputs rather than absolute outputs which in turn reduce the circuit complexity. Numbers of applications like image and video processing need higher dimensional DCT algorithms. So the existing architectures of one dimensional (1D) approximate DCTs are reviewed and extended to two dimensional (2D) approximate DCTs. Approximate 2D multiplier-free DCT architectures are coded in Verilog, simulated in Modelsim to evaluate the correctness, synthesized to evaluate the performance and implemented in virtexE Field Programmable Gate Array (FPGA) kit. A comparative analysis of approximate 2D DCT architectures is carried out in terms of speed and area.

Real-Valued Discrete Gabor Transform of Linear Time-Varying Systems: Exact Representation and Approximation

An efficient algorithm for the representation and approximation of linear time-varying systems is presented via the fast real-valued discrete Gabor transform. Compared with the existing algorithm based on the traditional complex-valued discrete Gabor transform, the proposed algorithm runs faster, can more easily be implemented in software or hardware, and leads to a more compact representation. Simulation results are given for demonstration.

Improved Speech Denoising Algorithm Based on Discrete Fractional Fourier Transform

The speech signal and noise signal are the typical non-stationary signals,however the speech signa is short-stationary synchronously.Presently,the denoising methods are always executed in frequency domain due to the short-time stationarity of the speech signal.In this article,an improved speech denoising algorithm based on discrete fractional Fourier transform（DFRFT）is pre sented.This algorithm contains linear optimal filtering and median filtering.The simulation shows that it can easily eliminate the noise compared to Wiener filtering improve the signal to noise ratio（SNR）,and enhance the original speech signal.

Attention-Based CNN Fusion Model for Emotion Recognition During Walking Using Discrete Wavelet Transform on EEG and Inertial Signals

Walking as a unique biometric tool conveys important information for emotion recognition.Individuals in different emotional states exhibit distinct walking patterns.For this purpose,this paper proposes a novel approach to recognizing emotion during walking using electroencephalogram(EEG)and inertial signals.Accurate recognition of emotion is achieved by training in an end-to-end deep learning fashion and taking into account multi-modal fusion.Subjects wear virtual reality head-mounted display(VR-HMD)equipment to immerse in strong emotions during walking.VR environment shows excellent imitation and experience ability,which plays an important role in awakening and changing emotions.In addition,the multi-modal signals acquired from EEG and inertial sensors are separately represented as virtual emotion images by discrete wavelet transform(DWT).These serve as input to the attention-based convolutional neural network(CNN)fusion model.The designed network structure is simple and lightweight while integrating the channel attention mechanism to extract and enhance features.To effectively improve the performance of the recognition system,the proposed decision fusion algorithm combines Critic method and majority voting strategy to determine the weight values that affect the final decision results.An investigation is made on the effect of diverse mother wavelet types and wavelet decomposition levels on model performance which indicates that the 2.2-order reverse biorthogonal(rbio2.2)wavelet with two-level decomposition has the best recognition performance.Comparative experiment results show that the proposed method outperforms other existing state-of-the-art works with an accuracy of 98.73%.