Fast Hadamard Transform Research Articles

Image encryption algorithm based on dynamic DNA coding operations and 3D chaotic systems

This paper presents a new image encryption algorithm based on 3D chaotic system and deoxyribonucleic acid (DNA) coding. It uses two keys, an external one of 128 bits long and an internal one of 64 gray values coming from the plain image. The initial conditions come from the two keys and vary from one line of the image to the other and from one image to the other and consequently the sequences of substitutions too. In general, in image encryption based on 3D chaotic systems, each chaotic variable is used independently of the others in one phase of the encryption. Here we use the zigzag process to combine the sequences from all the variables before using them simultaneously in the encryption process. DNA coding generally uses one of the 24 DNA rules and one of the 16 join operations to perform the encryption. Here we use all the 24 rules dynamically as well as the 16 join operations in the encryption. Also we apply the chaotic permutation on DNA chain. The logical DNA operations are used according to an algorithm similar to that of the Fast Walsh Transform (FWT) in those 24 DNA rules. The algorithm has been evaluated. It has good statistical properties of cipher images. The proposed system presents high sensitivity on the encryption-decryption keys and on the plain images. These latter features make the proposed algorithm very efficient, robust and resistant against brute force attacks and good for the future secure image communication.

Exploring Optimized Hadamard Methods to Design Energy-Efficient SATD Architectures

State-of-the-art video coding tools are submitted to severe performance and energy consumption requirements resulting from high complexity of video standards and from limited energy budgets of portable mobile devices. While providing most of the compression gains, inter frame and intra frame prediction techniques are the most demanding steps, since they compare a huge number of blocks. In such a process, the similarity metric employed affects both the quality of compression and the calculation effort. In this paper we propose the use of Hadamardbased Sum of Absolute Transformed Differences (SATD), in replacement of the traditionally used Sum of Absolute Differences (SAD), as a means of improving the efficiency of video coding. To allow that we explore two Hadamard Transform methods to design efficient SATD architectures, one using the Fast Hadamard Transform (FHT) butterfly and another one using the so-called Transform-Exempted (TE) SATD algorithm. Those methods were combined with architectural decisions (full parallelism, full parallelism with pipelining or multi-cycling) to build a total of six Hadamard-based SATD architectures that were synthesized for a commercial 45nm standard cell library for two operating frequencies. The architectures were simulated with pixel block data to obtain realistic dynamic power and energy estimates. The TE-SATD architectures achieved the lowest energy results: down to 13.13 pJ/SATD in the case of parallel architecture with pipeline. However, considering also the area results when evaluating energy, the best results are given by both methods using multi-cycling (transpose buffer): nearly 20.75 pJ/SATD with up to 63.54% smaller area compared with fully parallel architectures.

A Hybrid BCI Using Singular Value Decomposition Values of the Fast Walsh–Hadamard Transform Coefficients

One of the main goals of a brain computer interface (BCI) is to enable a communication channel between the brain and electronic devices by converting neural activity into control commands either for devices or applications. Because of the excellent temporal resolution, low set-up cost, and non-invasive nature, BCI systems generally use electroencephalography (EEG) for an input signal. However, EEG suffers from poor spatial resolution, and it is contaminated by various external and internal artifacts such as environmental magnetic noises and body movements. These limitations directly affect the performance of the EEG-based BCI system, and it might not work at the desired level. On the other hand, near-infrared spectroscopy (NIRS) has an advantage of relative robustness against body movements and electrical artifacts. Additionally, it is also a promising neural signal recording method which provides good spatial resolution. In this study, we particularly focused on compensating the limitations of EEG-based BCI system by adding simultaneous NIRS modality features. In order to show the effectiveness of our method, we used an open-access dataset, which was recorded from 29 subjects with simultaneous EEG-NIRS system during the imagination of opening and closing either a left-or right-hand. The features were extracted by calculating the singular value decomposition values of the Fast Walsh-Hadamard Transform coefficients. Afterward, the k-nearest neighbor algorithm was performed to classify the features. The performance of the proposed method was evaluated in terms of classification accuracy and kappa value metrics. The achieved results showed that combining a hybrid BCI system with EEG-NIRS modalities can enhance the performance of a BCI by 6.75% compared to the single-modality solution of EEG.

Detection of Focal and Non-Focal Electroencephalogram Signals Using Fast Walsh-Hadamard Transform and Artificial Neural Network.

The discrimination of non-focal class (NFC) and focal class (FC), is vital in localizing the epileptogenic zone (EZ) during neurosurgery. In the conventional diagnosis method, the neurologist has to visually examine the long hour electroencephalogram (EEG) signals, which consumes time and is prone to error. Hence, in this present work, automated diagnosis of FC EEG signals from NFC EEG signals is developed using the Fast Walsh–Hadamard Transform (FWHT) method, entropies, and artificial neural network (ANN). The FWHT analyzes the EEG signals in the frequency domain and decomposes it into the Hadamard coefficients. Five different nonlinear features, namely approximate entropy (ApEn), log-energy entropy (LogEn), fuzzy entropy (FuzzyEn), sample entropy (SampEn), and permutation entropy (PermEn) are extracted from the decomposed Hadamard coefficients. The extracted features detail the nonlinearity in the NFC and the FC EEG signals. The judicious entropy features are supplied to the ANN classifier, with a 10-fold cross-validation method to classify the NFC and FC classes. Two publicly available datasets such as the University of Bonn and Bern-Barcelona dataset are used to evaluate the proposed approach. A maximum sensitivity of 99.70%, the accuracy of 99.50%, and specificity of 99.30% with the 3750 pairs of NFC and FC signal are achieved using the Bern-Barcelona dataset, while the accuracy of 92.80%, the sensitivity of 91%, and specificity of 94.60% is achieved using University of Bonn dataset. Compared to the existing technique, the proposed approach attained a maximum classification performance in both the dataset.

Superimposed training low probability of detection underwater communications.

This paper proposes a superimposed training method for low probability of detection underwater acoustic communications. A long pilot sequence was superimposed to the message for equalization and synchronization purposes. A fast Hadamard transform (FHT) estimated the channel impulse response and compressed the pilot energy. A Wiener filter performed equalization. The interference signal was removed using hyperslice cancellation by coordinate zeroing. An inverse FHT decompressed the remaining sequence energy and the message was retrieved. Results from a shallow water experiment presented bit error rates <10-2 for signal-to-noise ratios <-8 dB.

Orthogonal AMP for Massive Access in Channels With Spatial and Temporal Correlations

We address the joint device activity detection and channel estimation (JACE) problem in a massive MIMO connectivity scenario in which a large number of mobile devices are connected to a base station (BS), while only a small portion are active at any given time. The main objective is to provide an efficient transmission and detection scheme with both spatial and temporal correlations. We formulate JACE as a multiple measurement vector (MMV) problem with correlated entries in the vectors to be estimated. We propose an MMV form of the orthogonal approximate message passing algorithm (OAMP-MMV). We derive a group Gram-Schmidt orthogonalization (GGSO) procedure for the realization of OAMP-MMV. We outline a state evolution (SE) procedure for OAMP-MMV and examine its accuracy using numerical results. We also compare OAMP-MMV with existing alternatives, including AMP-MMV and GTurbo-MMV. We show that OAMP-MMV outperforms AMP-MMV when pilot sequences are generated using Hadamard pilot matrices. Such a pilot design is attractive due to the low-cost signal processing technique using the fast Hadamard transform (FHT). We also show that OAMP-MMV outperforms GTurbo-MMV in correlated channels.

SVD-Based Image Watermarking Using the Fast Walsh-Hadamard Transform, Key Mapping, and Coefficient Ordering for Ownership Protection

Proof of ownership on multimedia data exposes users to significant threats due to a myriad of transmission channel attacks over distributed computing infrastructures. In order to address this problem, in this paper, an efficient blind symmetric image watermarking method using singular value decomposition (SVD) and the fast Walsh-Hadamard transform (FWHT) is proposed for ownership protection. Initially, Gaussian mapping is used to scramble the watermark image and secure the system against unauthorized detection. Then, FWHT with coefficient ordering is applied to the cover image. To make the embedding process robust and secure against severe attacks, two unique keys are generated from the singular values of the FWHT blocks of the cover image, which are kept by the owner only. Finally, the generated keys are used to extract the watermark and verify the ownership. The simulation result demonstrates that our proposed scheme is highly robust against numerous attacks. Furthermore, comparative analysis corroborates its superiority among other state-of-the-art methods. The NC of the proposed method is numerically one, and the PSNR resides from 49.78 to 52.64. In contrast, the NC of the state-of-the-art methods varies from 0.7991 to 0.9999, while the PSNR exists in the range between 39.4428 and 54.2599.

Electroencephalography applied compression algorithms qualitative analysis

ABSTRACT The objective of this work is study, implementation and evaluation of compression techniques used in bioelectrical signals, applied to electroencephalography. For that, the fundamental concepts of Fast Walsh Hadamard Transform (FWHT), the Discrete Cosine Transform (DCT) and the Discrete Wavelet Transform (DWT), in essence, the mathematical models were studied. In these systems, the applicability and principles of operation were considered the Peak Signal to Noise Ratio (PSNR), Signal to Noise Ratio (SNR), Mean Absolute Error (MAE) and mean squared error. Later, it is proposed the implementation of the compression algorithms. For the implementation of the techniques, computational tools of tests were developed, and for the purposes of validation and comparison of the results were used, with the appropriate adaptations, and described in the work, being these among the most recognised in terms of evaluation of signal quality. Finally, we present the results and the conclusions, where we sought a compromise of the implementations between the estimated percentage of DCT and the level of degradation of the signal provided by the compression application. In this sense, it was verified that they presented satisfactory results.

An audio encryption scheme based on Fast Walsh Hadamard Transform and mixed chaotic keystreams

This paper introduces an audio encryption algorithm based on permutation of audio samples using discrete modified Henon map followed by substitution operation with keystream generated from the modified Lorenz-Hyperchaotic system. In this work, the audio file is initially compressed by Fast Walsh Hadamard Transform (FWHT) for removing the residual intelligibility in the transform domain. The resulting file is then encrypted in two phases. In the first phase permutation operation is carried out using modified discrete Henon map to weaken the correlation between adjacent samples. In the second phase it utilizes modified-Lorenz hyperchaotic system for substitution operation to fill the silent periods within the speech conversation. Dynamic keystream generation mechanism is also introduced to enhance the correlation between plaintext and encrypted text. Various quality metrics analysis such as correlation, signal to noise ratio (SNR), differential attacks, spectral entropy, histogram analysis, keyspace and key sensitivity are carried out to evaluate the quality of the proposed algorithm. The simulation results and numerical analyses demonstrate that the proposed algorithm has excellent security performance and robust against various cryptographic attacks.

A Hybrid Secure Watermarking Scheme Using Nonnegative Matrix Factorization and FastWalsh-Hadamard Transform

We present a robust and unnoticeable secure image watermarking approach using Nonnegative Matrix Factorization (NMF) and Fast Walsh-Hadamard Transform (FWHT). The core idea of the proposed scheme consist of four key steps: The original cover image is divided into small blocks. The NMF is then applied to each block separately, followed by using the FWHT to the generated weight matrix. Finally, the singular values of the watermark image are distributed over the transformed blocks. The experimental results certainly show enhanced visual imperceptibility and exceptional resiliency against various types of attacks.

Performance Enhancement of Underwater Acoustic OFDM Communication Systems

The supported bandwidth of the underwater communication systems is limited to several kilo hertz, which considers as the main challenge for Underwater Acoustic (UWA) communications. Meanwhile, the Bit-Error-Rate (BER) performance of the UWA systems is degrades as a result of water temperature, water salinity, attenuation, and multi-path propagation. In this paper, we present a modification to the conventional Orthogonal Frequency Division Multiplexing (OFDM) based (FFT) using Fast Walsh–Hadamard transform (FWHT) instead of Fast Fourier Transform (FFT). Also, the proposed algorithm is encoded and decoded using Low Density Parity Check (LDPC) coding algorithm. Simulation results show that the proposed algorithm with LDPC coding can improve the BBER system performance than the corresponding traditional one.

Performance enhancement of UWA‐OFDM communication systems based on FWHT

SummaryThe available bandwidth of underwater environment tends to several kilohertz, which considers the main challenges of communications under sea water. On the other hand, the bit‐error‐rate (BER) performance degrades because of several reasons such as multipath propagation, time variabilities of the channel, attenuation, and water temperature. In this paper, we aim to improve the underwater acoustic (UWA) BER system performance by using orthogonal frequency division multiplexing (OFDM) based on fast Walsh‐Hadamard transform (FWHT) instead off fast Fourier transform (FFT). We proposed a low‐complexity equalization and carrier frequency offset (CFO) compensation for UWA‐OFDM–based FWHT using banded‐matrix approximation concept. Simulation results show that the UWA‐OFDM–based FWHT with low‐density parity check (LDPC) codes give a good improvement performance compared with traditional OFDM in UWA system especially in case of estimation errors.

Genetic Algorithm based Optimized Image Registration using Fast Walsh Hadamard Transform

Numerous medical means are mandatory with accuracy and totality of data about a patient for a doctor for healthcare predictive analytics and so as to treat and take care of their patients’ remedy. Medical image registration practices bestow more affluent diagnosis and medication information to the doctors in stipulating an all-embracing allusion resource for the beneficiaries entangled in image registration as an optimization crisis. In this research work, optimization of theGenetic Algorithm based image registration technique using Fast Walsh Hadamard Transform was implemented and their evaluation of results proved to be good.

Dual hybrid medical watermarking using walsh-slantlet transform

A hybrid robust lossless data hiding algorithm is proposed in this paper by using the Singular Value Decomposition (SVD) with Fast Walsh Transform (FWT) and Slantlet Transform (SLT) for image authentication. These transforms possess good energy compaction with distinct filtering, which leads to higher embedding capacity from 1.8 bit per pixel (bpp) up to 7.5bpp. In the proposed algorithm, Artificial Neural Network (ANN) is applied for region of interest (ROI) detection and two different watermarks are created. Embedding is done after applying FWH by changing the SVD coefficients and by changing the highest coefficients of SLT subbands. In dual hybrid embedding first watermark is the ROI and another watermark consists of three parts, i.e., patients’ personal details, unique biometric ID and the key for encryption. Comparison of the proposed algorithm is done with the existing watermarking techniques for analyzing the performance. Experiments are simulated on the proposed algorithm by casting numerous attacks for testing the visibility, robustness, security, authenticity, integrity and reversibility. The resultant outcome proves that the watermarked image has an improved imperceptibility with a high level of payload, low time complexity and high Peak Signal to Noise Ratio (PSNR) against the existing approaches.

Colour Image Blind Watermarking Scheme Based on Fast Walsh Hadamard Transform and Hessenberg Decomposition

Colour Image Blind Watermarking Scheme Based on Fast Walsh Hadamard Transform and Hessenberg Decomposition

Spiral-Phase Masked Optical Image Health Care Encryption System for Medical Images Based on Fast Walsh-Hadamard Transform for Security Enhancement

This article describes how a new digital spiral phase masked encryption scheme is proposed for health care system based on the Fast Walsh-Hadamard transform (FWHT) to enhance the security of the health-related information systems. The proposed encryption system uses the brain scan image to encrypt brain information from the unauthorized access. Spiral mask used here is a hybrid of Radial Hilbert Mask (RHM) and Toroidal Zone Plate (TZP) Mask which makes the key strong and enhances the security. Proposed schemes not only increase the key space but also increases the number of parameters which makes it difficult for an attacker to find exact key to recover original image. Another advantage of this proposed scheme is FWHT which reduces the quantization error that helps in reconstructing the brain image and information perfectly. The robustness of the proposed cryptosystem has been analysed by simulating on MATLAB 8.1.0(R2012b). The experimental results are provided to highlight the effectiveness, robustness and suitability of the proposed cryptosystem that prove the system can be used in healthcare data encryption.

Parallel Fast Walsh Transform Algorithm and Its Implementation with CUDA on GPUs

Abstract Some of the most important cryptographic characteristics of the Boolean and vector Boolean functions (nonlinearity, autocorrelation, differential uniformity) are connected with the Walsh spectrum. In this paper, we present several algorithms for computing the Walsh spectrum implemented in CUDA for parallel execution on GPU. They are based on the most popular sequential algorithm. The algorithms differ in the complexity of implementations, resources used, optimization strategies and techniques. In the end, we give some experimental results.

위성항법신호 적용을 위한 Walsh-Hadamard 코드 기반 직교변조 신호의 신호획득 성능

A signal acquisition scheme for a Walsh - Hadamard (WH) code-based orthogonal modulation signal is proposed for the application to the satellite navigation signals. The proposed scheme is a correlator that takes the advantage of the Fast Walsh - Hadamard Transform (FWHT) structure for the symbol demodulation of WH code. The proposed method’s signal acquisition performance is simulated in terms of false alarm probability and missing probability, and it is confirmed that a performance improvement of more than 1 dB can be achieved over the conventional LEX signal in the additive white Gaussian noise (AWGN) channel.

Channel estimation in ACO-OFDM employing different transforms for VLC

The pronounced eminency of assuring simultaneous illumination and communication has driven Visible Light Communication (VLC) to gain significant ubiquity in recent times. This paper proposes comb type pilot arrangement based channel estimation for Asymmetrically Clipped Optical OFDM (ACO-OFDM) and different multicarrier transmission systems like Discrete Hartley Transform (DHT)-based ACO-OFDM and Fast-Walsh Hadamard transform (FWHT)-based Hadamard Coded Modulation (HCM) over dispersive VLC channel. Various channel estimation algorithms like Least Square (LS), Minimum Mean Square Error (MMSE), and Interpolation techniques namely Linear, Spline, and Low-Pass are evaluated and compared for the aforesaid systems employing different orders of constellation. Here, an elaborate mathematical analysis is accomplished and Cramer Rao Lower Bound (CRLB) is derived for the channel estimation error. Simulated results emphasize that, ACO-OFDM and DHT-based ACO-OFDM have improved Bit Error Rate (BER) performance than HCM at lower Signal to Noise Ratio (SNR), while at higher SNRs HCM dominates the former. Furthermore, the simulated results evidences that, in all multicarrier systems MMSE algorithm has reducible probability of error than LS because, at higher SNRs LS is more susceptible to noise and Spline Interpolation outperforms both LS and MMSE. The simulated results are validated analytically demonstrating good agreement.

Solutions of nonlinear differential equations with feature detection using fast Walsh transforms

Walsh functions form an orthonormal basis set consisting of square waves. Square waves make the system well suited for detecting and representing functions with discontinuities. Given a uniform distribution of 2p cells on a one-dimensional element, it is proved that the inner product of the Walsh Root function for group p with every polynomial of degree ≤(p−1) across the element is identically zero. It is also proved that the magnitude and location of a discontinuous jump, as represented by a Heaviside function, are explicitly identified by its Fast Walsh Transform (FWT) coefficients. These two proofs enable an algorithm that quickly provides a Weighted Least Squares fit to distributions across the element that include a discontinuity. It is shown that flux reconstruction relative to the FWT fit in partial differential equations provides improved accuracy. The detection of a discontinuity further enables analytic relations to locally describe its evolution and provide increased accuracy. Examples are provided for time-accurate advection, Burgers' equation, and quasi-one-dimensional nozzle flow.