Hadamard Transform Research Articles

A Novel Blind Double-Color Image Watermarking Algorithm Utilizing Walsh–Hadamard Transform with Symmetric Embedding Locations

A Novel Blind Double-Color Image Watermarking Algorithm Utilizing Walsh–Hadamard Transform with Symmetric Embedding Locations

Reduction of OFDM PAPR Using a Combined Hadamard Transformation and Selective Mapping for Terrestrial DAB+ System under Rayleigh and AWGN Channel

Reduction of OFDM PAPR Using a Combined Hadamard Transformation and Selective Mapping for Terrestrial DAB+ System under Rayleigh and AWGN Channel

Hadamard transformation based frequency response mismatch calibration for a 4-channel TIADC

The time-interleaved analog-to-digital converter (TIADC) is one of the most effective solutions for improving the sampling rate of acquisition systems. However, the frequency response mismatch between channels can seriously degrade the performance of the system. In this paper, we propose a calibration method for frequency response mismatches in 4-channel TIADC systems. Following the construction of a four-channel TIADC model using a four-order Hadamard matrix, the error signals were extracted using three time-invariant filters and subsequently subtracted from the output to complete the calibration. It uses the Hadamard transform instead of the complex exponential modulator used in conventional time-varying filter methods, which can further simplify the signal processing without the necessity of complicated calculations. We have employed a stimulated four-channel TIADC system to validate the effectiveness of the proposed calibration technique. Moreover, in a commercial 12.5 GSPS four-channel TIADC system, it is also demonstrated that this approach is effective in improving the spurious-free dynamic range of the system.

Analysis of STC-GFDM with Walsh Hadamard in generalized η−μ fading channel

ABSTRACT This manuscript presents a comprehensive analytical framework for Walsh-Hadamard Transform (WHT) precoding in Space-Time Coded Generalized Frequency Division Multiplexing (STC-GFDM) systems. The investigation specifically targets the η - μ fading channel and employs the moment generating function (MGF) approach to establish an exact closed-form expression for the Symbol Error Rate (SER). The derived expression enables the examination of one-sided Gaussian, Rayleigh, Nakagami-m and Hoyt-q fading channels as specific cases of the η - μ fading channel. Additionally, the paper also delves into the impact of crucial system parameters, including modulation order, channel fading parameters ( η and μ ) and the number of transmit and receive antennas, on the WHT-STC-GFDM system’s performance. Furthermore, the paper conducts an in-depth complexity analysis of the WHT precoder, shedding light on the computational demands associated with its implementation. In summary, this research enhances the understanding of WHT precoding in STC-GFDM systems operating in η - μ fading channels, providing valuable insights for the design and optimisation of future communication systems. The numerical results are validated through Monte-Carlo simulations.

Two Indicators of Cross-Correlation for the Functions from Zqn to Z2q

Boolean functions play an important role in the design of secure cryptosystems and code division multiple access (CDMA) communication. Several possible generalizations of Boolean functions have been obtained in recent years. In this paper, we analyze the properties of functions from in terms of their Walsh-Hadamard transform (WHT). We provide a relationship between cross-correlation and the WHT of these functions. Also, we present a necessary and sufficient condition for the functions to have complementary autocorrelation. The Parseval’s identity for the current setup of these functions is obtained. Further, we obtained the modulus indicator (MI) and the sum-of-squares-modulus indicator (SSMI) of cross-correlation among two functions for the current setup.

Subsampled Randomized Hadamard Transformation-based Ensemble Extreme Learning Machine for Human Activity Recognition

Extreme Learning Machine (ELM) is becoming a popular learning algorithm due to its diverse applications, including Human Activity Recognition (HAR). In ELM, the hidden node parameters are generated at random, and the output weights are computed analytically. However, even with a large number of hidden nodes, feature learning using ELM may not be efficient for natural signals due to its shallow architecture. Due to noisy signals of the smartphone sensors and high dimensional data, substantial feature engineering is required to obtain discriminant features and address the “curse-of-dimensionality”. In traditional ML approaches, dimensionality reduction and classification are two separate and independent tasks, increasing the system’s computational complexity. This research proposes a new ELM-based ensemble learning framework for human activity recognition to overcome this problem. The proposed architecture consists of two key parts: (1) Self-taught dimensionality reduction followed by classification. (2) they are bridged by “Subsampled Randomized Hadamard Transformation” (SRHT). Two different HAR datasets are used to establish the feasibility of the proposed framework. The experimental results clearly demonstrate the superiority of our method over the current state-of-the-art methods.

Real-time ghost imaging algorithm on the multidimensional vector matrix Walsh transformation with spatiotemporal free-fps.

In this research, we propose a real-time spatiotemporal free-fps algorithm based on the multidimensional vector matrix Walsh transform with an adjustable ghost imaging video quality and a frame rate to address the issues of uneven imaging speed, fixed imaging frame rate, and uncomfortable appearance in real-time ghost imaging videos of moving objects. This algorithm utilizes the temporal and spatial correlation of ghost imaging videos to achieve free and adjustable video frame rates in time without being limited by DMD refresh rates. Improving the spatial information of a single frame in space enhances the smoothness of ghost imaging videos, making the appearance of ghost imaging videos more comfortable. To achieve this, a four-dimensional vector Walsh transform kernel matrix is used to transform and reconstruct the high-quality images of the target object. Then the reconstructed high-quality image is spatially interpolated to enhance spatial information. Reasonable frame rate parameters are set based on the corresponding relationship between the detection values of the adjacent frames and speckle, improving the ghost imaging video in both time and space and achieving a smooth real-time ghost imaging video with an adjustable quality and frame rate. The simulation and experimental results of moving objects show that our algorithm solves the limitation of a DMD refresh rate compared with the existing ghost imaging video methods and makes the ghost imaging video more comfortable and smoother in real time. The PSNR of the objective evaluation index is increased by 12%. Regarding a subjective evaluation, this paper proposes an adaptive parameterless evaluation algorithm (APEA) for images with different resolutions based on the NRSS, which improved the structure retention degree by 13% and the Brisque parameter evaluation by 70%. We propose an adaptive parameterless video comfort evaluation algorithm (APVCEA) to evaluate the subjective comfort of ghost imaging videos by 14% compared with traditional methods.

Multichannel Orthogonal Transform-Based Perceptron Layers for Efficient ResNets.

In this article, we propose a set of transform-based neural network layers as an alternative to the 3 x 3 Conv2D layers in convolutional neural networks (CNNs). The proposed layers can be implemented based on orthogonal transforms, such as the discrete cosine transform (DCT), Hadamard transform (HT), and biorthogonal block wavelet transform (BWT). Furthermore, by taking advantage of the convolution theorems, convolutional filtering operations are performed in the transform domain using elementwise multiplications. Trainable soft-thresholding layers, that remove noise in the transform domain, bring nonlinearity to the transform domain layers. Compared with the Conv2D layer, which is spatial-agnostic and channel-specific, the proposed layers are location-specific and channel-specific. Moreover, these proposed layers reduce the number of parameters and multiplications significantly while improving the accuracy results of regular ResNets on the ImageNet-1K classification task. Furthermore, they can be inserted with a batch normalization (BN) layer before the global average pooling layer in the conventional ResNets as an additional layer to improve classification accuracy.

Protected Face Templates Generation Based on Multiple Partial Walsh Transformations and Simhash

Protected Face Templates Generation Based on Multiple Partial Walsh Transformations and Simhash

Algorithm Optimization for PWM Signal Generation with Selective Harmonic Elimination Using the Walsh Transform.

The use of the Walsh transform in DC-AC PWM waveform generation allows the calculation of the switching angles by means of linear equations dependent on the fundamental amplitude. After the description of the mathematical method used to find the solutions, it is presented a method to reduce the computation time needed to find all the switching intervals that give a useful range variation of the fundamental amplitude.

Study on match filtering based on sequency spectrum characteristics of the Walsh transform for electromagnetic flowmeter signal measurement

The signal processing techniques are crucial in applying the electromagnetic flowmeter (EMF), and its filtering mechanism directly influences the measurement accuracy. Considering heavy noise frequently contaminates EMF signals, a sequency match filtering method based on the Walsh transform for processing EMF signals is proposed for the first time. The proposed method can accurately match the signal’s sequency and realize excellent harmonic extraction by analyzing features of the sequency spectrum. For method effectiveness validation, it not only has a high signal-to-noise ratio (SNR > 75 dB) in theoretical filtering but also has a low relative indication error (e<2%) in experiments on the water flow calibration and the slurry flow measurement and a low En number (En<0.5) on performance evaluation, which indicates that the proposed method enables the efficient and accurate extraction of EMF signals.

Mixed Multi-Chaos Quantum Image Encryption Scheme Based on Quantum Cellular Automata (QCA)

The advent of quantum computers could enable the resolution of complex computational problems that conventional cryptographic protocols find challenging. As a result, the formidable computing capabilities of quantum computers may render all present-day cryptographic schemes that rely on computational complexity ineffectual. Inspired by these possibilities, the primary purpose of this paper is to suggest a quantum image encryption scheme based on quantum cellular automata with mixed multi-chaos hybrid maps and a hyperchaotic system with quantum operations. To achieve desirable encryption outcomes, we designed an encryption scheme involving two main operations: (1) pixel-level diffusion and (2) pixel-level permutation. Initially, the secret keys generated using the hyperchaotic system were closely tied to the original image. During the first phase, the establishment of correlations among the image pixels, in addition to the three chaotic sequences obtained from the hyperchaotic system, was achieved with the application of a quantum-state superposition and measurement principle, wherein the color information of a pixel is described using a single qubit. Therefore, the three channels of the plain image were subjected to quantum operations, which involve Hadamard transformation and the quantum-controlled NOT gate, before the diffusion of each color channel with the hyperchaotic system. Subsequently, a quantum ternary Toffoli gate was used to perform the diffusion operation. Next, the appropriate measurement was performed on the three diffused channels. To attain the confusion phase, a blend of mixed multi-chaos hybrid maps and a two-dimensional quantum cellular automaton was used to produce random and chaotic sequence keys. Subsequently, the circular shift was utilized to additionally shuffle the rows and columns of the three diffused components, in order to alter the positions of their pixel values, which significantly contributes to the permutation process. Lastly, the three encoding channels, R, G, and B, were merged to acquire the encrypted image. The experimental findings and security analyses established that the designed quantum image encryption scheme possesses excellent encryption efficiency, a high degree of security, and the ability to effectively withstand a diverse variety of statistical attacks.

A Block-Based LMS Using the Walsh Transform for Digital Predistortion of Power Amplifiers

A Block-Based LMS Using the Walsh Transform for Digital Predistortion of Power Amplifiers

Nonlinear Equalization for Performance Enhancement of FBMC Systems Using Walsh Transform

The Filter Bank Multi-Carrier (FBMC) is an interesting recent technology for next-generation wireless radio communication systems. Equalization is a fundamental technique for enhancing Bit Error Rate (BER) performance. The traditional Linear Zero Forcing (LZF) and Linear Minimum Mean Square Error (LMMSE) equalizers have large noise amplification and high complexity, respectively. As the estimated error of the Signal-to-Noise Ratio (SNR) grows, the BER performance of the LMMSE equalizer degrades. In this paper, we present a Joint Low Complexity Optimized ZF-Successive Interference Cancellation (JLCOZF-SIC) equalizer for FBMC communication systems that are based on the Walsh–Hadamard Transform (WHT) rather than the Fast Fourier Transform (FFT). As in the MMSE-Successive Interference Cancellation (MMSE-SIC) equalizer, the proposed equalizer avoids the estimating error induced by average power per symbol estimation. The simulation results show that the proposed algorithm improves the system performance more than the existing algorithms. Furthermore, the proposed equalization provides stability in the BER performance at high levels of the co-Carrier Frequency Offset (co-CFO). In terms of computational complexity, the proposed scheme has a lower computational complexity than traditional schemes.

Multiplexer Based Error Efficient Fixed-Width Adder Tree Design for Signal Processing Applications

In copious mixed media applications, humans cannot necessarily discern error free or erroneous outputs, owing to the small range of perception abilities. Crucial information can still be obtained from marginally inexact outputs. Leveraging this, many algorithms such as Digital Signal Processing (DSP), Discrete Cosine Transform (DCT), Motion Compensation (MC) use approximate calculations while still maintaining appreciable computation accuracy. When data processing algorithms are taken into consideration, adders play an important role in the arithmetic module by managing the power and area utilization of the system. A fixed-width adder tree design for approximate calculations is proposed, that uses the trade-off between area and accuracy as the base for analysis. Our design uses 12.42%, 18.17% and 5.05% lesser area compared to the full width adder tree, FX-AT-PT and FX-AT-DT respectively. Additionally, when compared to FX-AT-DT, TFX-AT and ITFX-AT, the proposed design has an improved Maximum Error Distance (MED) of (33.33%, 29.03%), (63.64%, 65.63%) and (38.46%, 35.29%) for N = 8, 16 respectively. To cope with the inaccuracy caused by truncation, the proposed design employs mux-based radix-4 addition coupled with bias estimation. Further, to examine the error performance we have incorporated the proposed design and a few other existing designs into the Walsh-Hadamard Transform (WHT), to process images with different metrics and compare the Peak Signal to Noise Ratio (PSNR) of the images. It was observed that the proposed design showed significant improvement in the PSNR score when compared to ITFX-AT and maintains a score similar to that of FX-AT-PT.

An efficient lung cancer detection using optimal SVM and improved weight based beetle swarm optimization

Lung cancer is caused by uncontrolled cell growth in the lung tissue. Early detection of lung cancer is important for correct detection and availability of treatment. Diagnosing lung cancer by radiologists using medical imaging modalities such as computed tomography (CT) images is becoming gradually difficult and time-consuming. This research focused on developing a hybrid framework for lung cancer diagnosis through CT images combining a Discrete Local Binary Pattern (DLBP) and a Hybrid Wavelet Partial Hadamard Transform (Hybrid WPHT). The proposed model is first pre-processed using adaptive median filtering in lung cancer CT images. Then, DLBP and hybrid WPHT-based features are extracted from the pre-processed images. The adaptive Harris-Hawk optimization (AHHO) approach is then used to optimize the feature selection process by reducing the dimensionality of features. The optimal SVM (OSVM)-based classification and the improved weight-based beetle swarm (IW-BS) algorithm are used for parameter tuning in the classifier. The IW-BS approach is used to fine-tune the OSVM’s regularization and kernel parameters, significantly improving classifier performance. The proposed method categorizes input images as normal, benign, or malignant. The results show that the proposed methodology is superior in accuracy, precision, recall, specificity, F-score, running time, AUC (area under the curve) and ROC (receiver operating characteristics).

Multiplexer Based Error Efficient Fixed-Width Adder Tree Design for Signal Processing Applications

BACKGROUND: In copious mixed media applications, humans cannot necessarily discern error free or erroneous outputs, owing to the small range of perception abilities. Crucial information can still be obtained from marginally inexact outputs. Leveraging this, many algorithms such as Digital Signal Processing (DSP), Discrete Cosine Transform (DCT), Motion Compensation (MC) use approximate calculations while still maintaining appreciable computation accuracy. METHOD: When data processing algorithms are taken into consideration, adders play an important role in the arithmetic module by managing the power and area utilization of the system. A fixed-width adder tree design for approximate calculations is proposed, that uses the trade-off between area and accuracy as the base for analysis. Our design uses 12.42%, 18.17% and 5.05% lesser area compared to the full width adder tree, FX- AT-PT and FX-AT-DT respectively. Additionally, when compared to FX-AT-DT, TFX-AT and ITFX-AT, the proposed design has an RESULT: To cope with the inaccuracy caused by truncation, the proposed design employs mux-based radix-4 addition coupled with bias estimation. Further, to examine the error performance we have incorporated the proposed design and a few other existing designs into the Walsh-Hadamard Transform (WHT), to process images with different metrics and compare the Peak Signal to Noise Ratio (PSNR) of the images. CONCLUSION: It was observed that the proposed design showed significant improvement in the PSNR score when compared to ITFX-AT and maintains a score similar to that of FX-AT-PT.

Rapid Fluorescence EEM Spectroscopy Using Super-Cycle Hadamard-Transform Multiplexing.

Hadamard-transform (HT) multiplexing has recently been applied to increasingly complex spectroscopic techniques. It had been shown that the data acquisition time for fluorescence excitation emission matrix (EEM) spectroscopy can be reduced by 1 or 2 orders of magnitude using HT multiplexing of the excitation light using a programmable light source. In these previous studies, the data acquisition rate had been limited by the time it took to record an EEM, that is, to complete one cycle of multiplexed excitation spectra. The extraction of chemical information, such as concentration and chemical identity, is then obtained from parallel factor (PARAFAC) analysis of the sequence of EEMs. In this contribution, we increase the data acquisition rate by another order of magnitude, limited ultimately by the time it takes to record a single excitation spectrum. Our algorithm is entirely based on improved data processing, that is, it can be applied to previously recorded HT multiplexed data sets. The algorithm is based on three previously unexplored approaches: (1) we perform a PARAFAC multivariate analysis on the raw (multiplexed) data set, (2) the time-independent PARAFAC loading vectors are obtained prior to obtaining the time-dependent score vectors, and (3) when loading vectors are difficult to obtain from the EEMs, we instead use a rolling-average approach to considerably increase the stability of the fit. Analysis of experimental data shows that the scores of fluorescence EEMs with seven excitation wavelengths and over 1000 emission wavelengths can be obtained in less than 20 ms.

Image Steganography-based Copyright and Privacy-Protected Image Trading Systems

This paper proposes steganography-based copyright- and privacy-protected image trading systems using image transformation, i.e., either discrete cosine transform (DCT) or Hadamard transform (HT). In the systems, there are a content provider (CP), a consumer, the first trusted third party (TTP), and the second TTP. To protect the copyright of the image, the consumer ID is embedded into the amplitude components of the commercial image by the first TTP using the digital fingerprinting technique, and to protect the consumer's privacy against the first TTP and a malicious third party (s), the image steganography is applied to the commercial image by using image transformation. A color dummy image is used instead of a gray dummy image for security purposes. After applying the image transformation to both images, the coefficient signs of the commercial image are replaced by the coefficient signs of the dummy image pixel-by-pixel so that the inversely transformed commercial image looks like the dummy image instead of the commercial image. Once the consumer receives the fingerprinted image from the first TTP and the coefficient signs of the commercial image from the second TTP, the consumer reconstructs the fingerprinted commercial image without losing the hidden fingerprint at all because of the compatibility of the proposed image steganography method and the amplitude-based fingerprinting method. The experimental results confirm that the stego-images generated by the proposed systems do not look suspicious with higher qualities compared with those generated by existing systems. Moreover, the fingerprinted image quality and the correct fingerprint extracting rate have been improved by the proposed systems.

WALSH Functions and WALSH Transform. Mathematical Foundations and Some Applications

The purpose of this article is to popularize the Walsh functions. A methodology for teaching of Walsh functions is presented. The Descrete Walsh-Hadamard transform is described as well as their applications.