Hadamard Transform Research Articles

Hardware-Based Novel Applications to Locate Faults in Branched Distribution Systems

The investigations on short-circuit fault protection applications have shown that the majority of research are toward transmission networks. In the case of distribution networks, however, most studies have been focused on identifying the fault and its type or detecting the faulty bus, rather than locating the fault directly. This study presents two hardware-based applications, the first known prototype device attempts to directly predict fault location in branched distribution networks, which operate in real-time and off-line respectively. In the real-time application, a circuit is designed in Laboratory Virtual Instrument Engineering Workbench (LabVIEW) to transform 3 phase current-voltage modeling data into analog signals. The signals are then processed by a digital signal processor and the fault location is determined by the embedded algorithm in real time. The off-line application obtains results using the MATLAB Gui-based interface, which is integrated into the LattePanda development board. The algorithms inside both applications use Random Forest (RF) along with Fast Walsh Hadamard Transform (FWHT) feature to estimate the fault location. The performance of both systems is validated on a real 111-bus distribution feeder located in Turkey.

Using Hadamard Transform Multiplexed IR Spectroscopy Together with a Segmented Ion Trap for the Identification of Mobility-Selected Isomers.

The high isomeric complexity of glycans makes them particularly difficult to analyze. While ultra-high-resolution ion mobility spectrometry (IMS) can offer rapid baseline separation of many glycan isomers, their unambiguous identification remains a challenging task. One approach to solving this problem is to identify mobility-separated isomers by measuring their highly resolved cryogenic vibrational spectra. To be able to apply this approach to complex mixtures at high throughput, we have recently developed a Hadamard transform multiplexed spectroscopic technique that allows measuring vibrational spectra of all species separated in both IMS and mass spectrometry dimensions in a single laser scan. In the current work, we further develop the multiplexing technique using ion traps incorporated directly into the IMS device based on structures for lossless ion manipulations (SLIM). We also show that multiplexed spectroscopy using perfect sequence matrices can outperform standard multiplexing using Simplex matrices. Lastly, we show that we can increase the measurement speed and throughput further by running multiple multiplexing schemes using several SLIM ion traps in combination with simultaneous spectroscopic measurements in the segmented cryogenic ion trap.

Implementation of an Open-Source Multiplexing Ion Gate Control for High Kinetic Energy Ion Mobility Spectrometry (HiKE-IMS).

With ion mobility spectrometry increasingly used in mass spectrometry to enhance separation by increasing orthogonality, low ion throughput is a challenge for the drift-tube ion mobility experiment. The High Kinetic Energy Ion Mobility Spectrometer (HiKE-IMS) is no exception and routinely uses duty cycles of less than 0.1%. Multiplexing techniques such as Fourier transform and Hadamard transform represent two of the most common approaches used in the literature to improve ion throughput for the IMS experiment; these techniques promise increased duty cycles of up to 50% and an increased signal-to-noise ratio (SNR). With no instrument modifications required, we present the implementation of Hadamard Transform on the HiKE-IMS using a low cost, high-speed (600 MHz), open source microcontroller, a Teensy 4.1. Compared to signal average mode, 7- to 10-bit pseudorandom binary sequences resulted in increased analyte signal by over a factor of 3. However, the maximum SNR gain of 10 did not approach the theoretical gain largely due to capacitive coupling of the ion gate modulation with the Faraday plate used as a detector. Even when utilizing an inverse Hadamard technique, capacitive coupling was not completely eliminated. Regardless, the benefits of multiplexing IMS coupled to mass spectrometers are well documented throughout literature, and this first effort serves as a proof of concept for multiplexing HiKE-IMS. Finally, the highly flexible Teensy used in this effort can be used to multiplex other devices or can be used for Fourier transform instead of Hadamard transform.

A Probability-Based Zero-Block Early Termination Algorithm for QSHVC

To seamlessly adapt to time-varying network bandwidths, the Quality Scalable High-Efficiency Video Coding (QSHVC) is developed. However, its coding process is overly complex, and this seriously limits its wide applications in real-time environments. Therefore, it is of great significance to study fast coding algorithms for QSHVC. In this paper, we propose a novel probability-based zero-block early termination algorithm for QSHVC. First, we observed that the generated residual coefficients follow the Laplace distribution if a CU is accurately predicted. According to this observation, we derive the sum of squared differences based All-Zero Block (AZB) decision condition. Second, we develop the Hadamard Transform (HT)-based zero-valued quantized coefficient decision condition to obtain zero-valued quantized coefficients and the corresponding Partial-Zero Block (PZB). Third, the probability of each coding mode and coding depth being chosen as the best ones are combined with both AZBs and PZBs to derive the probability-based early termination condition. The experimental results show that the proposed algorithm can improve the average coding speed by 79.85% with a 0.34% decrease in BDBR.

Implementation and analysis of symmetrical signals in the sequency domain

Every transform has unique attributes and traits that are crucial to reducing computing costs and offering simple solutions. Many different frequency domain transformations, for instance, have properties that can be used in a variety of signal processing applications and analyses. Some of the Complex Hadamard Transform's variants' sequencies can be compared to those of the Discrete Fourier Transforms. It is proven the characteristics of the Conjugate Symmetric Sequency-Ordered Complex Hadamard Transform symmetry. These qualities are crucial for signal analysis and image processing. Due to duplicate spectra across the origin, it reduces computational complexity, makes an analytical analysis for symmetric signals simpler, and needs less storage. Its analysis shows that the Discrete Fourier Transform and this Complex Hadamard Transform version exhibit similar symmetry tendencies. By using elementary signals in the time domain to connect the positive and negative sequencies with their associated phasor conceptions, sequency domain spectra are used to highlight these properties. As a result of image representation, relative spectra are represented in related domains. Transform can be used to extract and analyze various aspects from a wide range of medical images.

OpenSpyrit: an ecosystem for open single-pixel hyperspectral imaging.

This paper describes OpenSpyrit, an open access and open source ecosystem for reproducible research in hyperspectral single-pixel imaging, composed of SPAS (a Python single-pixel acquisition software), SPYRIT (a Python single-pixel reconstruction toolkit) and SPIHIM (a single-pixel hyperspectral image collection). The proposed OpenSpyrit ecosystem responds to the need for reproducibility and benchmarking in single-pixel imaging by providing open data and open software. The SPIHIM collection, which is the first open-access FAIR dataset for hyperspectral single-pixel imaging, currently includes 140 raw measurements acquired using SPAS and the corresponding hypercubes reconstructed using SPYRIT. The hypercubes are reconstructed by both inverse Hadamard transformation of the raw data and using the denoised completion network (DC-Net), a data-driven reconstruction algorithm. The hypercubes obtained by inverse Hadamard transformation have a native size of 64 × 64 × 2048 for a spectral resolution of 2.3 nm and a spatial resolution that is comprised between 182.4 µm and 15.2 µm depending on the digital zoom. The hypercubes obtained using the DC-Net are reconstructed at an increased resolution of 128 × 128 × 2048. The OpenSpyrit ecosystem should constitute a reference to support benchmarking for future developments in single-pixel imaging.

Enhancing Tool Wear Prediction Accuracy Using Walsh-Hadamard Transform, DCGAN and Dragonfly Algorithm-Based Feature Selection.

Tool wear is an important concern in the manufacturing sector that leads to quality loss, lower productivity, and increased downtime. In recent years, there has been a rise in the popularity of implementing TCM systems using various signal processing methods and machine learning algorithms. In the present paper, the authors propose a TCM system that incorporates the Walsh-Hadamard transform for signal processing, DCGAN aims to circumvent the issue of the availability of limited experimental dataset, and the exploration of three machine learning models: support vector regression, gradient boosting regression, and recurrent neural network for tool wear prediction. The mean absolute error, mean square error and root mean square error are used to assess the prediction errors from three machine learning models. To identify these relevant features, three metaheuristic optimization feature selection algorithms, Dragonfly, Harris hawk, and Genetic algorithms, were explored, and prediction results were compared. The results show that the feature selected through Dragonfly algorithms exhibited the least MSE (0.03), RMSE (0.17), and MAE (0.14) with a recurrent neural network model. By identifying the tool wear patterns and predicting when maintenance is required, the proposed methodology could help manufacturing companies save money on repairs and replacements, as well as reduce overall production costs by minimizing downtime.

New fast Walsh–Hadamard–Hartley transform algorithm

<span lang="EN-US">This paper presents an efficient fast Walsh–Hadamard–Hartley transform (FWHT) algorithm that incorporates the computation of the Walsh-Hadamard transform (WHT) with the discrete Hartley transform (DHT) into an orthogonal, unitary single fast transform possesses the block diagonal structure. The proposed algorithm is implemented in an integrated butterfly structure utilizing the sparse matrices factorization approach and the Kronecker (tensor) product technique, which proved a valuable and fast tool for developing and analyzing the proposed algorithm. The proposed approach was distinguished by ease of implementation and reduced computational complexity compared to previous algorithms, which were based on the concatenation of WHT and FHT by saving up to 3N-4 of real multiplication and 7.5N-10 of real addition.</span>

Visual Quality Improvement of Watermarked Image Based on Singular Value Decomposition Using Walsh Hadamard Transform

Abstract Embedding the watermark is still a challenge in image watermarking. The watermark should not reduce the visual quality of the image being watermarked and hard to distinguish from its original. Embedding a watermark of a small size might be a good solution. However, the watermark might be easy to lose if there is any tampering with the watermarked image. This research proposes to increase the visual quality of the watermarked image using the Walsh Hadamard transform, which is applied to the singular value decomposition-based image watermarking. Technically, the watermark image is converted into a low bit-rate signal before being embedded in the host image. Using various watermark sizes, experimental results show that the proposed method could produce a good imperceptibility with 47.10 dB on average and also gives robustness close to the original watermark with a normalized correlation close to 1 on average. The proposed method can also recognize the original watermark from the tampered watermarked image at different levels of robustness.

Spectrometer-based wavelength interrogation SPR imaging via Hadamard transform.

We present spectrometer-based wavelength interrogation surface plasmon resonance imaging (SPRi) without mechanical scanning. A polarized broadband light source illuminates an object via a gold-coated prism; the reflected light is spatially modulated by a digital mirror device (DMD) and then measured with a spectrometer. Reflectance spectral images are reconstructed via the Hadamard transform (HT), and a refractive index (RI) map is visualized from the reflectance spectral images by analyzing the resonance peak shift of the spectrum at each image pixel. We demonstrate the feasibility of our method by evaluating the resolution, sensitivity, and dynamic detection range, experimentally obtained as ∼2.203 × 10-6 RI unit (RIU), ∼3,407 nm/RIU, and ∼0.1403 RIU, respectively. Furthermore, simulations are performed to validate the experimental results.

RADIC:A tool for diagnosing COVID-19 from chest CT and X-ray scans using deep learning and quad-radiomics

Deep learning (DL) algorithms have demonstrated a high ability to perform speedy and accurate COVID-19 diagnosis utilizing computed tomography (CT) and X-Ray scans. The spatial information in these images was used to train DL models in the majority of relevant studies. However, training these models with images generated by radiomics approaches could enhance diagnostic accuracy. Furthermore, combining information from several radiomics approaches with time-frequency representations of the COVID-19 patterns can increase performance even further. This study introduces "RADIC", an automated tool that uses three DL models that are trained using radiomics-generated images to detect COVID-19. First, four radiomics approaches are used to analyze the original CT and X-ray images. Next, each of the three DL models is trained on a different set of radiomics, X-ray, and CT images. Then, for each DL model, deep features are obtained, and their dimensions are decreased using the Fast Walsh Hadamard Transform, yielding a time-frequency representation of the COVID-19 patterns. The tool then uses the discrete cosine transform to combine these deep features. Four classification models are then used to achieve classification. In order to validate the performance of RADIC, two benchmark datasets (CT and X-Ray) for COVID-19 are employed. The final accuracy attained using RADIC is 99.4% and 99% for the first and second datasets respectively. To prove the competing ability of RADIC, its performance is compared with related studies in the literature. The results reflect that RADIC achieve superior performance compared to other studies. The results of the proposed tool prove that a DL model can be trained more effectively with images generated by radiomics techniques than the original X-Ray and CT images. Besides, the incorporation of deep features extracted from DL models trained with multiple radiomics approaches will improve diagnostic accuracy.

A new approach for fault diagnosis in TCSC compensated transmission lines using FWHT and machine learning techniques

In this research a new approach is introduced for detecting and classifying faults in a Thyristor-Controlled Series Capacitor (TCSC) compensated power system. Our proposed scheme utilizes both the Fast Walsh Hadamard Transform (FWHT) and machine learning algorithms. The FWHT is employed to extract fault features from current data obtained from the TCSC compensated transmission line, while machine learning algorithms such as K-Nearest Neighbor (K-NN) and Support Vector Machine (SVM) are used to classify the extracted features for the purpose of fault detection and identification. To evaluate the performance of our proposed scheme, simulation studies were conducted on a test system under various fault conditions. The simulation results demonstrate that our approach is highly effective in accurately and quickly detecting and classifying faults, even when noise and TCSC compensation are present. This scheme has the potential to enhance the reliability and efficiency of power transmission systems.

Classification of Electroencephalogram Signals Using LSTM and SVM Based on Fast Walsh-Hadamard Transform

Classification of Electroencephalogram Signals Using LSTM and SVM Based on Fast Walsh-Hadamard Transform

Non-Separable Two-Dimensional Hadamard Transform via a Discrete Hadamard Slice Theorem

Non-Separable Two-Dimensional Hadamard Transform via a Discrete Hadamard Slice Theorem

An Algorithm to Reduce Compression Ratio in Multimedia Applications

In recent years, it has been evident that internet is the most effective means of transmitting information in the form of documents, photographs, or videos around the world. The purpose of an image compression method is to encode a picture with fewer bits while retaining the decompressed image’s visual quality. During transmission, this massive data necessitates a lot of channel space. In order to overcome this problem, an effective visual compression approach is required to resize this large amount of data. This work is based on lossy image compression and is offered for static color images. The quantization procedure determines the compressed data quality characteristics. The images are converted from RGB to International Commission on Illumination CIE La*b*; and YCbCr color spaces before being used. In the transform domain, the color planes are encoded using the proposed quantization matrix. To improve the efficiency and quality of the compressed image, the standard quantization matrix is updated with the respective image block. We used seven discrete orthogonal transforms, including five variations of the Complex Hadamard Transform, Discrete Fourier Transform and Discrete Cosine Transform, as well as thresholding, quantization, de-quantization and inverse discrete orthogonal transforms with CIE La*b*; and YCbCr to RGB conversion. Peak to signal noise ratio, signal to noise ratio, picture similarity index and compression ratio are all used to assess the quality of compressed images. With the relevant transforms, the image size and bits per pixel are also explored. Using the (n, n) block of transform, adaptive scanning is used to acquire the best feasible compression ratio. Because of these characteristics, multimedia systems and services have a wide range of possible applications.

Voltage Based Electronic Control Unit (ECU) Identification with Convolutional Neural Networks and Walsh–Hadamard Transform

This paper proposes an identification approach for the Electronic Control Units (ECUs) in the vehicle, which are based on the physical characteristics of the ECUs extracted from their voltage output. Then, the identification is not based on cryptographic means, but it could be used as an alternative or complementary means to strengthen cryptographic solutions for vehicle cybersecurity. While previous research has used hand-crafted features such as mean voltage, max voltage, skew or variance, this study applies Convolutional Neural Networks (CNNs) in combination with the Walsh–Hadamard Transform (WHT), which has useful properties of compactness and robustness to noise. These properties are exploited by the CNN, and in particular, the pooling layers, to reduce the size of the feature maps in the CNN. The proposed approach is applied to a recently public data set of ECU voltage fingerprints extracted from different automotive vehicles. The results show that the combination of CNN and the WHT outperforms, in terms of identification accuracy, robustness to noise and computing times, and other approaches proposed in the literature based on shallow machine learning and tailor-made features, as well as CNN with other linear transforms such as the Discrete Fourier Transform (DFT) or CNN with the original time domain representations.

A MULTIPLE AND ROBUST IMAGE WATERMARKING APPROACH BASED ON LWT AND FWHT FOR MEDICAL DATA SECURITY

In the last years, the internet and multimedia technologies are widely used to exchange medical images and practicing telemedicine; which exposes this data to various illegitimate attacks due to their sensitivity. For this reason, many researchers work to afford a proper security and an efficient protection during the transmission. In this context, we propose a blind multi-watermarking approach for medical images using Lifting Wavelet Transform and Fast Walsh–Hadamard Transform. This approach proves the ability to embed a binary image ([Formula: see text]), used for integrity purposes, in addition to the patient information (EPR) associated with the medical cover image. Moreover, an error correcting code was used to improve the security of the EPR. We tested the proposed approach on different imaging modalities, and the obtained results show a good imperceptibility and robustness against several common attacks.

Improved Linear Cryptanalysis of Block Cipher BORON

Abstract BORON is a lightweight substitution–permutation network cipher proposed in 2017. We reduce the number of guessed key bits by key-bridging technology and first utilize Fast Walsh Transform on BORON to minimize the time complexity. Finally, this paper gives the better key-recovery attack against block cipher BORON than previously proposed by 2 rounds: we realize a 11-round key-recovery attack on BORON-80 and 13-round key-recovery attack on BORON-128. The attacks proposed in this paper are the best attacks against BORON-80/128 to date.

Image Compression Using Walsh Functions

Currently, image transfer and storage require compression. In this article, the hybrid compression algorithm is used for color/black and white images. It includes the discrete wavelet transformation and the Walsh transformation that is used for quantization. The Walsh transform coefficients are quantized and arithmetically encoded. At the output, the combined data is compressed and can be stored on any device or transmitted over any available network in the shortest time. The compressed image is decoded and the original image is decompressed using the inverse conversion operation.

Multilevel Authentication Employing Watermarking based on QR Codes, Mobile OTP, and Hadamard Transformation

High-speed internet technology has made it possible for users to transact with banks more quickly thanks to online banking services. The increased connectivity also creates numerous online security holes like phishing and pharming. By confirming the user's legitimacy, this mobile banking problem may be resolved. Here, we suggest a hybrid system that makes use of QR codes, One-Time Passwords (OTPs), and digital watermarking—a method of data concealment. The bank generates QR codes using OTP as the key to the watermark sequence. Here, OTP can be utilised for the initial authentication verification. The sequence for the second level of verification is concealed throughout the watermarking process using the Hadamard transformation. Online transactions may be made with maximum security thanks to the OTP and watermark combination. One benefit of this strategy is that the QR code may be created within a limited design window with a suitable real-time extraction method. Performance may be assessed by utilising an android application, including the real-time extraction using a mobile device.