Hadamard Measurement Matrix Research Articles

Compressed sensing for ECG signal compression using DWT based sensing matrices

ABSTRACT In this article, we have investigated the 1-D discrete wavelet transform (DWT)-based measurement matrices for electrocardiogram (ECG) compression. Moreover, the current work examines the suitability of the diverse DWT matrices, namely Symlets, Battle, Coiflets, Vaidyanathan, and Beylkin wavelet families, for ECG compression. Furthermore, this article shows the comparative performance study of the proposed DWT matrices with conventional deterministic and random measurement matrices. Overall, the Battle1 wavelet-based measurement matrices demonstrate the enhanced performance against the db3, coif5, and sym6 based measurement matrices in terms of Percentage Root-Mean Squared Difference (PRD), Root Mean Square Error (RMSE), and Signal-to-Noise Ratio (SNR). Finally, it was seen that the proposed Battle1 matrix demonstrates the improved performance against the conventional measurement matrices such as the Karhunen–Loeve transform (KLT), Discrete Cosine Transform (DCT) matrix, and random Hadamard measurement matrix. Thus, the result shows the adequacy of DWT measurement matrices for the compression of ECG.

An Under-Sampling Array Signal Processing Method Based on Improved Hadamard Matrix

The compressive sensing method is an effective way of under-sampling array signal processing, and the measurement matrix is a key technology of compressive sensing processing, which is of decisive significance to improve the performance of under-sampling array signal processing. In this paper, an under-sampling array signal processing method based on an improved Hadamard measurement matrix was proposed. This method improved the construction of the measurement matrix by a compressing zero method capable of reducing the redundant data, enhancing the non-correlation between columns, improving the RIP condition, and improving the performance of the compressive sensing method. The performance was verified by simulation and real data from the lake, and the results showed that the method proposed in this paper has obvious performance advantages compared with the Toeplitz Circular Matrix, the m-sequence-based matrix, and the partial Hadamard matrix under the same conditions.

Secure image block compressive sensing using complex Hadamard measurement matrix and bit‐level XOR

This paper proposes a novel image compression-encryption scheme based on compressive sensing and bit-level XOR. In the proposed scheme, the encrypted sequences are generated from a 4-D hyper-chaotic Lorenz system and a Logistic system. First, an original image is sampled by a secure block parallel compressive sensing (PCS) scheme. In the PCS phase, a key-controlled discrete cosine transform sparse basis matrix and a key-controlled complex Hadamard measurement matrix are employed. Next, the real part and imaginary part of the resulting complex-valued data are quantized and transformed into bit streams, respectively. After that, the two generated bit streams are combined into one bit stream. Then, the resulting bit stream is further encrypted by a bit-level XOR operation, where the encrypted key is generated from a chaotic system. The experiment results show the effectiveness and reliability of the proposed joint compression-encryption scheme. The proposed scheme can not only enhance the security of the compressed image but also improve the reconstructed quality of the compressed image.

Multi-source feature extraction of rolling bearing compression measurement signal based on independent component analysis

With the update of the sampling rate, automation and computation, data volume is increasing, it's critical to reduce the burden on the real-time data processing and remote diagnostics. In this paper, a composite fault diagnosis method of rolling bearing based on compressed sensing (CS) framework is proposed. Firstly, the influence of measurement matrix on the gaussianity of signal was analyzed, and Hadamard measurement matrix was used to compress and collect data. Then independent component analysis (ICA) was used to process the data collected by compression, and the data was separated and transformed based on the statistical independence. Finally, the reconstructed signal was analyzed by envelope spectrum, and the characteristic frequency of compound faults signal was extracted for fault diagnosis. The experiment result shows that the method can improve the reconstruction precision and the separation stability of fault signal and can effectively extract fault characteristics and realize fault diagnosis.

Non-Scanning Three-Dimensional Imaging System with a Single-Pixel Detector: Simulation and Experimental Study

Existing scanning laser three-dimensional (3D) imaging technology has slow measurement speed. In addition, the measurement accuracy of non-scanning laser 3D imaging technology based on area array detectors is limited by the resolution and response frequency of area array detectors. As a result, applications of laser 3D imaging technology are limited. This paper completed simulations and experiments of a non-scanning 3D imaging system with a single-pixel detector. The single-pixel detector can be used to achieve 3D imaging of a target by compressed sensing to overcome the shortcomings of the existing laser 3D imaging technology. First, the effects of different sampling rates, sparse transform bases, measurement matrices, and reconstruction algorithms on the measurement results were compared through simulation experiments. Second, a non-scanning 3D imaging experimental platform was designed and constructed. Finally, an experiment was performed to compare the effects of different sampling rates and reconstruction algorithms on the reconstruction effect of 3D imaging to obtain a 3D image with a resolution of 8 × 8. The simulation results show that the reconstruction effect of the Hadamard measurement matrix and the minimum total variation reconstruction algorithm performed well.

Painting Psychotherapy Image Measurement and Reconstruction Algorithm based on Improved Hadamard Matrix

Painting psychotherapy based on Internet technology has become a method of mental health testing and treatment. This method will produce a large number of digital images of painting psychotherapy. How to measure and reconstruct the image is the basis of automatic analysis and processing. This study aimed to propose a painting psychotherapy image measurement and reconstruction algorithm based on the improved Hadamard matrix. Moreover, the construction of a measurement matrix was analyzed using the compressed sensing theory and the Hadamard matrix construction algorithm was improved and optimized. Also, four different measurement matrices were compared and analyzed. The findings revealed that the improved Hadamard measurement matrix achieved good experimental results in terms of signal reconstruction accuracy and Peak Signal-to-Noise Ratio (PSNR) value. In the experimental analysis of painting psychotherapy image reconstruction, the reconstruction algorithm based on the improved Hadamard measurement matrix had a shorter reconstruction time and the algorithm achieved satisfactory results in terms of the number of iterations and the PSNR value of the reconstructed image. For painting psychotherapy images, the algorithm provided a theoretical basis for later digital processing, large-sample training and analysis and automatic machine recognition and judgment.

Image fusion algorithm based on improved K-singular value decomposition and Hadamard measurement matrix

To solve the problem of high time and space complexity of traditional image fusion algorithms, this paper elaborates the framework of image fusion algorithm based on compressive sensing theory. A new image fusion algorithm based on improved K-singular value decomposition and Hadamard measurement matrix is proposed. This proposed algorithm only acts on a small amount of measurement data after compressive sensing sampling, which greatly reduces the number of pixels involved in the fusion and improves the time and space complexity of fusion. In the fusion experiments of full-color image with multispectral image, infrared image with visible light image, as well as multispectral image with full-color image, this proposed algorithm achieved good experimental results in the evaluation parameters of information entropy, standard deviation, average gradient, and mutual information.

Object detection among multimedia big data in the compressive measurement domain under mobile distributed architecture

Multimedia big data is difficult to handle because of its enormous amount and the elusive property of underlying information. To study how to explore valuable information among multimedia big data with low complexity, this paper proposes an object detection method of big data, which is in compressive measurement domain under a mobile distributed computing architecture. It includes the sparse representation and object detection processes. Considering the unbalanced computation capacity between a mobile center cloud and mobile edge sites, we shift large storage burden into the cloud, while performing the dictionary learning by using compressive measurements in the mobile edge sites. Specifically, after getting the measurements at the edge sites, we perform dictionary learning to obtain the sparse representation in pixel domain, then select significant images and their feature vectors to be stored in the center cloud. In addition, we also analyze the trained dictionary in the measurement domain employing measurements. In order to reveal the two kinds of dictionaries’ relationship, we conduct a formulation process into each of them and find that the relationship depends on the uniqueness relation between the original signal and the sparse coefficient in the measurement domain. At the same time, we keep coefficients for a certain time period at the mobile edge sites in order to realize real time object detection, taking the advantage of low latency of the mobile edge computing ends. Since the sparse coefficients and the original signal have a one-to-one correspondence relationship, we can just search for the matched coefficients of the image block for detecting object. Experimental results show that Hadamard measurement matrix can better preserve the characteristics of the original signal than Gaussian matrix and that the proposed method can achieve a favorable detection performance. Meanwhile, the computation cost and storage cost of the proposed detection process can be significantly reduced compared with traditional methods, which is suitable for the multimedia big data. This can also be used in smart cities for looking for lost children and other specific events.

Cognitive Computation of Compressed Sensing for Watermark Signal Measurement

As an important tool for protecting multimedia contents, scrambling and randomizing of original messages is used in generating digital watermark for satisfying security requirements. Based on the neural perception of high-dimensional data, compressed sensing (CS) is proposed as a new technique in watermarking for improved security and reduced computational complexity. In our proposed methodology, watermark signal is extracted from the CS of the Hadamard measurement matrix. Through construction of the scrambled block Hadamard matrix utilizing a cryptographic key, encrypting the watermark signal in CS domain is achieved without any additional computation required. The extensive experiments have shown that the neural inspired CS mechanism can generate watermark signal of higher security, yet it still maintains a better trade-off between transparency and robustness.

Object Detection Algorithm in Traffic Video Surveillance Based on Compressed Sensing

To adapt the contradiction between the increasing information quantity of highway traffic network monitoring and the limited network bandwidth resources, this paper proposes an object detection algorithm based on Bayesian compressed sensing. Video are sparse in a wavelet base, and a partial Hadamard measurement matrix is adopted to compress the video. The object detection method combines background difference and Bayesian compressed sensing of wavelet tree structure. To get more accurate foreground, an adaptive background model is proposed. Experiments results show the accuracy and effectiveness of the method, and can robustly detect the targets under changing light and reduce the price of video transmission.