Quaternion Wavelet Research Articles

A deep learning phase-based solution in 2D echocardiography motion estimation.

In this paper, we propose a new deep learning method based on Quaternion Wavelet Transform (QWT) phases of 2D echocardiographic sequences to estimate the motion and strain of myocardium. The proposed method considers intensity and phases gained from QWT as the inputs of customized PWC-Net structure, a high-performance deep network in motion estimation. We have trained and tested our proposed method performance using two realistic simulated B-mode echocardiographic sequences. We have evaluated our proposed method in terms of both geometrical and clinical indices. Our method achieved an average endpoint error of 0.06 mm per frame and 0.59 mm between End Diastole and End Systole on a simulated dataset. Correlation analysis between ground truth and the computed strain shows a correlation coefficient of 0.89, much better than the most efficient methods in the state-of-the-art 2D echocardiography motion estimation. The results show the superiority of our proposed method in both geometrical and clinical indices.

On Benedicks–Amrein–Berthier uncertainty principles for continuous quaternion wavelet transform

The continuous quaternion wavelet transform (CQWT) can refine a quaternion function in the multiscale framework by stretching and translation to achieve an effect of the localized analysis. In this paper, we are devoted to some different types of uncertainty principles (UPs) for the two‐dimensional CQWT. More precisely, we obtain the Benedicks–Amrein–Berthier UP and the logarithmic Sobolev‐type UP for the CQWT. As a direct consequence, we also deduce some significant corollaries, such as the Benedicks UP, the general Heisenberg‐type UP, the general concentration UP, and the concentration logarithmic Sobolev‐type UP for the CQWT.

The continuous quaternion wavelet transform on function spaces

In this paper, boundedness results for the continuous quaternion wavelet transform on Besov, $BMO$ and Hardy $H^{p}$ spaces are established. Furthermore, the continuous quaternion wavelet transform is also studied on the weighted Besov, $BMO_k$ and $H^{p}_{k}$ spaces associated with a tempered weighted function.

Some Uncertainty Principles for the Right-Sided Multivariate Continuous Quaternion Wavelet Transform

Some Uncertainty Principles for the Right-Sided Multivariate Continuous Quaternion Wavelet Transform

Multi-component Seismic Data Random Noise Attenuation via Quaternion Wavelet Transform

In this paper, we present a new method with quaternion wavelet transform (QWT) to suppress the random noise of multi-component seismic data simultaneously. The proposed method could preserve the vector nature of the wavefield compared with the traditional wavelet threshold denoising approaches. Artificial data are used to test the new method’s performance. The experimental results show that QWT gets higher SNRs and better preserves weak reflecting energy.

Embedding vector field into image features to enhance classification

Classical methods, including sparse representation classification (SRC) and neural networks (NNs), classify image object(s) using features like intensity, color, texture, and geometry extracted from the image. For the purpose of classification the present study proposes to augment the set of image features with vector field (VF) features, like singular points (SPs) and trajectories. To generate VFs with such features, our approach solves the Poisson Image (PI) equation. Using its solution uˆ(x,y), our approach defines two functions ϕˆ(x,y) and ψˆ(x,y) and develops two Poisson gradient VFs (PGVFs) ∇ϕˆ(x,y) and ∇ψˆ(x,y), used to embed features into a database of images. The embedding of VF features into image objects constitutes the main novelty of this study. The advantage that comes from the novelty is increased statistics of machine learning (ML) classifiers. To validate the advantage, the PGVFs ∇ϕˆ(x,y) and ∇ψˆ(x,y) were embedded into the public image databases COIL100, YaleB, ISIC2018, and ISIC2020. The original and the eight VF covered databases were classified with two ML classifiers: sparse representation wavelet classification (SRWC) and SRC in the quaternion wavelets (SRCQW) domain. The results obtained are presented in the paper and confirm the claimed advantage.

AQWT: adaptive quaternion wavelet transform and hybrid heuristic improvement for multi-modal medical image fusion model

AQWT: adaptive quaternion wavelet transform and hybrid heuristic improvement for multi-modal medical image fusion model

Compression of photographic images by the quaternion Wavelet transform associated with SPIHT coding and comparative study with wavelet transform

Compression of photographic images by the quaternion Wavelet transform associated with SPIHT coding and comparative study with wavelet transform

Crack recognition on concrete structures based on machine crafted and hand crafted features

Concrete structures play a critical role in infrastructure development, and their safety is of utmost importance. Cracks in concrete structures can be a sign of deterioration, which may affect the overall safety of the building. Regular inspections and monitoring of surface cracks are essential to ensure the structural integrity of the building. However, human inspection can be time-consuming and subjective, leading to inconsistent findings. Hence, computer vision based crack recognition is necessary. In this work, we propose three custom designed deep networks and a multi resolution framework, named, Quaternionic wavelet transform (QWT) for crack recognition. The efficiency of deep network (machine crafted features) and QWT (hand crafted features) is studied in detail on three datasets namely SDNET2018, METU (Middle East Technical University) concrete crack image dataset and Historical-crack18-19 dataset. Also, the effect of wavelet scale on crack recognition and the implication of the fully connected layers in deep convolutional neural networks are studied in this research work. Finally, we infer that QWT features achieve a maximum accuracy of 98.44%, 99.80% and 94.67% respectively on the above said datasets, and their performance is comparable to that of machine-crafted (deep) features and with the other state of art methods.

Quaternion Wavelet Transform and a Feedforward Neural Network-Aided Intelligent Distributed Optical Fiber Sensing System.

In this paper, aiming at a large infrastructure structural health monitoring network, a quaternion wavelet transform (QWT) image denoising algorithm is proposed to process original data, and a depth feedforward neural network (FNN) is introduced to extract physical information from the denoised data. A Brillouin optical time domain analysis (BOTDA)-distributed sensor system is established, and a QWT denoising algorithm and a temperature extraction scheme using FNN are demonstrated. The results indicate that when the frequency interval is less than 4 MHz, the temperature error is kept within ±0.11 °C, but is ±0.15 °C at 6 MHz. It takes less than 17 s to extract the temperature distribution from the FNN. Moreover, input vectors for the Brillouin gain spectrum with a frequency interval of no more than 6 MHZ are unified into 200 input elements by linear interpolation. We hope that with the progress in technology and algorithm optimization, the FNN information extraction and QWT denoising technology will play an important role in distributed optical fiber sensor networks for real-time monitoring of large-scale infrastructure.

Integration of nondecimated quaternion wavelet transform and neighborhood texture patterns for disease classification in banana (Musa spp.) foliage

Integration of nondecimated quaternion wavelet transform and neighborhood texture patterns for disease classification in banana (Musa spp.) foliage

Tighter Heisenberg–Weyl type uncertainty principle associated with quaternion wavelet transform

Tighter Heisenberg–Weyl type uncertainty principle associated with quaternion wavelet transform

Cross-scale feature fusion-based JND estimation for robust image watermarking in quaternion DWT domain

Owing to the rapid development of just-noticeable difference (JND) and the high robustness of discrete wavelet transform (DWT) based watermarking, robust watermarking methods based on JND models have been extensively adopted in the area of image copyright protection. In general, in existing JND model-based methods, transform domain-based features play an important role during the quantization strength measurement. However, most existing methods only use the subband-specific features from the final multi-scale wavelet transform domain, ignoring the feature relevance among subband-specific features with different scales among RGB channels. To address this issue, in this study, we put forward a JND estimation based on cross-scale feature fusion (CFJnd) mechanism in quaternionic DWT domain for robust image watermarking. For the proposed CFJnd, we first design different quaternionic wavelet scales for the JND modeling, which can be used to measure the minimum distortion level of the embedding-specific subband relevance. Furthermore, the cross-scale features among different subbands are adopted to jointly generate the pattern, texture and color measurement, making the final perceptual masking more representative. In addition, we further develop a CFJnd-based robust image watermarking, and the watermark is embedded by quantifying the candidate quaternionic DWT coefficients of the embedding-specific subband on a level which is adaptively defined according to the proposed CFJnd. Experimental results based on the publicly available image database show that the proposed method can produce reliable and promising results, compared to other state-of-the-art image watermarking methods.

High-Accuracy 3D Contour Measurement by Using the Quaternion Wavelet Transform Image Denoising Technique

In this paper, we propose an image denoising algorithm based on the quaternion wavelet transform (QWT) to address sinusoidal fringe images under strong noise in structured light 3D profilometry. The analysis of a quaternion wavelet shows that the amplitude image of the quaternion wavelet is easily affected by noise. However, the three phase images, which mainly reflect edge and texture information, are randomly and disorderly distributed with respect to noise. The QWT denoising algorithm is suitable for processing sinusoidal fringe images of complex structures in a high-accuracy 3D measurement system. Sinusoidal fringe images are collected and denoised by using the QWT algorithm and classical Gaussian smoothing (GS) denoising algorithm, and GS is used as a reference for the QWT algorithm. The results indicate that the standard deviation is reduced from 0.1448 for raw sinusoidal fringe images to 0.0192, and the signal-to-noise ratio is improved from 4.6213 dB to 13.3463 dB by using the QWT algorithm. The two algorithms have the same denoising effect for a surface with less information. For a surface with rich information, the details of the 3D contour are lost because of the image “blurring” caused by using the GS algorithm, while all edge details of the 3D contour are reconstructed by using the QWT denoising algorithm because of its characteristic of information and noise being separated from the source. For the measured face mask, the error is less than ±0.02 mm. In addition, it takes less than 20 s to run the QWT algorithm to process eight sinusoidal fringe images, which meets the requirements of high-precision measurements.

Medical Image Fusion Multi Model Based on Quaternion Wavelet Transform

Medical image fusion can combine multi-modal images into an integrated higher-quality image, which can provide more comprehensive and accurate pathological information than individual image does. Traditional transform domain-based image fusion methods usually ignore the dependencies between coefficients and may lead to the inaccurate representation of source image. To improve the quality of fused image, a medical image fusion method based on the dependencies of quaternion wavelet transform coefficients is proposed. First, the source images are decomposed into low-frequency component and high-frequency component by quaternion wavelet transform. Then, a clarity evaluation index based on quaternion wavelet transform amplitude and phase is constructed and a contextual activity measure is designed. These measures are utilized to fuse the high-frequency coefficients and the choose-max fusion rule is applied to the lowfrequency components. Finally, the fused image can be obtained by inverse quaternion wavelet transform. The experimental results on some brain multi-modal medical images demonstrate that the proposed method has achieved advanced fusion result.

Distributed Optical Fiber Sensing System for Large Infrastructure Temperature Monitoring

In this article, a distributed optical fiber sensing system for large infrastructure temperature monitoring is proposed. To meet the requirements of monitoring networks in terms of measurement accuracy, spatial resolution, and real-time or quasireal-time performance, a quaternion wavelet transform (QWT) image denoising algorithm is proposed to address the original edge node data for the structural monitoring networks of large infrastructures. A distributed Brillouin optical time-domain analysis (BOTDA) sensing system with a 40-km sensing fiber is established. The raw Brillouin gain spectrum (BGS) image is decomposed into one magnitude image and three phase images by QWT. The phase images of the OWT are distributed randomly and disorderly with respect to the noise, while the magnitude image of the quaternion wavelet is greatly affected by the noise. The useful message energy of the magnitude image is concentrated on a small number of coefficients with large amplitude, while the noise mainly corresponds to the coefficients with smaller amplitude. Then, the Bayes shrink threshold method is introduced to filter out noise in the magnitude image. The results indicate that the signal-to-noise ratio (SNR) and the frequency uncertainty have been improved significantly. The accuracy of the retrieved Brillouin frequency shift from denoised BGS images reaches 0.2 MHz, which corresponds to a temperature error of ±0.1 °C. Less than 4 s are required to process a BGS image with 50 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times $ </tex-math></inline-formula> 40 000 pixels by the QWT denoising technique. The uploaded data obtained from 40 M bytes of raw data are reduced to 0.08 M bytes for each measurement. We hope that with technological progress and algorithm optimization, the distributed optical fiber sensing system based on the QWT image denoising algorithm will have an important role in the real-time application of large-scale infrastructure structural health monitoring for the Internet of Things.

Infrared and visible image fusion based on QNSCT and Guided Filter

Image fusion is the process of fusing multiple images of the same scene to obtain a more informative image for human eye perception. In this paper, a new fusion framework based on Quaternion Non-Subsampled Contourlet Transform (QNSCT) and Guided Filter detail enhancement is designed to address the problems of inconspicuous infrared targets and poor background texture in Infrared and visible image fusion. The proposed method uses the quaternion wavelet transform for the first time instead of the traditional Non-Subsampled Pyramid Filter Bank structure in the Non-Subsampled Contourlet Transform (NSCT). The flexible multi-resolution of quaternion wavelet and the multi-directionality of NSCT are fully utilized to refine the multi-scale decomposition scheme. On the other hand, the coefficient matrix obtained from the proposed QNSCT algorithm is fused using a weight refinement algorithm based on the guided filter. The fusion scheme is divided into four steps. First, the Infrared and visible images are decomposed into multi-directional and multiscale coefficient matrices using QNSCT. The experimental results show that the proposed algorithm not only extracts important visual information from the source image, but also preserves the texture information in the scene better. Meanwhile, the scheme outperforms state-of-the-art methods in both subjective and objective evaluations.

Image Classification Based on Sparse Representation in the Quaternion Wavelet Domain

In this study, we propose a novel sparse representation learning method in the Quaternion Wavelet (QW) domain for multi-class image classification. The proposed method takes advantages from: i) the QW decomposition, which promotes sparsity and provides structural information about the image data while allowing approximate shift-invariance, to extract meaningful features from low-frequency QW sub-bands, ii) the dimensionality reduction method using Principal Component Analysis (PCA) for reducing the complexity of the problem, and iii) the sparse representation of the generated QW features to efficiently learn and capture the meaningful and compact information of this data. After the QW decomposition, the features extracted from low-frequency image sub-bands information are projected, by the PCA, into a new feature space with lower dimensionality. The features extracted from the training samples are used to construct a dictionary, while the features of the test samples are sparsely coded for the classification step. The sparse coding problem is formulated in a QW Least Absolute Shrinkage and Selection Operator (QWLasso) model applying quaternion <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$l_{1}$ </tex-math></inline-formula> minimization. A novel Quaternion Fast Iterative Shrinkage-Thresholding Algorithm (QFISTA) is developed to solve the QWLasso model. The experiments conducted on various public image datasets validated that the proposed method possesses higher accuracy, sparsity, and robustness in comparison with several contemporary methods in the field including Neural Networks.

Hybrid Successive CFA Image Encryption-Watermarking Algorithm Based on the Quaternionic Wavelet Transform (QWT)

In this paper, we present a new robust hybrid algorithm combining successively chaotic encryption and blind watermarking of images based on the quaternionic wavelet transform (QWT) to ensure the secure transfer of digital data. The calculations of the different evaluation parameters have been performed in order to determine the robustness of our algorithm to certain attacks. The application of this hybrid algorithm on CFA (Color Filter Array) images, allowed us to guarantee the integrity of the digital data and to propose an autonomous transmission system. The results obtained after simulation of this successive hybrid algorithm of chaotic encryption and then blind watermarking are appreciated through the values of the evaluation parameters which are the peak signal-to-noise ratio (PSNR) and the correlation coefficient (CC), and by the visual observation of the extracted watermarks before and after attacks. The values of these parameters show that this successive hybrid algorithm is robust against some conventional attacks.

Robust image watermarking algorithm based on QWT and QSVD using 2D Chebyshev-Logistic map

In this paper, a novel watermarking algorithm based on quaternion wavelet transform(QWT) and quaternion singular value decomposition(QSVD) is proposed for copyright protection. Firstly, color images are converted from RGB space to YCbCr space. Then one-level QWT transform is applied to the luminance component Y. The LL component is split to 4×4 non-overlapping blocks. Every block is decomposed by QSVD, and the bits of watermark are embedded in singular vectors or singular values. Moreover, 2D Chebyshev-Logistic map is proposed to encrypt the watermarks and scramble the embedding positions. In the watermarking extraction process, both blind and semi-blind watermarking extraction methods are introduced. Experiments show that proposed watermarking algorithm has good robust against common attacks and has good invisibility.