The development of the quaternion wavelet transform

Fletcher, Peter A.; Sangwine, Stephen J.

doi:10.1016/j.sigpro.2016.12.025

Cited by 54 publications

(27 citation statements)

References 98 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…[22][23][24][25][26][27] The main advantage is that color images can be studied and processed holistically as a vector field. 22,26,27 Many gray-scale image processing methods have been extended to color image processing using the quaternion algebra, for instance, Fourier transform, 26 wavelet transform, 28 principal component analysis, 29 independent component analysis, 30 and quaternion dictionary learning algorithm. [31][32][33] Recently, Han et al 23 have proposed a QMC model of recovering a color image under a low sampling ratio without noise corruption.…”

Section: Introductionmentioning

confidence: 99%

Robust quaternion matrix completion with applications to image inpainting

Jia

Song

2019

Numerical Linear Algebra App

View full text Add to dashboard Cite

Summary In this paper, we study robust quaternion matrix completion and provide a rigorous analysis for provable estimation of quaternion matrix from a random subset of their corrupted entries. In order to generalize the results from real matrix completion to quaternion matrix completion, we derive some new formulas to handle noncommutativity of quaternions. We solve a convex optimization problem, which minimizes a nuclear norm of quaternion matrix that is a convex surrogate for the quaternion matrix rank, and the ℓ1‐norm of sparse quaternion matrix entries. We show that, under incoherence conditions, a quaternion matrix can be recovered exactly with overwhelming probability, provided that its rank is sufficiently small and that the corrupted entries are sparsely located. The quaternion framework can be used to represent red, green, and blue channels of color images. The results of missing/noisy color image pixels as a robust quaternion matrix completion problem are given to show that the performance of the proposed approach is better than that of the testing methods, including image inpainting methods, the tensor‐based completion method, and the quaternion completion method using semidefinite programming.

show abstract

Section: Introductionmentioning

confidence: 99%

Robust quaternion matrix completion with applications to image inpainting

Jia

Song

2019

Numerical Linear Algebra App

View full text Add to dashboard Cite

show abstract

“…Wavelet analysis was proposed by Molet in the early 1980s [36]. It can reveal the variety of periodicity in time series and forecast the developing tendency of the system in different time scales.…”

Section: Moving Average Difference Methods Combined With Wavelet Analysismentioning

confidence: 99%

A Method for Detecting Abrupt Change of Sediment Discharge in the Loess Plateau, China

Shen

Bao

2018

Water

View full text Add to dashboard Cite

In recent decades, the streamflow and sediment of the Yellow River has decreased sharply, especially the sediment discharge. The factors that lead to this phenomenon have become a widely concerned problem of the whole society. The analysis of abrupt change points of hydrological series is the key to divide datum period, so it is an important work in the research of streamflow and sediment reduction cause. So far, many methods have been proposed to detect abrupt change. However, most methods have great uncertainty due to the deficiencies of irrational structure of test statistics, ideal hypothesis or subjectivity. In this paper, a new method called moving average difference method for abrupt change points detection is proposed. It is proved to be effective through comparison with four commonly used methods via both synthetic series and real data case study. The results show that the proposed method has four distinct advantages: (1) The test statistic structure of the method has physical significance and is intuitive to understand; (2) It is more accurate in abrupt change detection; (3) It can detect all of the abrupt change points at one time; (4) It can detect the abrupt changes and calculate the corresponding mutation intensity simultaneously.

show abstract

“…STFT is applied by shifting the window function on the short segments and enforcing the Fourier transform (FT) analysis on each of these segments [21]. In this paper, STFT is investigated to produce a 2D image representation of EEG signals and the mathematical formula is defined as [22], [23]:…”

Section: A Time-frequency Representationmentioning

confidence: 99%

Classification Epileptic Seizures in EEG Using Time-Frequency Image and Block Texture Features

Sun

Chen

et al. 2020

IEEE Access

View full text Add to dashboard Cite

With the rapid development in technology, computer aided detection or diagnosis has become an indispensable part of the medical industry. Automatic detection of epileptic events is one of the important subjects that have aroused wide interest from more and more investigators. This paper proposes a new model in classification of multi-category electroencephalogram (EEG) signals using time-frequency image and block texture features. The one-dimensional EEG is first mapped to time-frequency domain by means of short-time Fourier transform (STFT), which is adapted to obtain a two-dimensional time-frequency image (2D-TFI). With the idea of multi-scale blocking, the obtained phase images and amplitude images are divided into several sub-blocks corresponding to different frequency ranges and time periods. Then the texture features are calculated to describe the behaviour of EEG signals. Particularly, a novel quadratic feature selection method based on kernel entropy component analysis (KECA) and Kruskal-Wallis test (KW) has been proposed for dimension reduction, by which the features that contained most distinctive information were provided. Eventually, the optimal KECA-based features are fed to support vector machine (SVM) for deciding the class of corresponding EEG. The proposed model is found to achieve at least 99.30% accuracy, 98.0% sensitivity and 100% specificity for each of the eight clinical problems. Our scheme is proven to be effective for seizure detection, which can help doctors optimize the diagnosis workflow, reduce workload and improve detection precision. INDEX TERMS Seizure, EEG, two-dimensional time-frequency image, multi-scale blocking, texture features, kernel entropy component analysis, quadratic feature selection.

show abstract

The development of the quaternion wavelet transform

Cited by 54 publications

References 98 publications

Robust quaternion matrix completion with applications to image inpainting

Robust quaternion matrix completion with applications to image inpainting

A Method for Detecting Abrupt Change of Sediment Discharge in the Loess Plateau, China

Classification Epileptic Seizures in EEG Using Time-Frequency Image and Block Texture Features

Contact Info

Product

Resources

About