Matrix-Valued and Quaternion Wavelets

Ginzberg, Paul; Walden, A. T.

doi:10.1109/tsp.2012.2235434

Cited by 25 publications

(15 citation statements)

References 25 publications

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“…Each of these basic functions has its own characteristics that make it suitable for specific application. For instance, the Daubechies wavelet is devised so that the vanishing moment of its mother function becomes zero . This condition creates a smooth frequency response for the filters in the filter bank (FB).…”

Section: Introductionmentioning

confidence: 99%

“…For instance, the Daubechies wavelet is devised so that the vanishing moment of its mother function becomes zero. 14,15 This condition creates a smooth frequency response for the filters in the filter bank (FB). Nearly linear phase response of the filter in Symlet wavelet is used to avoid phase distortion in the under process signal.…”

Section: Introductionmentioning

confidence: 99%

“…Adders increase the hardware complexity, and shifters lead to more computational error. For example, division number 15 by 16 through four right shifts of dividend (15) results in quotient of zero. So by repetition of shift operations, the computational error becomes more critical.…”

Section: Introductionmentioning

confidence: 99%

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A new discrete wavelet transform appropriate for hardware implementation

Meshkat

Dehghani

2020

Circuit Theory & Apps

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Summary A new method for computation of discrete wavelet transform is introduced. The impulse response of the finite impulse response (FIR) filter, as the main block in filter bank method, is realized such that orthonormal wavelet transform is achieved without using any multiplier as the most challenging part of the FIR filters. It is proved that the calculated Sobolev regularity of the proposed wavelet is higher than that of Daubechies for the same support width. Compared with most popular known wavelets, simulation results of the newly introduced wavelet for signal denoising prove remarkable advantage of our wavelet especially in terms of complexity and power consumption. The proposed wavelet and well‐known Daubechies wavelet are separately implemented on the Spartan‐6 FPGA (Field Programmable Gate Array) to compare the performance of them. The occupied slices and LUTs (Lookup Table) in realization of the proposed wavelet in comparison with those of Daubechies wavelet are decreased by 50% and 56%, respectively. Its power consumption at 100 MHz is also reduced by 86% in comparison with the Daubechies wavelet, and maximum frequency is increased by 186%. Implementation with standard cells of a 0.18‐μm CMOS (Complementary Metal Oxide Semiconductor Field Effect Transistor) technology shows 75% and 85% reduction in the power and chip area, respectively.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A new discrete wavelet transform appropriate for hardware implementation

Meshkat

Dehghani

2020

Circuit Theory & Apps

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“…The success is due to the fact that the image signals have sparse representations with respect to fixed bases. In recent years, the new sparse representation models based on quaternion wavelet transform [14][15][16], which is shift invariant and consist of one magnitude and three phases. Two phases denote local image shifts and the third phase can describe the image texture information.…”

Section: Introductionmentioning

confidence: 99%

Banknote Classification Based on Convolutional Neural Network in Quaternion Wavelet Domain

Huang

Gai

2020

IEEE Access

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In this paper, we propose a new framework for banknote classification based on quaternion wavelet transform (QWT) and deep convolutional neural network. Firstly, the QWT is applied to describe the phase and magnitude of different banknote images which has inherent directional sensitivity and multi-scale framework. Then we design a deep convolutional neural network which is trained on banknote images along with the magnitude and phase of quaternion wavelet coefficients. We assign the neural weights on the output probabilities of deep convolutional neural network and update these weights by utilizing the back propagation algorithm. Finally, the trained networks with decision of a weighted sum and the magnitude and the phase of quaternion wavelet networks are utilized for banknote image classification. The performance of our algorithm is experimentally verified on a variety of banknote databases. Experimental results show that the proposed algorithm achieves superior performance compared with other state-of-the-art banknote classification algorithms. The proposed algorithm can also satisfy the real-time requirements of the banknote sorting system. INDEX TERMS Quaternion wavelet transform, Convolutional neural network, Banknote classification, mixture model.

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“…To achieve a more compact spatially spectral analysis, some researchers have investigated colour quaternion wavelet transform (CQWT) [14][15][16], which is shift invariant and is made of one magnitude and three phases. Two phases denote local image shifts and the third phase captures the image texture information.…”

Section: Introductionmentioning

confidence: 99%

Vector extension of quaternion wavelet transform and its application to colour image denoising

Gai

Bao

Zhang³

2019

IET signal process.

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In this study, the authors study and give a new framework for colour image representation based on colour quaternion wavelet transform (CQWT). The new colour quaternion filter bank is constructed by using radon transform. Starting from link with structure tensors, the authors propose a new multi-scale tool for vector-valued signals which can provide efficient analysis of local features by using the concepts of amplitude, phase, and orientation. To demonstrate the properties of CQWT, new colour image denoising algorithm is proposed by using CQWT and bivariate shrinkage function. The performance of the proposed algorithm is experimentally verified on a variety of noise levels. Experimental results show that the proposed algorithm achieves superior performance both in visual quality and objective peak-signal-to-noise ratio, mean square error, and structure similarity values, compared with other state-of-the-art denoising algorithms. 2 Quaternion wavelet transform In this section, we will review the basic concepts of quaternion wavelet transform. As it was shown in [14], the quaternion wavelet transform of 2D function f (x, y) can be represented as

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Matrix-Valued and Quaternion Wavelets

Cited by 25 publications

References 25 publications

A new discrete wavelet transform appropriate for hardware implementation

A new discrete wavelet transform appropriate for hardware implementation

Banknote Classification Based on Convolutional Neural Network in Quaternion Wavelet Domain

Vector extension of quaternion wavelet transform and its application to colour image denoising

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