• Kyungpook Mathematical Journal
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• v.61 no.2
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• pp.371-381
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• 2021

In this paper, we attempt to obtain sufficient conditions for the existence of tight wavelet frame sets in locally compact abelian groups. The condition is generated by modulating a collection of characteristic functions that correspond to a generalized shift-invariant system via the Fourier transform. We present two approaches (for stationary and non-stationary wavelets) to construct the scaling function for L²(G) and, using the scaling function, we construct an orthonormal wavelet basis for L²(G). We propose an open problem related to the extension principle for Riesz wavelets in locally compact abelian groups.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2004.05b
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• pp.47-53
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• 2004

The paper shows that the combination of the hardware, NI PCI 6110E board and the software, Fourier and continuous wavelet transform(CWT) can be used to implement for extracting the important features of the real-time signal. The results confirmed that CWT produces the fast computation enough for the application of the real-time signal processing except the negligible time delay. In denoising case, because of the lack of translation invariance of wavelet basis, traditional wavelet thresholding leads to pseudo-Gibbs phenomena in the vicinity of discontinuities of signal. In this paper, in order to reduce the pseudo-Gibbs phenomena, wavelet coefficients are threshold and reconstruction algorithm is implement through shift-invariant gibbs free denoising algorithm based on wavelet transform footprint. The proposed algorithm can potentially be extended to more general signals like piecewise smooth signals and represents an effective solution to problems like signal denoising.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.12 no.2
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• pp.221-232
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• 2012

The double-density discrete wavelet transform(DWT) is an improvement upon the critically sampled DWT with important additional properties. It employs one scaling function and two distinct wavelets, which are designed to be offset from one another by one half. And it is overcomplete by a factor of two. Also, this transformation is nearly shift-invariant. But there is room for improvement because not all of the wavelets are directional. That is, although the double-density DWT utilizes more wavelets, some lack a dominant spatial orientation, which prevents them from being able to isolate those directions. Proposed method is a DWT that combines the double-density DWT and quincunx sampling, each of which has its own characteristics and advantages. Especially, the quincunx sampling treats the different directions more homogeneously. As a result, since proposed method can generate sub-images of multiple degrees rotated versions, this method provides an improved performance in image processing fields.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.9 no.4
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• pp.59-68
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• 2009

This paper addresses a hybrid multi-focus image fusion scheme using the recent curvelet transform constructions. Hybridization is obtained by combining the MS fusion rule with a novel "copy" method. The proposed scheme use MS rule to fuse the m most significant terms in spectrum of an image at each decomposition level. The scheme is dubbed in this work as m-term fusion in adherence to its use of the MSC (most significant coefficients) in the transform set at any given scale, orientation, and translation. We applied the edge-sensitive objective quality measure proposed by Xydeas and Petrovic to evaluate the method. Experimental results show that the proposed scheme is a potential alternative to the redundant, shift-invariant Dual-Tree Complex Wavelet transforms. In particular, it was confirmed that a 50% m-term fusion produces outputs with no visible quality degradation.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.7 no.7
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• pp.1671-1689
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• 2013

The key issue of block-based multi-focus image fusion is to determine the size of the sub-block because different sizes of the sub-block will lead to different fusion effects. To solve this problem, this paper presents a novel genetic algorithm (GA) based multi-focus image fusion method, in which the block size can be automatically found. In our method, the Sum-modified-Laplacian (SML) is selected as an evaluation criterion to measure the clarity of the image sub-block, and the edge information retention is employed to calculate the fitness of each individual. Then, through the selection, crossover and mutation procedures of the GA, we can obtain the optimal solution for the sub-block, which is finally used to fuse the images. Experimental results show that the proposed method outperforms the traditional methods, including the average, gradient pyramid, discrete wavelet transform (DWT), shift invariant DWT (SIDWT) and two existing GA-based methods in terms of both the visual subjective evaluation and the objective evaluation.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.7 no.3
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• pp.539-557
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• 2013

A novel multifocus image fusion algorithm based on NSCT is proposed in this paper. In order to not only attain the image focusing properties and more visual information in the fused image, but also sensitive to the human visual perception, a local multidirection variance (LEOV) fusion rule is proposed for lowpass subband coefficient. In order to introduce more visual saliency, a modified local contrast is defined. In addition, according to the feature of distribution of highpass subband coefficients, a direction vector is proposed to constrain the modified local contrast and construct the new fusion rule for highpass subband coefficients selection The NSCT is a flexible multiscale, multidirection, and shift-invariant tool for image decomposition, which can be implemented via the atrous algorithm. The proposed fusion algorithm based on NSCT not only can prevent artifacts and erroneous from introducing into the fused image, but also can eliminate 'block effect' and 'frequency aliasing' phenomenon. Experimental results show that the proposed method achieved better fusion results than wavelet-based and CT-based fusion method in contrast and clarity.