• Journal of Korea Multimedia Society
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• v.8 no.6
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• pp.776-782
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• 2005

This paper presents a SPIHT image compression method using biorthogonal multi wavelets on [-1,1]. A family of biorthogonal scaling vectors is constructed using fractal interpolation function, and the associated biorthogonal multi wavelets are constructed. This paper uses biorthogonal multi wavelets to be supported in [-1,1] associated with biorthogonal scaling vectors to be supported in [-1,1]. The scaling vectors and wavelets remain biorthogonal when restricted to integer intervals, making them well suited for bounded domains. The experiment results of simulation of the proposed image compression using biorthogonal multiwavelets on [-1,1] based on SPIHT were found to be excellent PSNR for LENA and PEPPERS images except for BABOON image than already existing single wavelets and DGHM multi wavelets.

• Proceedings of the KSRS Conference
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• 2003.11a
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• pp.724-726
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• 2003

Currently available image fusion methods are not efficient for fusing the Landsat 7 images. Significant color distortion is one of the major problems. In this paper, using the well-known wavelet based method for data fusion between high-resolution panchromatic and low-resolution multispectral satellite images, we performed Landsat 7 image fusion. Based on the experimental results obtained from this study, we analyzed some reasons for color distortion. A new approach using the biorthogonal wavelets based method for data fusion is presented. This new method has reached an optimum fusion result - with the same spectral resolution as the multispectral image and the same spatial resolution as the panchromatic image with minimum artifacts.

• Journal of applied mathematics & informatics
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• v.9 no.1
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• pp.423-431
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• 2002

In this paper, we find $n^{th}$ order wavelet derivatives of a sufficiently smooth function using biorthogonal wavelet bases and derive the order of convergence of the $n^{th}$ order wavelet derivatives.

• Journal of the Korean Mathematical Society
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• v.36 no.6
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• pp.1075-1090
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• 1999

This paper deals with Littlewood-Paley type estimates of the Besov spaces {{{{ { B}`_{p,q } ^{$\alpha$ } }}}} on the d-dimensional unit cube for 0< p,q<$\infty$ by two certain classes. These classes are including biorthogonal wavelet systems or dual multiscale systems but not necessarily obtained as the dilates or translates of certain fixed functions. The main assumptions are local supports of both classes, sufficient smoothness for one class, and sufficiently many vanishing moments for the other class. With these estimates, we characterize the Besov spaces by coefficient norms of decompositions with respect to biorthogonal wavelet systems on the cube.

• Journal of the Korean Mathematical Society
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• v.51 no.5
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• pp.941-953
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• 2014

In this paper, a 2-circular matrix theory is developed, and a concept of spectral radius for biorthogonal wavelet is introduced. We propose a novel design method by minimizing the spectral radius and obtain a wavelet which has better performance than the famous 9-7 wavelet in terms of image compression coding.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.463-473
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• 2009

A family of quasi-interpolatory wavelet system was introduced in [10], extending and unifing the biorthogonal Coiffman wavelet system. The corresponding refinable functions and wavelets have vanishing moment of a certain order (say, L), which is a key property for data representation and approximation. One of main advantages of this wavelet systems is that we can get optimal smoothness in the sense of smoothing factors in the scaling filters. In this paper, we first discuss the biorthogonality condition of the quisi-interpolatory wavelet system. Then, we study the properties of the scaling and wavelet filters, related to the polynomial reproduction and the vanishing moment respectively, which in fact determines the approximation orders of biorthogonal projections. In addition, we discuss the approximation orders of the wavelet projections.

• Journal of Korea Society of Industrial Information Systems
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• v.22 no.1
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• pp.41-51
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• 2017

This Paper Describes a Method for the Evaluation of Sleep Apnea, Namely, the Peak Signal-to-noise ratio (PSNR) of Wavelet Transformed Electroencephalography (EEG) Data. The Purpose of this Study was to Investigate EEG Properties with Regard to Differences between Sleep Spindles and K-complexes and to Characterize Obstructive Sleep Apnea According to Sleep Stage. We Examined Non-REM and REM Sleep in 20 Patients with OSA and Established a New Approach for Detecting Sleep Apnea Base on EEG Frequency Changes According to Sleep Stage During Sleep Apnea Events. For Frequency Bands Corresponding to A3 Decomposition with a Sampling Applied to the KC and the Sleep Spindle Signal. In this Paper, the KC and Sleep Spindle are Ccalculated using MSE and PSNR for 4 Types of Mother Wavelets. Wavelet Transform Coefficients Were Obtained Around Sleep Spindles in Order to Identify the Frequency Information that Changed During Obstructive Sleep Apnea. We also Investigated Whether Quantification Analysis of EEG During Sleep Apnea is Valuable for Analyzing Sleep Spindles and The K-complexes in Patients. First, Decomposition of the EEG Signal from Feature Data was Carried out using 4 Different Types of Wavelets, Namely, Daubechies 3, Symlet 4, Biorthogonal 2.8, and Coiflet 3. We Compared the PSNR Accuracy for Each Wavelet Function and Found that Mother Wavelets Daubechies 3 and Biorthogonal 2.8 Surpassed the other Wavelet Functions in Performance. We have Attempted to Improve the Computing Efficiency as it Selects the most Suitable Wavelet Function that can be used for Sleep Spindle, K-complex Signal Processing Efficiently and Accurate Decision with Lesser Computational Time.

• Proceedings of the IEEK Conference
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• 2003.07e
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• pp.1731-1734
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• 2003

In this paper, we describe an approach for image denoising using the lifting construction, with the spatial adaptive wavelet transform. The adaptive lifting scheme is implemented in spatial domain to be adjusted thresholds to reduce noise. In this approach we represent adaptive characteristics of biorthogonal wavelets for choosing predictors effectively. Predict filter is changed from sample to sample according to local signal features with their vanishing moments. We in this approach have implemented and applied to image denoising by finding a relevant minimax threshold. Experimental results show that the adaptive method of denoising process is compared with existing ones, such as non-adaptive wavelet, CRF(13, 7) and SWE(13, 7) wavelets used by JPEG2000.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.11 no.3
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• pp.21-28
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• 2007

The symmetric dual filters are essential for the construction of biorthogonal multiresolution an analyses and wavelets. We propose an algorithm to seek for dual symmetric trigonometric filters $\tilde{m}_0$ for for the given symmetric trigonometric filter $m_0$ and illustrate our algorithm by examples.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.49 no.9
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• pp.425-432
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• 2000

Wavelet transform is a new method fro electric power quality analysis. Several types of mother wavelets are compared using voltage sag data. Investigations on the use of some mother wavelets, namely Daubechies, Symlets, Coiflets, Biorthogonal, are carried out. On the basis of extensive investigations, optimal mother wavelets for the detection of voltage sag are chosen. The recommended mother wavelet is 'Daubechies 4(db4)' wavelet. 'db4', the most commonly applied mother wavelet in the power quality analysis, can be used most properly in disturbance phenomena which occurs rapidly for a short time. This paper presents a discrete wavelet transform approach for determining the beginning time and end time of voltage sags. The technique is based on utilising the maximum value of d1(at scale 1) coefficients in multiresolution analysis(MRA) based on the discrete wavelet transform. The procedure is fully described, and the results are compared with other methods for determining voltage sag duration, such as the RMS voltage and STFT(Short-Time Fourier Transform) methods. As a result, the voltage sag detection using wavelet transform appears to be a reliable method for detecting and measuring voltage sags in power quality disturbance analysis.