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

• Bulletin of the Korean Mathematical Society
• /
• v.56 no.3
• /
• pp.585-596
• /
• 2019

It is shown that a pair of Hilbert space operators V and W such that $V^*W=I$ (called a biisometric pair) shares some common properties with unilateral shifts when orthonormal bases are replaced with biorthogonal sequences, and it is also shown how such a pair of biisometric operators yields a pair of biorthogonal sequences which are shifted by them. These are applied to a class of Laguerre operators on $L^2[0,{\infty})$.

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

• Bulletin of the Korean Mathematical Society
• /
• v.60 no.3
• /
• pp.845-848
• /
• 2023

Erratum/Addendum to the paper "Biisometric operators and biorthogonal sequences" [Bull. Korean Math. Soc. 56 (2019), No. 3, pp. 585-596].

• Journal of Korea Society of Industrial Information Systems
• /
• v.7 no.5
• /
• pp.59-66
• /
• 2002

Many important scientific and engineering problems require the computation of a small number of eigenvalues for large nonsymmetric matrices. The biorthogonal Lanczos method is one of the methods to solve that problem, but it faces serious breakdown problems. In this paper, we introduce a modified biorthogonal Lanczos method to find a few eigenvalues of a large sparse nonsymmetric matrix. The proposed method generates reduction matrices that are similar to those generated by the standard biorthogonal Lanczos method. We prove that the breakdown conditions of our method are less stringent than the standard method. We then implement the modified biorthogonal Lanczos method on the CRAY machine and discuss the decreased breakdown conditions.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.30 no.3C
• /
• pp.69-76
• /
• 2005

In this paper, we propose a biorthogonal modulation employing a constant-amplitude transmission of multi-code signals by introducing a simple constant-amplitude coding scheme with redundant bits. The proposed constant-amplitude biorthogonal multi-code (CABM) modulation can provide high spectral efficiency compared with a conventional direct sequence/spread spectrum (DS/SS) modulation. Nevertheless the proposed CABM modulation can keep up a constant-amplitude signal. Additionally, we propose various types of demodulation structures for the CABM modulation. Simulation results show that bit error rate (BER) performance and hardware complexity of the proposed CABM modulation are highly improved in comparison with those of a constant-amplitude orthogonal multi-code (CAOM) modulation.

• Journal of the Korea Academia-Industrial cooperation Society
• /
• v.8 no.3
• /
• pp.522-527
• /
• 2007

In this paper, we propose an error control coding scheme for constant-amplitude multicode-biorthogonal modulation. The product code is appropriate to the constant-amplitude multicode-biorthogonal modulation for the bit error rate performance improvement. In the constant-amplitude multicode-biorthogonal modulation, the vertical redundant bits are used for the constant amplitude coding. The proposed product code can be constructed by using the additional horizontal redundant bits. The hardware complexity of the encoder/decoder pair is very low. The simulation results show that the bit error rate performance of the proposed coding scheme is improve

• Bulletin of the Korean Mathematical Society
• /
• v.48 no.6
• /
• pp.1157-1167
• /
• 2011

We consider totally interpolating biorthogonal multiwavelet systems with finite impulse response two-band multifilter banks, a study balancing order conditions of such systems. Based on FIR and interpolating properties, we show that approximation order condition is completely equivalent to balancing order condition. Consequently, a prefiltering can be avoided if a totally interpolating biorthogonal multiwavelet system satisfies suitable approximation order conditions. An example with approximation order 4 is provided to illustrate the result.

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

• Korean Journal of Mathematics
• /
• v.21 no.3
• /
• pp.247-263
• /
• 2013

By analyzing one-parameter families of totally interpolating multiwavelet systems of minimal total length with low approximation orders, whose explicit formulas were obtained with the aid of well-known relations of filters, we demonstrate the infinitude of such systems.