• The Journal of Korean Institute of Communications and Information Sciences
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• v.28 no.5C
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• pp.461-467
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• 2003

We propose an efficient method for separable symmetric linear filtering in the DCT domain. First, separable 2-D linear filtering is decomposed into the cascade of 1-D filtering in the DCT domain. We investigate special characteristics of DCT domain filtering matrices when the filter coefficients are symmetric. Then we present the DCT domain 2-D filtering method using these characteristics. The proposed method requires smaller number of multiplications including typical sparseness of DCT coefficients compared to previous DCT domain linear filtering methods. Also, the proposed method is composed of simple and regular operations, which would be appropriate for efficient VLSI implementation.

• Journal of Korea Society of Digital Industry and Information Management
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• v.7 no.4
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• pp.119-131
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• 2011

In this paper, we explore the application of 2-D dual-tree discrete wavelet transform (DDWT), which is a directional and redundant transform, for image coding. DDWT main property is a more computationally efficient approach to shift invariance. Also, the DDWT gives much better directional selectivity when filtering multidimensional signals. The dual-tree DWT of a signal is implemented using two critically-sampled DWTs in parallel on the same data. The transform is 2-times expansive because for an N-point signal it gives 2N DWT coefficients. If the filters are designed is a specific way, then the sub-band signals of the upper DWT can be interpreted as the real part of a complex wavelet transform, and sub-band signals of the lower DWT can be interpreted as the imaginary part. The quincunx lattice is a sampling method in image processing. It treats the different directions more homogeneously than the separable two dimensional schemes. Quincunx lattice yields a non separable 2D-wavelet transform, which is also symmetric in both horizontal and vertical direction. And non-separable wavelet transformation can generate sub-images of multiple degrees rotated versions. Therefore, non-separable image processing using DDWT services good performance.