• 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 the Semiconductor & Display Technology
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• v.5 no.2 s.15
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• pp.19-25
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• 2006

This paper focuses on lossy medical image compression methods for medical images that operate on three-dimensional(3-D) irreversible integer wavelet transform. We offer an application of unbalanced tree structure algorithm to medical images, using a 3-D unbalanced wavelet decomposition and a 3-D unbalanced spatial dependence tree. The wavelet decomposition is accomplished with integer wavelet filters implemented with the lifting method. We have tested our encoder on volumetric medical images using different integer filters and coding unit sizes. The coding unit sizes of 16 slices save considerable dynamic memory(RAM) and coding delay from full sequence coding units used in previous works. If we allow the formation of trees of different lengths, then we can accomodate more transaxial scales than three. The encoder and decoder can then keep track of the length of the tree in which each pixel resides through the sequence of decompositions. Results show that, even with these small coding units, our algorithm with certain filters performs as well and better in lossy coding than previous coding systems using 3-D integer unbalanced wavelet transforms on volumetric medical images.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.7 no.4
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• pp.567-574
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• 2006

This paper focuses on lossy medical image compression methods for medical images that operate on three-dimensional(3-D) irreversible integer wavelet transform. We offer an application of unbalanced tree structure algorithm to medical images, using a 3-D unbalanced wavelet decomposition and a 3-D unbalanced spatial dependence tree. The wavelet decomposition is accomplished with integer wavelet filters implemented with the lifting method. We have tested our encoder on volumetric medical images using different integer filters and 16 coding unit size. The coding unit sizes of 16 slices save considerable dynamic memory(RAM) and coding delay from full sequence coding units used in previous works. If we allow the formation of trees of different lengths, then we can accomodate more transaxial scales than three. Then the encoder and decoder can then keep track of the length of the tree in which each pixel resides through the sequence of decompositions. Results show that, even with these small coding units, our algorithm with I(5,3)filter performs as well and better in lossy coding than previous coding systems using 3-D integer unbalanced wavelet transforms on volumetric medical images.