Let Π = B1/B2/… /Bk be any set partition of[n]= {1,2,...,n} satisfying that entries are increasing in each block and blocks are arranged in increasing order of their first entries.Then Callan defined the flattened ...Let Π = B1/B2/… /Bk be any set partition of[n]= {1,2,...,n} satisfying that entries are increasing in each block and blocks are arranged in increasing order of their first entries.Then Callan defined the flattened Π to be the permutation of[n]obtained by erasing the divers between its blocks,and Callan also enumerated the number of set partitions of[n]whose flattening avoids a single3-letter pattern.Mansour posed the question of counting set partitions of[n]whose flattening avoids a pattern of length 4.In this paper,we present the number of set partitions of[n]whose flattening avoids one of the patterns：1234,1243,1324,1342,1423,1432,3142 and 4132.展开更多
As an elegant generalization of wavelet transform, wavelet packet （WP） provides an effective representation tool for adaptive waveform analysis. Recent work shows that image-coding methods based on WP decomposition ...As an elegant generalization of wavelet transform, wavelet packet （WP） provides an effective representation tool for adaptive waveform analysis. Recent work shows that image-coding methods based on WP decomposition can achieve significant gain over those based on a usual wavelet transform. However, most of the work adopts a tree-structured quantization scheme, which is a successful technique for wavelet image coding, but not appropriate for WP subbands. This paper presents an image-coding algorithm based on a rate-distortion optimized wavelet packet decomposition and on an intraband block-partitioning scheme. By encoding each WP subband separately with the block-partitioning algorithm and the JPEG2000 context modeling, the proposed algorithm naturally avoids the difficulty in defining parent-offspring relationships for the WP coefficients, which has to be faced when adopting the tree-structured quanUzation scheme. The experimental results show that the proposed algorithm significantly outperforms SPIHT and JPEG2000 schemes and also surpasses state-of-the-art WP image coding algorithms, in terms of both PSNR and visual quality.展开更多
文摘Let Π = B1/B2/… /Bk be any set partition of[n]= {1,2,...,n} satisfying that entries are increasing in each block and blocks are arranged in increasing order of their first entries.Then Callan defined the flattened Π to be the permutation of[n]obtained by erasing the divers between its blocks,and Callan also enumerated the number of set partitions of[n]whose flattening avoids a single3-letter pattern.Mansour posed the question of counting set partitions of[n]whose flattening avoids a pattern of length 4.In this paper,we present the number of set partitions of[n]whose flattening avoids one of the patterns：1234,1243,1324,1342,1423,1432,3142 and 4132.
基金the Major State Basic Research Development Program(973 Program)(Grant No.2004CB318005)
文摘As an elegant generalization of wavelet transform, wavelet packet （WP） provides an effective representation tool for adaptive waveform analysis. Recent work shows that image-coding methods based on WP decomposition can achieve significant gain over those based on a usual wavelet transform. However, most of the work adopts a tree-structured quantization scheme, which is a successful technique for wavelet image coding, but not appropriate for WP subbands. This paper presents an image-coding algorithm based on a rate-distortion optimized wavelet packet decomposition and on an intraband block-partitioning scheme. By encoding each WP subband separately with the block-partitioning algorithm and the JPEG2000 context modeling, the proposed algorithm naturally avoids the difficulty in defining parent-offspring relationships for the WP coefficients, which has to be faced when adopting the tree-structured quanUzation scheme. The experimental results show that the proposed algorithm significantly outperforms SPIHT and JPEG2000 schemes and also surpasses state-of-the-art WP image coding algorithms, in terms of both PSNR and visual quality.
