T. D. Tran and T. Q. Nguyen, "A progressive transmission image coder using linear phase uniform filterbanks as block transforms," IEEE Transactions on Signal Processing 8, pp. 1493--1507, November 1999.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....image, with some parts having mostly edges and high frequency information, and other parts blocks from the original image. For residual blocks that contain significant high frequency information a uniform band partitioning (such as with DCT) works better than octave band signal decomposition (see [15]) while octave band decomposition is desirable in blocks of the original image. Note that the Haar transform only uses two neighboring pixels to compute the low and high frequency coefficients, then moves on to the next pair. If k, the block size is even, starting at the left edge of the block, ....

T. D. Tran and T. Q. Nguyen, "A progressive transmission image coder using linear phase uniform filterbanks as block transforms," IEEE Trans. on Image Proc., vol. 8, no. 11, pp. 1493--1507, Nov. 1999.

....image, with some parts having mostly edges and high frequency information, and other parts blocks from the original image. For residual blocks that contain significant high frequency information, a uniform band partitioning (such as with DCT) works better than octave band signal decomposition (see [83]) while octave band decomposition is desirable in blocks of the original image. Note that the Haar transform only uses two neighboring pixels to compute the low and high frequency coefficients, then moves on to the next pair. If the block size k is even, then starting at the left edge of the ....

T. D. Tran and T. Q. Nguyen. A progressive transmission image coder using linear phase uniform filterbanks as block transforms. IEEE Transactions on Image Processing, 8(11):1493--1507, November 1999.

....to thank the people who graciously provided code for image compression. This includes: G. Davis et al. for the Baseline Wavelet Transform Coder Construction Kit [11] H. S. Malvar for code that computes the DCT, LOT, and LBT transforms [36] and T. Tran for code that computes the GLBT transform [54]. Finally, I would also like to thank the people that encouraged and supported me during the time I worked on this thesis. This includes both of my parents Mark Hong and Grace xi Hong, as well as some of my friends from my church. xii Chapter 1 INTRODUCTION In the past decade, the ....

....that were optimized for both image compression efficiency and low computational requirements. We use EZLOT (EZ LBT) to refer to Xiong et al. s embedded zerotree technique when applied to the Malvar s fast version of the LOT (LBT) transforms. Tran s Hierarchical Lapped Transforms Tran et al. [54] focused on designing the best lapped transforms for image compression, and did not consider the speed of computation to be a crucial factor. They designed several lapped transforms, including 8 40 generalized LOT (GLOT) 8 16 generalized LBT (GLBT) and 16 32 GLBT. These transforms were ....

[Article contains additional citation context not shown here]

T. D. Tran and T. Q. Nguyen. A progressive transmission image coder using linear phase uniform filterbanks as block transforms. IEEE Transactions on Image Processing, 8(11):1493--1507, November 1999.

....One main goal of this work is to discover the appropriate class definitions for each type of transform that will result in good performance. Our work was partially motivated by previous work that applied zerotree coding (introduced in [6] to these alternative transforms (see [7] 8] 9] 10] [11]) with some success. The zerotree technique was motivated by the multi resolution struc Short preliminary versions of some sections this paper appeared in the 2001 Data Compression Conference and the 35th Asilomar Conference on Signals, Systems, and Computers. Research supported by NSF grant ....

....in the wavelet transform, the subbands sizes decrease by a factor of 2 with every additional level of the DWT performed. In other words, block transforms offer a uniform band frequency partitioning of the input, in contrast to the octaveband frequency partitioning of the wavelet transform (see [11]) For the DCT transform, the DC coefficient of an output block represents an average of the 8 8 input block. Since adjacent image blocks often are similar, adjacent coefficients in the DC subband will be correlated. For the lapped transforms, each traditional M M output block is computed from ....

[Article contains additional citation context not shown here]

T. D. Tran and T. Q. Nguyen, "A progressive transmission image coder using linear phase uniform filterbanks as block transforms," IEEE Transactions on Image Processing, vol. 8, no. 11, pp. 1493--1507, November 1999.

.... techniques are typically applied to wavelet transformed coefficients, Xiong et al. 10] have shown that zerotree coding can also be effective when used for encoding coefficients generated from an 8 8 discrete cosine transform (DCT) Zerotree coding has also been applied to lapped transforms (see [6, 9]) which are block based transforms originally designed to reduce blocking artifacts [5] In this paper, we extend our group testing technique from our group testing for wavelets algorithm (GTW) 2] to coefficients generated from block based transforms. The zerotree technique [8] was motivated by ....

.... GTBT on several different transforms: the 8 8 DCT; the 8 16 type I fast lapped orthogonal transform (LOT) with angles ( 0 ; 1 ; 2 ) 0:145 ; 0:17 ; 0:16 ) 5] the 8 16 lapped biorthogonal transform (LBT) from [4] and the 8 16 generalized lapped biorthogonal transform (GLBT) from [9]. For convenience, we refer to GTBT using the DCT, LOT, LBT, or GLBT transforms as GT DCT, GT LOT, GT LBT, and GT GLBT, respectively. First, we compare the PSNR results of a nonhierarchical version of GT DCT with those of Xiong s Embedded Zerotree DCT (EZ DCT) scheme presented in [10] Note that ....

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T. D. Tran and T. Q. Nguyen. A progressive transmission image coder using linear phase uniform filterbanks as block transforms. IEEE Transactions on Image Processing, 8(11):1493--1507, November 1999.

....for other transformations as well. For instance, they were sucessfuly employed together with 8 Theta 8 DCTs, and even better results are obtained with 16 Theta 16 DCTs, 32, 11] Among several exciting developments we have schemes for wavelet packets [33] and general lapped block transforms [28]. The lifting scheme [27] allows the development of better transforms for lossless compression [1] and wavelets on manifolds [20] Tree based embedded coding methods are readily adapted anywhere the lifting scheme can be used. For example, an interesting application is efficient (and embedded) ....

T. Tran and T. Nguyen, "A progressive transmission image coder using linear phase paraunitary filter banks," Asilomar Conf. Signals, Syst., Computers, Pacific Grove, CA, Nov. 1997.

....the maximum set number of sub blocks or pixels. Those binary masks are also coded using codes conditioned upon their corresponding maximum set number. 6 Magnitude Set Number Magnitude Interval Sign Bit Index Length 0 [0] No 0 1 [1] Yes 0 2 [2] Yes 0 3 [3] Yes 0 4 [4, 5] Yes 1 5 [6, 7] Yes 1 6 [8, 11] Yes 2 7 [12, 15] Yes 2 8 [16, 23] Yes 3 9 [24, 31] Yes 3 10 [32, 47] Yes 4 11 [48, 63] Yes 4 12 [64, 127] Yes 6 13 [128, 255] Yes 7 14 [256, 511] Yes 8 15 [512, 1023] Yes 9 16 [1024, 2047] Yes 10 17 [2048, 4095] Yes 11 18 [4096, 8191] Yes 12 19 [8192, 16383] Yes 13 ....

T. D. Tran and T. Q. Nguyen, "A progressive transmission image coder using linear phase paraunitary filter banks," Proc. 31st IEEE Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA, Nov. 1997.

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T. D. Tran and T. Q. Nguyen, "A progressive transmission image coder using linear phase uniform filterbanks as block transforms," IEEE Trans. Image Processing, vol. 8, pp. 1493--1507, Nov. 1999.

....Baltimore, MD 21218 USA (e mail: cjtu jhu.edu; jieliang jhu.edu; trac jhu.edu) Digital Object Identifier 10.1109 LSP.2002.807873 yet consistently outperform baseline JPEG by a large margin. If pre and postfiltering are added to the block DCT based framework as illustrated in Fig. 1, EZ [5] and CEB [4] achieve competitive rate distortion (R D) performances compared with the wavelet based JPEG2000 coder [6] Furthermore, annoying block artifacts at low bitrates are suppressed. The cost for implementing pre and postfiltering is low, since various fast algorithms exist [7] The ....

....used: 512 512 Lena, Goldhill, and Barbara; 2048 2560 Bike, Cafe, and Woman; and the first luminance frames of quarter common intermediate format (176 144) sequences News and Glasgow. Baseline JPEG (with optimized Huffman coding) and JPEG with arithmetic coding (AC JPEG) 1] the improved EZ coder [5], and JPEG2000 in the single layer mode (JPEG2000 SL) 6] serve as benchmarks. As many levels of dyadic wavelet decompositions as possible are employed in JPEG2000 SL and for EZ s dc subbands. The popular biorthogonal 9 7 filters are used. Table II tabulates the coding results. With the same level ....

T. D.Tran and T. Q. Nguyen, "A progressive transmission image coder using linear phase uniform filterbanks as block transforms," IEEE Trans. Image Processing, vol. 8, pp. 1493--1507, Nov. 1999.

....On the other hand, research on integer coefficient channel systems is still at an early stage. It has been shown recently that multiband transforms with floating point coefficients, when appropriately designed and utilized, can outperform state of the art wavelets by significant margins [6] [7], 9] 11] The overlapping basis functions of these transforms can eliminate annoying blocking artifacts just as efficiently as any wavelet. However, the wavelet transform requires many more operations per output coefficient, and it may need a large memory buffer in its implementation. LTs are ....

....uniform band block transform cases, we used a modified zerotree structure, where the transform coefficients are grouped in wavelet like quad trees, and the dc band can have several levels of wavelet decomposition, depending on the image size. For more details on the embedded coding algorithms, see [7], 11] and [14] Compared with other popular transforms, our lifted ILT performs well on all test images (Lena, Barbara, and Goldhill) as shown by the objective coding results in Table II and the reconstructed images in Fig. 5(a) d) Despite having only one long filter of 24 taps, the lifted ....

T. D. Tran and T. Q. Nguyen, "A progressive transmission image coder using linear phase paraunitary filter banks," presented at the Asilomar Conf. SSC, Pacific Grove, CA, Nov. 1997.

....distribution of the binDCT coefficients is different from that of the original DCT coefficients when the scaling factors are bypassed. In the SPIHT method, we rearrange the binDCT coefficients according to the pattern of the wavelet transform coefficients before applying zerotree processing [50]. The binDCT based lossless transforms are compared with two advanced context model based prediction methods: the HP LOCO I [51] and CALIC [52] The results are summarized in Table VIII, showing that the overall compression ratio of the binDCT based method is not as good as these methods. ....

T. D. Tran and T. Q. Nguyen, "A progressive transmission image coder using linear phase filter banks as block transforms," IEEE Trans. Image Processing, vol. 8, pp. 1493--1507, Nov. 1999.

....in an image coding experiment where the floating point implementation of the DCT provides the benchmark. To encode the transform coefficients, we use a progressive transmission zerotree coder, where each block of transform coefficients is treated analogously to a wavelet tree, as described in [4]. The DC subband can be further decomposed using several wavelet iterations. Integer wavelets can be employed to keep the transform stage entirely integer based. The objective coding results are presented in Table III. The binDCT is only around 0.1 0.5 dB below the DCT in the peak TABLE II ....

T. D. Tran and T. Q. Nguyen, "A progressive transmission image coder using linear phase filter banks as block transforms," IEEE Trans. Image Processing, vol. 8, pp. 1493--1507, Nov. 1999.

....it offers a fair comparison between the transforms since the SPIHT coder uses up to six levels of wavelet decomposition on 512 512 images, whereas the 8 channel block transforms only provide an equivalence of 3level decomposition. For more details on the embedded coding algorithms, see [14] [17], and [18] The three images chosen for the coding experiments are Barbara, Boat, and Lena. All of them are standard, wellknown 512 512 8 bit gray scale test images. The objective distortion measure is the popular peak signal to noise ratio (PSNR) PSNR MSE dB where MSE denotes the mean ....

T. D. Tran and T. Q. Nguyen, "A progressive transmission image coder using linear phase filter banks as block transforms," IEEE Trans. Image Processing, to be published.

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T. D. Tran and T. Q. Nguyen, \A progressive transmission image coder using linear phase lter banks as block transforms," IEEE Trans. on Image Processing, vol. 8, pp. 1493-1507, Nov. 1999.

....are compiled in Table II; the DCT [20] the LOT [19] and the 8 40 GenLOT [33] are included for comparison purposes. C. Application in Image Coding To test the performance of the new family of LT s, new GLBT s are incorporated into the block transform progressive coding framework described in [32] and [33] where each block of lapped transform coefficients is treated analogously to a tree of wavelet coefficients. The resulting GLBT based embedded coders provide unrivaled objective and subjective performance, as indicated in Table III and Fig. 15. For a smooth image like Lena, which the ....

T. D. Tran and T. Q. Nguyen, "A progressive transmission image coder using linear phase filter banks as block transforms," , submitted for publication.

.... that the FBI designed to compress ngerprints actually imitates a 4 band decomposition using the popular 9 7 tap biorthogonal wavelet [25] On other image types, M band FBs, wavelets and wavelet packets almost always yield higher coding performances [16] 17] 19] 23] 24] 26] 27] 28] [29]. Furthermore, M channel perfect reconstruction lter banks in reverse (the synthesis bank comes rst) are also useful in communications as crosstalk free transmultiplexers [2] commonly seen in ADSL technology [30] When M 2, there is no simple spectral factorization method which has worked ....

....The test images are Goldhill and Barbara, both standard 512 512 8 bit grayscale images. The results obtained with the 9 7 tap wavelet (6 levels of decomposition here) are exactly those from the original SPIHT algorithm [40] In the four 8 channel cases, we use the modi ed zerotree structure in [29], 41] where each block of transform coecients are treated analogously to a full wavelet tree and three more levels of wavelet decomposition are employed to decorrelate the DC subband further. The objective coding results (PSNR in dB) are tabulated in Table V. The LiftLT I outperforms all ....

T. D. Tran and T. Q. Nguyen, \A progressive transmission image coder using linear-phase uniform lter banks as block transforms," IEEE Transaction on Image Processing, vol. 8, pp. 1493-1507, Nov. 1999.

....the one in the JPEG standard, since the statistic distribution of the binDCT coecients is di erent from that of the original DCT coecients. In the SPIHT method, we rearrange the binDCT coecients according to the pattern of the wavelet transform coecients before applying zerotree processing [50]. The binDCT based lossless transforms are compared with two advanced context model based prediction methods: the HP LOCO I [51] and CALIC [52] The results are summarized in Table VIII, showing that the overall compression ratio of the binDCT based method is not as good as these methods. ....

T. D. Tran and T. Q. Nguyen, \A progressive transmission image coder using linear phase lter banks as block transforms," IEEE Trans. on Img. Process., vol. 8, pp. 1493-1507, Nov. 1999.

....cases, we used a modified zerotree structure where the transform coefficients are grouped in wavelet like quadtrees and the DC band can have several levels of wavelet 13 decomposition depending on the image size. For more details on the embedded coding algorithms, the reader is referred to [13, 15, 16]. The two test images chosen (one is a photograph of a church and the other is a photograph of Seattle s space needle) are standard natural images with a balanced mixture of texture, smooth background, and hard, well defined edges which make ringing very susceptible. Figure 9 and Figure 11 show ....

T. D. Tran and T. Q. Nguyen, "A progressive transmission image coder using linear phase paraunitary filter banks," 31st Asilomar Conference on SSC, Pacific Grove, CA, Nov. 1997.

....cases, we used a modified zerotree structure where the transform coefficients are grouped in wavelet like quadtrees and the DC band can have several levels of wavelet 13 decomposition depending on the image size. For more details on the embedded coding algorithms, the reader is referred to [13, 15, 16]. The two test images chosen (one is a photograph of a church and the other is a photograph of Seattle s space needle) are standard natural images with a balanced mixture of texture, smooth background, and hard, well defined edges which make ringing very susceptible. Figure 9 and Figure 11 show ....

T. D. Tran and T. Q. Nguyen, "A progressive transmission image coder using linear phase filter banks as block transforms," submitted to IEEE Trans. Image Processing, May 1997.

....to the wavelet transform; it can be utilized with various LTs as well. In fact, the combination of a LT and several levels of wavelet decomposition of the DC band can provide much finer frequency spectrum partitioning, leading to significant improvement over current embedded wavelet coders [60] [57]. The EZC approach relies on the fundamental idea that more important information 0.11. TRANSFORM BASED IMAGE COMPRESSION SYSTEMS 49 lsb msb sign 5 4 3 2 1 0 s s s s s s s s s s s s s 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 Figure 36: Embedded zerotree coding ....

T. D. Tran and T. Q. Nguyen, "A progressive transmission image coder using linear phase uniform filter banks as block transforms," IEEE Trans. on Image Processing, to appear.

....coefficient ae when ae 1 [2] Since the KLT is signal dependent, and therefore, computationally complex and expensive, the DCT has proven to be a much better alternative in practice. It is signal independent, it has linear phase, real coefficients, and fast algorithms. x[0] x[1] x[2] x[3] x[4] x[5] x[6] x[7] X[0] X[4] X[2] X[6] X[1] X[5] X[3] X[7] p 4 7p 16 C S S C p 4 p 4 p 4 p 4 C S S C p 4 p 4 p 4 3p 8 C S S C 3p 8 3p 8 3p 8 7p 16 7p 16 7p 16 3p 16 C S S C 3p 16 3p 16 3p 16 C C S S Figure 1: The forward fast floating point DCT. Exploiting the symmetry of the basis ....

....ae 1 [2] Since the KLT is signal dependent, and therefore, computationally complex and expensive, the DCT has proven to be a much better alternative in practice. It is signal independent, it has linear phase, real coefficients, and fast algorithms. x[0] x[1] x[2] x[3] x[4] x[5] x[6] x[7] X[0] X[4] X[2] X[6] X[1] X[5] X[3] X[7] p 4 7p 16 C S S C p 4 p 4 p 4 p 4 C S S C p 4 p 4 p 4 3p 8 C S S C 3p 8 3p 8 3p 8 7p 16 7p 16 7p 16 3p 16 C S S C 3p 16 3p 16 3p 16 C C S S Figure 1: The forward fast floating point DCT. Exploiting the symmetry of the basis functions, the DCT transform ....

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T. D. Tran and T. Q. Nguyen, "A progressive transmission image coder using linear phase filter banks as block transforms," IEEE Trans. on Image Processing, Nov. 1999.

....known up to date [2] Eight DCT coefficients X[i] can be computed using 13 multiplications and 29 additions. Note that all resulting coefficients X[i] have been scaled up by a factor of 2. Despite all of the nice attributes mentioned above, there x[0] x[1] x[2] x[3] x[4] x[5] x[6] x[7] X[0] X[4] X[2] X[6] X[1] X[5] X[3] X[7] p 4 7p 16 C S S C p 4 p 4 p 4 p 4 C S S C p 4 p 4 p 4 3p 8 C S S C 3p 8 3p 8 3p 8 7p 16 7p 16 7p 16 3p 16 C S S C 3p 16 3p 16 3p 16 C C S S Figure 1. The forward fast floating point DCT. is still room for ....

....[2] Eight DCT coefficients X[i] can be computed using 13 multiplications and 29 additions. Note that all resulting coefficients X[i] have been scaled up by a factor of 2. Despite all of the nice attributes mentioned above, there x[0] x[1] x[2] x[3] x[4] x[5] x[6] x[7] X[0] X[4] X[2] X[6] X[1] X[5] X[3] X[7] p 4 7p 16 C S S C p 4 p 4 p 4 p 4 C S S C p 4 p 4 p 4 3p 8 C S S C 3p 8 3p 8 3p 8 7p 16 7p 16 7p 16 3p 16 C S S C 3p 16 3p 16 3p 16 C C S S Figure 1. The forward fast floating point DCT. is still room for improvement. The DCT is a ....

[Article contains additional citation context not shown here]

T. D. Tran and T. Q. Nguyen, "A progressive transmission image coder using linear phase filter banks as block transforms," IEEE Trans. on Image Processing, to appear.

....are utilized to encode the coefficients of every transform. The transforms in comparison are: the 8 Theta 8 DCT, the new 8 Theta 16 LiftLT, and the 5 popular 9=7 tap biorthogonal wavelet with a 6 level decomposition. In the two block transform cases, we use the modified zerotree structure in [8] where each block of transform coefficients are treated analogously to a full wavelet tree and three more levels of decomposition are employed to decorrelate the DC subband further. The objective coding results (PSNR in dB) for standard 512 Theta 512 Lena, Goldhill, and Barbara test images are ....

T. D. Tran and T. Q. Nguyen, "A progressive transmission image coder using linear phase filter banks as block transforms," IEEE Trans. on Image Processing, Nov. 1999.

....are much smoother than the analysis. Design example VII in Figure 29 has 5 channels and filters of 15 taps, optimized for coding gain and DC attenuation. Important properties of several high performance design examples are compiled in Table 3; the DCT [67] the LOT [47] and the 8 Theta 40 GenLOT [89] are included for comparison purposes. DCT LOT Transform Property Transform Coding Gain (dB) DC Attenuation ( dB) 8.83 310.62 9.96 8x8 8x16 Stopband Attenuation ( dB) Mirror Freq. Attenuation ( dB) 322.10 9.22 312.56 19.38 317.24 GLBT (II) 8x16 9.62 327.40 13.50 55.54 GLBT (III) 16x32 9.96 303.32 ....

....(PSNR in dB) for standard 512 Theta 512 Lena, Barbara, and Goldhill test images are tabulated in Table 7. The transforms in comparison are ffl 9=7 tap biorthogonal wavelet [3] ffl 8 Theta 8 DCT [67] shown in Figure 9. ffl 8 Theta 16 LOT [45] shown in Figure 11. ffl 8 Theta 40 GenLOT [89] shown in Figure 13. ffl 4 Theta 24 4 Theta 8 VLLOT in Figure 42(a) of Chapter 6. ffl 2 Theta 24 6 Theta 8 VLGLBT in Figure 45 of Chapter 6. ffl 8 Theta 16 GLBT in Figure 24 of Chapter 4. ffl 16 Theta 32 GLBT in Figure 25 of Chapter 4. Except the 9=7 tap biorthogonal wavelet, all of the ....

T. D. Tran and T. Q. Nguyen, "A progressive transmission image coder using linear phase paraunitary filter banks," Proc. 31st Asilomar Conference on SSC, Pacific Grove, Nov. 1997.

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T. D. Tran and T. Q. Nguyen, "A progressive transmission image coder using linear phase filter banks as block transforms," submitted to IEEE Trans. on Image Processing, May 1997.

....X[i] can be computed using 13 multiplications and 29 additions. Note that all resulting coefficients X[i] have been scaled up by a factor of 2. Despite all of the nice attributes mentioned above, there is still room for improvement. The DCT is a floating point x[0] x[1] x[2] x[3] x[4] x[5] x[6] x[7] X[0] X[4] X[2] X[6] X[1] X[5] X[3] X[7] p 4 7p 16 C S S C p 4 p 4 p 4 p 4 C S S C p 4 p 4 p 4 3p 8 C S S C 3p 8 3p 8 3p 8 7p 16 7p 16 7p 16 3p 16 C S S C 3p 16 3p 16 3p 16 C C S S Figure 1. The forward fast floating point DCT. transform. It cannot map integers to integers ....

....using 13 multiplications and 29 additions. Note that all resulting coefficients X[i] have been scaled up by a factor of 2. Despite all of the nice attributes mentioned above, there is still room for improvement. The DCT is a floating point x[0] x[1] x[2] x[3] x[4] x[5] x[6] x[7] X[0] X[4] X[2] X[6] X[1] X[5] X[3] X[7] p 4 7p 16 C S S C p 4 p 4 p 4 p 4 C S S C p 4 p 4 p 4 3p 8 C S S C 3p 8 3p 8 3p 8 7p 16 7p 16 7p 16 3p 16 C S S C 3p 16 3p 16 3p 16 C C S S Figure 1. The forward fast floating point DCT. transform. It cannot map integers to integers losslessly. More importantly, ....

[Article contains additional citation context not shown here]

T. D. Tran and T. Q. Nguyen, "A progressive transmission image coder using linear phase filter banks as block transforms," IEEE Trans. on Image Processing, to appear.

....comparison between the transforms since the SPIHT coder uses up to 6 levels of wavelet decomposition on 512 Theta 512 images whereas the 8 channel block transforms only provide an equivalence of 3 level decomposition. For more details on the embedded coding algorithms, the reader is referred to [14, 17, 18]. The three images chosen for the coding experiments are Barbara, Boat, and Lena. All of them are standard, well known 512 Theta 512 8 bit gray scale test images. The objective distortion measure is the popular peak signal to noise ratio (PSNR) PSNR = 10 log 10 255 MSE dB; where MSE ....

T. D. Tran and T. Q. Nguyen, "A progressive transmission image coder using linear phase filter banks as block transforms," IEEE Trans. Image Processing, to appear.

....and references therein) On the other hand, research on integer coefficient M channel systems is still at an embryonic stage. Moreover, it has been shown recently that multi band transforms, when appropriately designed and utilized, can outperform state of the art wavelets by significant margins [3, 4, 5, 6]. The overlapping basis functions of these transforms can eliminate annoying blocking artifacts just as efficiently as any wavelets. An example of M channel transform with integer coefficients is the Walsh Hadamard transform (WHT) whose coefficients consist of either 1 or 1. However, the WHT is ....

....cases, we used a modified zerotree structure where the transform coefficients are grouped in wavelet like quad trees and the DC band can have several levels of wavelet decomposition depending on the image size. For more details on the embedded coding algorithms, the reader is referred to [4, 6, 9]. Comparing to other popular transforms, our IGLBT performs well on all test images (Lena, Barbara, and Goldhill) as testified by the objective coding results tabulated in Table 1 and the reconstructed images in Figure 4(a) d) Despite having only one long filter of 24 taps, the IGLBT proves to ....

T. D. Tran and T. Q. Nguyen, "A progressive transmission image coder using linear phase paraunitary filter banks," Asilomar Conference on SSC, Pacific Grove, Nov. 1997.

....stage helps increase the coding efficiency of the DC coefficients thanks to a deeper coefficient trees. In all coding results presented later in this paper, we use the 9=7 tap biorthogonal in [12] The complete coder s diagram is depicted in Figure 3. For more details, the reader is refered to [13]. M M M H (z) M 1 H (z) 1 H (z) 0 x[n] Block transform 1 H 0 H 1 H 0 H 2 2 2 2 wl wl wl wl Wavelet transform DC modified embedded bit plane coder compressed bit stream Figure 3. Complete embedded coder diagram. A mere replacement of the DCT in [1] by more complex lapped transforms ....

....energy compaction, smoothly decaying impulse responses for complete blocking artifacts elimination, and unequal length filters for ringing artifacts suppression. A comparison of various transform characteristics is presented in Table 1. More details in transform design procedure can be found in [13]. For the GLBT s lattice structure, design, and optimization, the reader is referred to [8] 4. CODING RESULTS The objective coding results (PSNR in dB) for standard 512 Theta 512 Lena, Barbara, and Goldhill test images are tabulated in Table 2. The transforms in comparison are: the popular 8 ....

T. D. Tran and T. Q. Nguyen, "A progressive transmission image coder using linear phase uniform filter banks as block transforms," submitted to IEEE Trans. on Image Processing, June 1997.

....D. Tran 1 Truong Q. Nguyen 2 1 University of Wisconsin, ECE Department, Madison, WI, 53706 2 Boston University, ECE Department, Boston, MA 02215 trac saigon.ece.wisc.edu, nguyent bu.edu ABSTRACT Several block transform based embedded image coders have been proposed recently in literature [1, 2, 3, 4]. The innovation here is to replace the wavelet transform in the EZW or SPIHT progressive image coding framework [5, 6] by popular block transforms such as the DCT or lapped transforms which can offer finer frequency spectrum partitioning and better energy compaction. However, most of the block ....

....the best corresponding reconstructed image) and many other advantages such as exact bit rate control and idempotency capability. Researchers soon start to realize that the same idea can be applied to block transform coefficients as well if they are grouped in a wavelet like octave band fashion [1, 2, 3, 4]. However, a mere transform replacement is not enough to compete consistently with the best wavelet based progressive coder SPIHT [6] In this paper, we will improve lapped transform based embedded coding further: ffl We present a general definition of octave tree data structure for uniform band ....

[Article contains additional citation context not shown here]

T. D. Tran and T. Q. Nguyen, "A progressive transmission image coder using linear phase paraunitary filter banks," Asilomar Conference on SSC, Pacific Grove, Nov. 1997.

.... can be truncated at any point by the decoder to yield the best corresponding reconstructed image) Although these embedded coders are designed primarily for the dyadic wavelet transform, it has been confirmed recently that the algorithm also works well on coefficients of various block transforms [3, 4]. In fact, if the transform is designed appropriately, block transformbased embedded coders can consistently yield higher PSNR comparing to the state of the art wavelet based version [4] Besides a finer frequency spectrum partitioning and higher energy compaction, block transforms also facilitate ....

.... it has been confirmed recently that the algorithm also works well on coefficients of various block transforms [3, 4] In fact, if the transform is designed appropriately, block transformbased embedded coders can consistently yield higher PSNR comparing to the state of the art wavelet based version [4]. Besides a finer frequency spectrum partitioning and higher energy compaction, block transforms also facilitate hardware implementation with efficient lattice structures which employ a minimal number of delay elements, are robust under the quantization of lattice coefficients, and are capable of ....

[Article contains additional citation context not shown here]

T. D. Tran and T. Q. Nguyen, "A progressive transmission image coder using linear phase paraunitary filter banks," 31st Asilomar Conference on SSC, Pacific Grove, CA, Nov. 1997.

....functions are much smoother than the analysis. Design example VI in Figure 14 has 5 channels and filters of 15 taps, optimized for coding gain and DC attenuation. Various properties of highperformance design examples are compiled in Table 2; the DCT [20] the LOT [19] and the 8 Theta 40 GenLOT [31] are included for comparison purposes. VI.3 Application in Image Coding To test the performance of the new family of LT, new GLBT are incorporated into the blocktransform progressive coding framework described in [30] 31] where each block of lapped trans17 form coefficients is treated ....

....in Table 2; the DCT [20] the LOT [19] and the 8 Theta 40 GenLOT [31] are included for comparison purposes. VI.3 Application in Image Coding To test the performance of the new family of LT, new GLBT are incorporated into the blocktransform progressive coding framework described in [30] [31] where each block of lapped trans17 form coefficients is treated analogously to a tree of wavelet coefficients. The resulting GLBT based embedded coders provide unrivaled objective and subjective performance as indicated in Table 1 and Figure 15. For a smooth image like Lena which the wavelet ....

[Article contains additional citation context not shown here]

T. D. Tran and T. Q. Nguyen, "A progressive transmission image coder using linear phase paraunitary filter banks," 31st Asilomar Conference on SSC, Pacific Grove, CA, Nov. 1997.

....are compiled in Table 2; the DCT [20] the LOT [19] and the 8 Theta 40 GenLOT [31] are included for comparison purposes. VI.3 Application in Image Coding To test the performance of the new family of LT, new GLBT are incorporated into the blocktransform progressive coding framework described in [30], 31] where each block of lapped trans17 form coefficients is treated analogously to a tree of wavelet coefficients. The resulting GLBT based embedded coders provide unrivaled objective and subjective performance as indicated in Table 1 and Figure 15. For a smooth image like Lena which the ....

T. D. Tran and T. Q. Nguyen, "A progressive transmission image coder using linear phase filter banks as block transforms," submitted to IEEE Trans. on Image Processing, May 1997.

....at DC, near DC, and mirror frequencies to ensure high visual quality in the reconstructed images as well. The 16 Theta 32 GLBT in Figure 3(d) achieves an impressive coding gain of 9.96 dB. When the new transforms are incorporated into the block transform progressive coding framework described in [9], the resulting GLBT based embedded coders provide unrivaled objective and subjective performance as indicated in Table 1 and Figure 4(b) d) For a smooth image like Lena which the wavelet transform can sufficiently decorrelate, the best wavelet based embedded coder SPIHT [7] provides a ....

....32 GLBT coder can provide a PSNR gain of around 2:5 dB over a wide range of bit rates. The visual reconstructed image quality is also superior: texture is beautifully preserved, blocking is completely eliminated, and ringing is barely noticeable. Comparing to the optimal 8 Theta 40 GenLOT in [9], the 8 Theta 16 GLBT in Figure 3(a) already offers comparable performance at much lower computational complexity. More objective and subjective evaluation of GLBT based progressive coders can be found at http: saigon.ece.wisc.edu waveweb Coder index.html along with more details on the coding ....

T. D. Tran and T. Q. Nguyen, "A progressive transmission image coder using linear phase paraunitary filter banks," 31st Asilomar Conference on SSC, Pacific Grove, CA, Nov. 1997. (a) (b) (c) (d)

No context found.

T. D. Tran and T. Q. Nguyen, "A progressive transmission image coder using linear phase uniform filterbanks as block transforms," IEEE Transactions on Signal Processing 8, pp. 1493--1507, November 1999.

No context found.

T. D. Tran and T. Q. Nguyen, "A progressive transmission image coder using linear phase uniform filter banks as block transforms," IEEE Trans. on Image Proc., vol. 8, pp. 1493-- 1507, Nov. 1999.

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