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46
Fast Multiplierless Approximations of the DCT with the Lifting Scheme
 IEEE Trans. on Signal Processing
, 2001
"... In this paper, we present the design, implementation and application of several families of fast multiplierless approximations of the discrete cosine transform (DCT) with the lifting scheme, named the binDCT. These binDCT families are derived from Chen's and Loeffler's plane rotationbased ..."
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Cited by 72 (11 self)
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In this paper, we present the design, implementation and application of several families of fast multiplierless approximations of the discrete cosine transform (DCT) with the lifting scheme, named the binDCT. These binDCT families are derived from Chen's and Loeffler's plane rotationbased factorizations of the DCT matrix, respectively, and the design approach can also be applied to DCT of arbitrary size. Two design approaches are presented. In the first method, an optimization program is de ned, and the multiplierless transform is obtained by approximating its solution with dyadic values. In the second method, a general liftingbased scaled DCT structure is obtained, and the analytical values of all lifting parameters are derived, enabling dyadic approximations with different accuracies. Therefore the binDCT can be tuned to cover the gap between the WalshHadamard transform and the DCT. The corresponding 2D binDCT allows a 16bit implementation, enables lossless compression, and maintai...
The BinDCT: Fast Multiplierless Approximation of The Dct
 IEEE SIGNAL PROCESSING LETTERS, VOL. 7, NO. 6, JUNE 2000 141
, 2000
"... This paper presents a family of fast biorthogonal block transforms called binDCT that can be implemented using only shift and add operations. The transform is based on a VLSIfriendly lattice structure that robustly enforces both linear phase and perfect reconstruction properties. The lattice coeffi ..."
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Cited by 45 (5 self)
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This paper presents a family of fast biorthogonal block transforms called binDCT that can be implemented using only shift and add operations. The transform is based on a VLSIfriendly lattice structure that robustly enforces both linear phase and perfect reconstruction properties. The lattice coefficients are parameterized as a series of dyadic lifting steps providing fast, efficient, inplace computation of the transform coefficients as well as the ability to map integers to integers. The new 8 8 transforms all approximate the popular 8 8 DCT closely, attaining a coding gain range of 8.778.82 dB, despite requiring as low as 14 shifts and 31 additions per eight input samples. Application of the binDCT in both lossy and lossless image coding yields very competitive results compared to the performance of the original floatingpoint DCT.
Mchannel Linear Phase Perfect Reconstruction Filter Bank with Rational Coefficients
 IEEE Trans. on Signal Processing
, 1999
"... This paper introduces a general class of Mchannel linear phase perfect reconstruction lter banks with rational coefficients. A subset of the presented solutions has dyadic coefficients, leading to multiplierless implementations suitable for lowpower mobile computing. All of these filter banks are ..."
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Cited by 36 (19 self)
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This paper introduces a general class of Mchannel linear phase perfect reconstruction lter banks with rational coefficients. A subset of the presented solutions has dyadic coefficients, leading to multiplierless implementations suitable for lowpower mobile computing. All of these filter banks are constructed from a lattice structure that is VLSIfriendly, employs the minimum number of delay elements, and robustly enforces both linear phase and perfect reconstruction properties. The lattice coefficients are parameterized as a series of zeroorder lifting steps, providing fast, efficient, inplace computation of the subband coefficients. Despite the tight rational or integer constraint, image coding experiments show that these novel filter banks are very competitive with current popular transforms such as the 8 8 discrete cosine transform and the wavelet transform with 9=7tap biorthogonal irrationalcoefficient filters.
Fast progressive image coding without wavelets
 Data Compression Conference (DCC
, 2000
"... We introduce a new image compression algorithm that allows progressive image reconstruction – both in resolution and in fidelity, with a fully embedded bitstream. The algorithm is based on bitplane entropy coding of reordered transform coefficients, similar to the progressive wavelet codec (PWC) pr ..."
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Cited by 29 (2 self)
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We introduce a new image compression algorithm that allows progressive image reconstruction – both in resolution and in fidelity, with a fully embedded bitstream. The algorithm is based on bitplane entropy coding of reordered transform coefficients, similar to the progressive wavelet codec (PWC) previously introduced. Unlike PWC, however, our new progressive transform coder (PTC) does not use wavelets; it performs the spacefrequency decomposition step via a new lapped biorthogonal transform (LBT). PTC achieves a rate vs. distortion performance that is comparable (within 2%) to that of the stateoftheart SPIHT (set partitioning in hierarchical trees) codec. However, thanks to the use of the LBT, the spacefrequency decomposition step in PTC reduces the number of multiplications per pixel by a factor of 2.7, and the number of additions by about 15%, when compared to the fastest possible implementation of the “9/7 ” wavelet transform via lifting. Furthermore, since most of the computation in the LBT is in fact performed by a DCT, our PTC codec can make full use of fast software and hardware modules for 1D and 2D DCTs. 1.
LinearPhase Perfect Reconstruction Filter Bank: Lattice Structure, Design, and Application in Image Coding
 IEEE Trans. Signal Processing
, 2000
"... A lattice structure for anchannel linearphase perfect reconstruction filter bank (LPPRFB) based on the singular value decomposition (SVD) is introduced. The lattice can be proven to use a minimal number of delay elements and to completely span a large class of LPPRFB's: All analysis and synth ..."
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Cited by 29 (8 self)
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A lattice structure for anchannel linearphase perfect reconstruction filter bank (LPPRFB) based on the singular value decomposition (SVD) is introduced. The lattice can be proven to use a minimal number of delay elements and to completely span a large class of LPPRFB's: All analysis and synthesis filters have the same FIR length, sharing the same center of symmetry. The lattice also structurally enforces both linearphase and perfect reconstruction properties, is capable of providing fast and efficient implementation, and avoids the costly matrix inversion problem in the optimization process. From a block transform perspective, the new lattice can be viewed as representing a family of generalized lapped biorthogonal transform (GLBT) with an arbitrary number of channels and arbitrarily large overlap. The relaxation of the orthogonal constraint allows the GLBT to have significantly different analysis and synthesis basis functions, which can then be tailored appropriately to fit a particular application. Several design examples are presented along with a highperformance GLBTbased progressive image coder to demonstrate the potential of the new transforms.
Linear Phase Paraunitary Filter Bank With Filters Of Different Lengths And Its Application In Image Compression
 IEEE Trans. Signal Processing
, 1997
"... In this paper, the theory, structure, design, and implementation of a new class of linear phase paraunitary filter banks (LPPUFB) are investigated. This new class of filter banks with filters of different lengths can be viewed as generalized lapped orthogonal transforms (GenLOT) with variablelength ..."
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Cited by 18 (11 self)
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In this paper, the theory, structure, design, and implementation of a new class of linear phase paraunitary filter banks (LPPUFB) are investigated. This new class of filter banks with filters of different lengths can be viewed as generalized lapped orthogonal transforms (GenLOT) with variablelength basis functions. Our main motivation of the new transform is its application in blocktransformbased image coding. Besides having all of the attractive properties of other lapped orthogonal transforms, the new transform takes advantage of its long basis functions to represent smooth signal and to reduce blocking artifacts, while reserves its short basis functions for highfrequency signal components like edges and texture to reduce ringing. Two design methods are presented, each with its own set of advantages: the first is based on a direct lattice factorization and the second enforces certain relationships between GenLOT's lattice coefficients to obtain variable length filters. Various n...
Lattice Structure for Regular Paraunitary LinearPhase Filterbanks and MBand Orthogonal Symmetric Wavelets
 IEEE Trans. Signal Processing
, 2001
"... Orthogonal Mchannel uniform linearphase lter banks (GenLOT) can be designed and implemented using lattice structure. This paper discusses the conditions of the lattice structures that yield regular GenLOTs. For one regularity, the relations among the plane rotation angles in the lattice structure ..."
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Cited by 18 (5 self)
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Orthogonal Mchannel uniform linearphase lter banks (GenLOT) can be designed and implemented using lattice structure. This paper discusses the conditions of the lattice structures that yield regular GenLOTs. For one regularity, the relations among the plane rotation angles in the lattice structure will be derived, and can be used to design regular GenLOTs. Since the conditions for higher degree of regularity are much more complex, in the paper, we shall study these conditions for two regularities. Some examples of lter bank designs are presented, and applied to image coding. The simulation results show that lter bank with higher degree of regularity provides smoother reconstruction images. 1
Residual Image Coding for Stereo Image Compression
 Optical Engineering
, 2003
"... One main focus of research in stereo image coding has been disparity estimation, a technique used to reduce the coding rate by taking advantage of the redundancy in a stereo image pair. Significantly less effort has been put into the coding of the residual image. These images display characteristics ..."
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Cited by 15 (2 self)
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One main focus of research in stereo image coding has been disparity estimation, a technique used to reduce the coding rate by taking advantage of the redundancy in a stereo image pair. Significantly less effort has been put into the coding of the residual image. These images display characteristics that are different from that of natural images. We propose a new method for the coding of residual images that takes into account the properties of residual images. Particular attention is paid to the effects of occlusion and the correlation properties of residual images that result from blockbased disparity estimation. The embedded, progressive nature of our coder enables one to stop decoding at any time. We demonstrate that it is possible to achieve good results with a computationally simple method. 2003 Society of PhotoOptical Instrumentation Engineers. IDOl: 10.1117/1.1526492] Subject terms: stereo image; residual image compression; progressive image coding.
A class of regular biorthogonal linearphase filterbanks: theory, structure, and application in image coding
 IEEE Trans. Signal Process
, 2003
"... Abstract—This paper discusses a method of regularity imposition onto biorthogonal linearphaseband filterbanks using the lattice structure. A lifting structure is proposed for lattice matrix parameterization where regularity constraints can be imposed. The paper focuses on cases with analysis and s ..."
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Cited by 12 (6 self)
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Abstract—This paper discusses a method of regularity imposition onto biorthogonal linearphaseband filterbanks using the lattice structure. A lifting structure is proposed for lattice matrix parameterization where regularity constraints can be imposed. The paper focuses on cases with analysis and synthesis filterbanks having up to two degrees of regularity. Necessary and sufficient conditions for regular filterbanks in terms of the filter impulse response, frequency response, scaling function, and wavelets are revisited and are derived in terms of the lattice matrices. This also leads to a constraint on the minimum filter length. Presented design examples are optimized for the purpose of image coding, i.e., the main objectives are coding gain and frequency selectivity. Simulation results from an image coding application also show that these transforms yield improvement in the perceptual quality in the reconstruction images. The approach has also been extended to the case of integer/rational lifting coefficients, which are desirable in many practical applications. Index Terms—Biorthogonal filterbanks, GenLOT, integer transforms, lattice structure, regularity, vanishing moment.
The Generalized Lapped Biorthogonal Transform
, 1997
"... A lattice structure based on the singular value decomposition (SVD) is introduced. The lattice can also be proven to use a minimal number of delay elements and to completely span a large class of Mchannel linear phase perfect reconstruction filter bank (LPPRFB): all analysis and synthesis filters h ..."
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Cited by 11 (7 self)
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A lattice structure based on the singular value decomposition (SVD) is introduced. The lattice can also be proven to use a minimal number of delay elements and to completely span a large class of Mchannel linear phase perfect reconstruction filter bank (LPPRFB): all analysis and synthesis filters have the same FIR length of L = KM; sharing the same center of symmetry. The lattice also structurally enforces both linear phase and perfect reconstruction properties, is capable of providing fast and efficient implementation, and avoids the costly matrix inversion problem in the optimization process. From a block transform perspective, the new lattice represents a family of generalized lapped biorthogonal transform (GLBT) with arbitrary integer overlapping factor K. The relaxation of the orthogonal constraint allows the GLBT to have significantly different analysis and synthesis basis functions which can then be tailored appropriately to fit a particular application. Several design example...