The JPEG still picture compression standard
Communications of the ACM - Special issue on digital multimedia systems
Algorithm 749: fast discrete cosine transform
ACM Transactions on Mathematical Software (TOMS)
Digital signal processing (3rd ed.): principles, algorithms, and applications
Digital signal processing (3rd ed.): principles, algorithms, and applications
MPEG Video Compression Standard
MPEG Video Compression Standard
Digital Coding of Waveforms: Principles and Applications to Speech and Video
Digital Coding of Waveforms: Principles and Applications to Speech and Video
Embedded DCT Coding with Significance Masking
ICASSP '97 Proceedings of the 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '97) -Volume 4 - Volume 4
A new embedded lossless/quasi-lossless image coder based on the Hadamard transform
ICIP '97 Proceedings of the 1997 International Conference on Image Processing (ICIP '97) 3-Volume Set-Volume 1 - Volume 1
Lossless Image Compression Using Integer to Integer Wavelet Transforms
ICIP '97 Proceedings of the 1997 International Conference on Image Processing (ICIP '97) 3-Volume Set-Volume 1 - Volume 1
IEEE Transactions on Computers
On Computing the Discrete Cosine Transform
IEEE Transactions on Computers
Fast multiplierless approximations of the DCT with the liftingscheme
IEEE Transactions on Signal Processing
Matrix factorizations for reversible integer mapping
IEEE Transactions on Signal Processing
A new algorithm to compute the DCT and its inverse
IEEE Transactions on Signal Processing
Embedded image coding using zerotrees of wavelet coefficients
IEEE Transactions on Signal Processing
New fast recursive algorithms for the computation of discretecosine and sine transforms
IEEE Transactions on Signal Processing
Integer DCTs and fast algorithms
IEEE Transactions on Signal Processing
New networks for perfect inversion and perfect reconstruction
IEEE Journal on Selected Areas in Communications
An image multiresolution representation for lossless and lossy compression
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
Lossless quantization of Hadamard transform coefficients
IEEE Transactions on Image Processing
A new, fast, and efficient image codec based on set partitioning in hierarchical trees
IEEE Transactions on Circuits and Systems for Video Technology
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Reversible integer-to-integer (I2I) mapping of orthonormal transforms are vital for developing lossless coding with scalable decoding functionalities. A general framework for reversible I2I mapping of N-point, where N is a positive integer power of 2, orthonormal block transforms using recursive factorization of such transform matrices and the lifting scheme is presented. Designs include the discrete cosine transform (DCT) that maps integers to integers (I2I-DCT), the discrete sine transform that maps integers to integers (I2I-DST) and the Walsh-Hadamard transform that maps integer to integers (I2I-WHT). The main significant feature of these designs is that the transform coefficients are normalized according to the conventional scaling factors, which is vital for embedded coding, while preserving the integer-to-integer mapping and perfect reconstruction. This makes these transforms usable in both lossless and lossy image coding, especially in scalable lossless coding. These generic N-point design of the above transforms enables evaluating the effect of block sizes of such transforms in lossless coding. The performance is evaluated in terms of lossless image and video coding, quality scalable decoding, complexity and lifting step rounding effects.