- Research Article
Video Coding Using 3D Dual-Tree Wavelet Transform
EURASIP Journal on Image and Video Processingvolume 2007, Article number: 042761 (2007)
This work investigates the use of the 3D dual-tree discrete wavelet transform (DDWT) for video coding. The 3D DDWT is an attractive video representation because it isolates image patterns with different spatial orientations and motion directions and speeds in separate subbands. However, it is an overcomplete transform with 4: 1 redundancy when only real parts are used. We apply the noise-shaping algorithm proposed by Kingsbury to reduce the number of coefficients. To code the remaining significant coefficients, we propose two video codecs. The first one applies separate 3D set partitioning in hierarchical trees (SPIHT) on each subset of the DDWT coefficients (each forming a standard isotropic tree). The second codec exploits the correlation between redundant subbands, and codes the subbands jointly. Both codecs do not require motion compensation and provide better performance than the 3D SPIHT codec using the standard DWT, both objectively and subjectively. Furthermore, both codecs provide full scalability in spatial, temporal, and quality dimensions. Besides the standard isotropic decomposition, we propose an anisotropic DDWT, which extends the superiority of the normal DDWT with more directional subbands without adding to the redundancy. This anisotropic structure requires significantly fewer coefficients to represent a video after noise shaping. Finally, we also explore the benefits of combining the 3D DDWT with the standard DWT to capture a wider set of orientations.
Hsiang S-T, Woods JW: Embedded video coding using invertible motion compensated 3-D subband/wavelet filter bank. Signal Processing: Image Communication 2001,16(8):705-724. 10.1016/S0923-5965(01)00002-9
Xu J, Xiong Z, Li S, Zhang Y-Q: Memory-constrained 3-D wavelet transform for video coding without boundary effects. IEEE Transactions on Circuits and Systems for Video Technology 2002,12(9):812-818. 10.1109/TCSVT.2002.803231
Andreopoulos Y, van der Schaar M, Munteanu A, Barbarien J, Schelkens P, Cornelis J: Fully-scalable wavelet video coding using in-band motion compensated temporal filtering. Proceedings of IEEE International Conference on Accoustics, Speech, and Signal Processing (ICASSP '03), April 2003, Hong Kong 3: 417-420.
Secker A, Taubman D: Lifting-based invertible motion adaptive transform (LIMAT) framework for highly scalable video compression. IEEE Transactions on Image Processing 2003,12(12):1530-1542. 10.1109/TIP.2003.819433
Joint Scalable Video Model 2.0 Reference Encoding Algorithm Description ISO/IEC JTC1/SC29/WG11/N7084. Buzan, Korea, April 2005
Kingsbury N: A dual-tree complex wavelet transform with improved orthogonality and symmetry properties. Proceedings of IEEE International Conference on Image Processing (ICIP '00), September 2000, Vancouver, BC, Canada 2: 375-378.
Do MN, Vetterli M: The contourlet transform: an efficient directional multiresolution image representation. IEEE Transactions on Image Processing 2005,14(12):2091-2106.
Reeves TH, Kingsbury NG: Overcomplete image coding using iterative projection-based noise shaping. Proceedings of IEEE International Conference on Image Processing (ICIP '02), September 2002, Rochester, NY, USA 3: 597-600.
Sivaramakrishnan K, Nguyen T: A uniform transform domain video codec based on dual tree complex wavelet transform. Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP '01) , May 2001, Salt Lake City, Utah, USA 3: 1821-1824.
Selesnick I, Li KY: Video denoising using 2D and 3D dual-tree complex wavelet transforms. Wavelets: Applications in Signal and Image Processing X, August 2003, San Diego, Calif, USA, Proceedings of SPIE 5207: 607-618.
Selesnick I, Baraniuk RG, Kingsbury NC: The dual-tree complex wavelet transform. IEEE Signal Processing Magazine 2005,22(6):123-151.
Wang B, Wang Y, Selesnick I, Vetro A: An investigation of 3D dual-tree wavelet transform for video coding. Proceedings of International Conference on Image Processing (ICIP '04), October 2004, Singapore 2: 1317-1320.
Kim B-J, Xiong Z, Pearlman WA: Low bit-rate scalable video coding with 3-D set partitioning in hierarchical trees (3-D SPIHT). IEEE Transactions on Circuits and Systems for Video Technology 2000,10(8):1374-1387. 10.1109/76.889025
Wang B, Wang Y, Selesnick I, Vetro A: Video coding using 3-D dual-tree discrete wavelet transforms. Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP '05), March 2005, Philadelphia, Pa, USA 2: 61-64.
Xu D, Do MN: Anisotropic 2D wavelet packets and rectangular tiling: theory and algorithms. Wavelets: Applications in Signal and Image Processing X, August 2003, San Diego, Calif, USA, Proceedings of SPIE 5207: 619-630.
Xu D, Do MN: On the number of rectangular tilings. IEEE Transactions on Image Processing 2006,15(10):3225-3230.
Mallat SG, Zhang Z: Matching pursuits with time-frequency dictionaries. IEEE Transactions on Signal Processing 1993,41(12):3397-3415. 10.1109/78.258082
Gribonval R, Vandergheynst P: On the exponential convergence of matching pursuits in quasi-incoherent dictionaries. IEEE Transactions on Information Theory 2006,52(1):255-261.
Neff R, Zakhor A: Very low bit-rate video coding based on matching pursuits. IEEE Transactions on Circuits and Systems for Video Technology 1997,7(1):158-171. 10.1109/76.554427
Bolcskei H, Hlawatsch F: Oversampled filter banks: optimal noise shaping, design freedom, and noise analysis. Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP '97), April 1997, Munich, Germany 3: 2453-2456.
Hua J, Xiong Z, Wu X: High-performance 3-D embedded wavelet video (EWV) coding. Proceedings of 4th IEEE Workshop on Multimedia Signal Processing (MMSP '01), October 2001, Cannes, France 569-574.
Boettcher JB, Fowler JE: Video coding using a complex wavelet transform and set partitioning. to appear in IEEE Signal Processing Letters, September 2007