Wavelet-domain approximation and compression of piecewise smooth images

IEEE Transactions on Image Processing

Volumn 15, Issue 5, 2006, Pages 1071-1087

  Wakin, Michael B ^a   Romberg, Justin K ^b   Choi, Hyeokho ^c   Baraniuk, Richard G ^a  

^a Rice University   (United States)

^b CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^c North Carolina State University   (United States)

Author keywords

Edges; Image compression; Nonlinear approximation; Rate distortion; Wavelets; Wedgelets; Wedgeprints

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; COMPUTATIONAL GEOMETRY; IMAGE QUALITY; MATHEMATICAL MODELS; WAVELET TRANSFORMS;

GEOMETRIC MODELING; NONLINEAR APPROXIMATION; PIECEWISE SMOOTH IMAGES; RATE-DISTORTION; WAVELET-DOMAIN APPROXIMATION;

IMAGE COMPRESSION;

ALGORITHM; ARTICLE; COMPUTER ASSISTED DIAGNOSIS; COMPUTER GRAPHICS; IMAGE ENHANCEMENT; INFORMATION PROCESSING; MATHEMATICAL COMPUTING; METHODOLOGY; SIGNAL PROCESSING;

ALGORITHMS; COMPUTER GRAPHICS; DATA COMPRESSION; IMAGE ENHANCEMENT; IMAGE INTERPRETATION, COMPUTER-ASSISTED; NUMERICAL ANALYSIS, COMPUTER-ASSISTED; SIGNAL PROCESSING, COMPUTER-ASSISTED;

EID: 33645986468     PISSN: 10577149     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIP.2005.864175     Document Type: Article

References (41)

1. D. L. Donoho, "Denoising by soft-thresholding," IEEE Trans. Inf. Theory, vol. 41, no. 3, pp. 613-627, May 1995.
2. H. Choi and R. G. Baraniuk, "Multiscale image segmentation using wavelet-domain hidden Markov models," IEEE Trans. Image Process., vol. 10, no. 9, pp. 1309-1321, Sep. 2001.
3. S. Mallat and S. Zhong, "Characterization of signals from multiscale edges," IEEE Trans. Pattern Anal. Mach. Intell., vol. 14, no. 7, pp. 710-732, Jul. 1992.
4. J. Shapiro, "Embedded image coding using zerotrees of wavelet coefficients," IEEE Trans. Signal Process., vol. 41, no. 12, pp. 3445-3462, Dec. 1993.
5. A. Said and W. A. Pearlman, "Anew fast and efficient image codec based on set partitioning in hierarchical trees," IEEE Trans. Circuits Syst. Video Technol., vol. 6, no. 3, pp. 243-250, Jun. 1996.
6. Z. Xiong, K. Ramchandran, and M. T. Orchard, "Space-frequency quantization for wavelet image coding," IEEE Trans. Image. Process., vol. 6, no. 5, pp. 677-693, May 1997.
7. S. LoPresto, K. Ramchandran, and M. T. Orchard, "Image coding based on mixture modeling of wavelet coefficients and a fast estimation-quantization framework," in Proc. IEEE Data Compression Conf., Snowbird, UT, Mar. 1997, pp. 221-230.
8. D. S. Taubman and M. W. Marcellin, JPEG2000: Image Compression Fundamentals, Standards, and Practice. Boston, MA: Kluwer, 2002.
9. S. Mallat, A Wavelet Tour of Signal Processing, 2nd ed. San Diego, CA: Academic, 1999.
10. R. A. DeVore, B. Jawerth, and B. J. Lucier, "Image compression through wavelet transform coding," IEEE Trans. Inf. Theory, vol. 38, no. 2, pp. 719-746, Mar. 1992.
11. D. L. Donoho, "Unconditional bases are optimal bases for data compression and for statistical estimation," J. Appl. comput. Harm. Anal., vol. 1, no. 1, pp. 100-115, Dec. 1993.
12. A. Cohen, W. Dahmen, I. Daubechies, and R. DeVore, "Tree approximation and optimal encoding," J. Appl. comput. Harm. Anal., vol. 11, pp. 192-226, 2001.
13. A. Cohen, I. Daubechies, O. G. Guleryuz, and M. T. Orchard, "On the importance of combining wavelet-based nonlinear approximation with coding strategies," IEEE Trans. Inf. Theory, vol. 48, no. 7, pp. 1895-1921, Jul. 2002.
14. E. J. Candès and D. L. Donoho, "Curvelets - A suprisingly effective nonadaptive representation for objects with edges," in Curve and Surface Fitting, A. Cohen, C. Rabut, and L. L. Schumaker, Eds. Nashville, TN: Vanderbilt Univ. Press, 1999.
15. I. Daubechies, Ten Lectures on Wavelets. New York: SIAM, 1992.
16. L. Breiman, J. Friedman, R. Olshen, and C. Stone, Classification and Regression Trees. Belmont, CA: Wadsworth, 1984.
17. D. Marr, Vision. San Francisco, CA: Freeman, 1982.
18. Standard Test Images. [Online] Available: Www.dsp.rice.edu/~wakin/images/
19. M. D. Adams. The JasPer Project Home Page. [Online] Available: www.ece.uvic.ca/~mdadams/jasper/
20. J. Froment, "Image compression through level lines and wavelet packets," in Wavelets in Signal and Image Analysis, A. A. Petrosian and F. G. Meyer, Eds. Norwell, MA: Kluwer, 2001.
21. L. Peotta, L. Granai, and P. Vanderghenyst, "Very low bit rate image coding using redundant dictionaries," in Proc. Wavelets X, SPIE's 48th Annu. Mtg., vol. 5207, San Diego, CA, 2003, pp. 228-229.
22. R. Shukla, P. L. Dragotti, M. Do, and M. Vetterli, "Rate-distortion optimized tree-structured compression algorithms for piecewise polynomial images," IEEE Trans. Image Process., vol. 14, no. 3, pp. 343-359, Mar. 2005.
23. 2 singularities," commun. Pure Appl. Math., vol. 57, pp. 219-266, 2004.
24. M. N. Do and M. Vetterli, "The contourlet transform: An efficient directional multiresolution image representation," IEEE Trans. Image Process., vol. 14, no. 12, pp. 2091-2016, Dec. 2005.
25. E. Le Pennec and S. Mallat, "Sparse geometric image representations with bandelets," IEEE Trans. Image. Process., vol. 14, no. 4, pp. 423-438, Apr. 2005.
26. F. Arandiga, A. Cohen, M. Doblas, R. Donat, and B. Matei, "Sparse representations of images by edge adapted nonlinear multiscale transforms," in Proc. IEEE Int. Conf. Image Processing, Barcelona, Spain, Sep. 2003, pp. 701-704.
27. P. L. Dragotti and M. Vetterli, "Wavelet footprints: Theory, algorithms and applications," IEEE Trans. Signal Process., vol. 51, no. 5, May 2003.
28. D. L. Donoho, "Wedgelets: Nearly-minimax estimation of edges," Ann. Stat., vol. 27, pp. 859-897, 1999.
29. D. L. Donoho and X. Huo, "Beamlets and multiscale image analysis," in Multiscale and Multiresolution Methods, T. J. Barth, T. Chan, and R. Haimes, Eds. New York: Springer, 2002, vol. 20, Springer Lecture Notes in Computer Science, pp. 149-196.
30. R. Willett and R. Nowak, "Platelets: A multiscale approach for recovering edges and surfaces in photon-limited medical imaging," IEEE Trans. Med. Imag., vol. 22, no. 3, pp. 332-350, Mar. 2003.
31. J. K. Romberg, M. B. Wakin, and R. G. Baraniuk, "Multiscale Geometric Image Processing," Proc. SPIE Visual Commun. Image Process., vol. 5150, pp. 1265-1272, 2003.
32. V. Chandrasekaran, M. B. Wakin, D. Baron, and R. Baraniuk, "Compression of higher dimensional functions containing smooth discontinuities," in Proc. Conf. Inf. Sci. Syst., Princeton, NJ, Mar. 2004.
33. P. L. Dragotti and M. Vetterli, "Footprints and edgeprints for image denoising and compression," in Proc. IEEE Int. Conf. Image Processing, Thessaloniki, Greece, Oct. 2001, pp. 237-240.
34. R. A. DeVore, "Nonlinear approximation," Acta Numer., vol. 7, pp. 51-150, 1998.
35. J. K. Romberg, "Multiscale geometric image processing," Ph.D. dissertation, Dept. Elect. Comput. Eng., Rice Univ., Houston, TX, 2003.
36. M. N. Do, P. L. Dragotti, R. Shukla, and M. Vetterli, "On the compression of two-dimensional piecewise smooth functions," in IEEE Int. Conf. Image Proc., vol. 1, Thessaloniki, Greece, Oct. 2001, pp. 14-17.
37. A. Ortega and K. Ramchandran, "Rate-distortion methods for image and video compression," IEEE Signal Process. Mag., vol. 15, no. 6, Nov. 1998.
38. M. B. Wakin, D. L. Donoho, H. Choi, and R. G. Baraniuk, "High-resolution navigation on nondifferentiable image manifolds," in Proc. IEEE Int. Conf. Acoust., Speech, Signal Process., vol. 5, Philadelphia, PA, Mar. 2005, pp. 1073-1076.
39. M. Tsai, J. Villasenor, and F. Chen, "Stack-run image coding," IEEE Trans. Circuits Syst. Video Technol., vol. 6, no. 5, pp. 519-521, Oct. 1996.
40. I. Witten, R. Neal, and J. Cleary, "Arithmetic coding for data compression," commun. ACM, vol. 30, no. 6, pp. 520-540, Jun 1987.
41. J. K. Romberg, M. B. Wakin, and R. G. Baraniuk, "Multiscale wedgelet image analysis: Fast decompositions and modeling," in Proc. IEEE Int. Conf. Image Process., vol. 3, Sep. 2002, pp. 585-588.