Nonlinear approximation based image recovery using adaptive sparse reconstructions and iterated denoising - Part I: Theory

IEEE Transactions on Image Processing

Volumn 15, Issue 3, 2006, Pages 539-554

  Guleryuz, Onur G ^a  

^a DOCOMO USA LABS   (United States)

Author keywords

Error concealment; Image recovery; Inpainting; Iterated denoising; Nonlinear approximation; Sparse recovery; Sparse representations

Indexed keywords

APPROXIMATION THEORY; ERROR ANALYSIS; ESTIMATION; MATHEMATICAL TRANSFORMATIONS;

ADAPTIVE SPARSE RECONSTRUCTIONS; ERROR CONCEALMENT; IMAGE RECOVERY; INPAINTING; ITERATED DENOISING; NONLINEAR APPROXIMATION; SPARSE RECOVERY; SPARSE REPRESENTATIONS;

IMAGE PROCESSING;

ALGORITHM; ARTICLE; ARTIFICIAL INTELLIGENCE; AUTOMATED PATTERN RECOGNITION; COMPUTER ASSISTED DIAGNOSIS; COMPUTER GRAPHICS; COMPUTER SIMULATION; EVALUATION; IMAGE ENHANCEMENT; INFORMATION RETRIEVAL; METHODOLOGY; NONLINEAR SYSTEM; REPRODUCIBILITY; SENSITIVITY AND SPECIFICITY; SIGNAL PROCESSING; STATISTICAL MODEL; THREE DIMENSIONAL IMAGING;

ALGORITHMS; ARTIFICIAL INTELLIGENCE; COMPUTER GRAPHICS; COMPUTER SIMULATION; IMAGE ENHANCEMENT; IMAGE INTERPRETATION, COMPUTER-ASSISTED; IMAGING, THREE-DIMENSIONAL; INFORMATION STORAGE AND RETRIEVAL; MODELS, STATISTICAL; NONLINEAR DYNAMICS; PATTERN RECOGNITION, AUTOMATED; REPRODUCIBILITY OF RESULTS; SENSITIVITY AND SPECIFICITY; SIGNAL PROCESSING, COMPUTER-ASSISTED;

EID: 32944474079     PISSN: 10577149     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIP.2005.863057     Document Type: Article

References (43)

1. Z. Alkachouh and M. G. Bellanger, "Fast DCT-based spatial domain interpolation of blocks in images," IEEE Trans. Image Process., vol. 9, no. 4, pp. 729-732, Apr. 2000.
2. C. Ballester, M. Bertalmio, V. Caselles, G. Sapiro, and J. Verdera, "Filling-in by joint interpolation of vector fields and gray levels," IEEE Trans. Image Process., vol. 10, no. 8, pp. 1200-1210, Aug. 2001.
3. M. Bertalmio, L. Vese, G. Sapiro, and S. Osher, "Simultaneous structure and texture image inpainting," IEEE Trans. Image Process., vol. 12, no. 8, pp. 882-889, Aug. 2003.
4. 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.
5. R. R. Coifman and D. L. Donoho, "Translation invariant denoising," in Wavelets and Statistics, Springer Lecture Notes in Statistics 103. New York: Springer-Verlag, pp. 125-150.
6. J. S. De Bonet, "Multiresolution sampling procedure for analysis and synthesis of texture images," presented at the ACM SIGGRAPH, Jul. 1997.
7. M. N. Do, P. L. Dragotti, R. Shukla, and M. Vetterli, "On the compression of two-dimensional piecewise smooth functions," presented at the IEEE Int. Conf. Image Processing, Thessaloniki, Greece, Oct. 2001.
8. D. L. Donoho and I. M. Johnstone, "Ideal spatial adaptation via wavelet shrinkage," Biometrika, vol. 81, pp. 425-455, 1994.
9. D. L. Donoho, "Nonlinear solution of linear inverse problems by wavelet-vaguelette decomposition," Appl. Comput. Harmon. Anal., vol. 2, pp. 101-126, 1995.
10. J. P. D'Ales and A. Cohen, "Nonlinear Approximation of Random functions," Siam J. Appl. Math 57-2, pp. 518-540, 1997.
11. R. De Vore, "Nonlinear approximation," Acta Numer, no. 7, pp. 51-150, 1998.
12. D. Donoho, M. Elad, and V. Temlyakov, Stable Recovery of Sparse Overcomplete Representations in the Presence of Noise, Tech. Rep., 2004.
13. P. J. S. G. Ferreira and A. J. Pinho, "Errorless restoration algorithms for band-limited images," in Proc. IEEE Conf. Image Processing, vol. III, 1994, pp. 157-161.
14. G. H. Golub and C. F. Loan, Matrix Computations, 3rd ed. Baltimore, MD: Johns Hopkins Univ., 1996.
15. O. G. Guleryuz, "On missing data prediction using sparse signal models: A comparison of atomic decompositions with iterated denoising," presented at the SPIE Conf. Wavelets XI, Mathematical Methods, San Diego, CA, Aug. 2005.
16. O. G. Guleryuz, "Nonlinear approximation based image recovery using adaptive sparse reconstructions and iterated denoising - Part II: Adaptive algorithms," IEEE Trans. Image Process., vol. 15, no. 3, pp. 555-571, Mar. 2006.
17. O. G. Guleryuz, "Predicting wavelet coefficients over edges using estimates based on nonlinear approximants," presented at the Data Compression Conf., Apr. 2004.
18. O. G. Guleryuz, "Iterated denoising for image recovery," in Proc. Data Compression Conf., Apr. 2002, pp. 3-12.
19. O. G. Guleryuz, "Nonlinear approximation based image recovery using adaptive sparse reconstructions," presented at the IEEE Int. Conf. Image Processing, Barcelona, Spain, Sep. 2003.
20. O. G. Guleryuz, E. Lutwak, D. Yang, and G. Zhang, "Information-theoretic inequalities for contoured probability distributions," IEEE Trans. Inf. Theory, vol. 48, no. 8, pp. 2377-2383, Aug. 2002.
21. T. Hastie, R. Tibshrirani, and J. Friedman, The Elements of Statistical Learning. New York: Springer, 2001.
22. S. S. Hemami and T. H.-Y. Meng, "Transform coded image reconstruction exploiting interblock correlation," IEEE Trans. Image Process., vol. 4, no. 7, pp. 1023-1027, Jul. 1995.
23. A. Hirani and T. Totsuka, "Combining frequency and spatial domain information for fast interactive image noise removal," in Proc. SIGGRAPH Conf., 1996, pp. 269-276.
24. Generic Coding of Moving Pictures and Associated Audio Information: Part 2-Video, 1995. ISO/IEC Int. Standard 13 818-2.
25. Information Technology - Digital Compression and Coding of Continuous - Tone Still Images, 1993. JPEG: ITU-T Rec. T.81-ISO/IEC no. 10918-1.
26. N. G. Kingsbury, "A dual-tree complex wavelet transform with improved orthogonality and symmetry properties," presented at the IEEE Conf. Image Processing, Vancouver, BC, Canada, Sep. 2000.
27. P. Kisilev, M. Zibulevshy, and Y. Y. Zeevi, "Blind separation of mixed images using multiscale transforms," presented at the IEEE Conf. Image Processing, Barcelona, Spain, 2003.
28. R. Koenen, Overview of the MPEG-4 standard, Jul. 1997. ISO/IEC JTC1/SC29/ WG11 N1730.
29. A. C. Kokaram, R. D. Morris, W. J. Fitzgerald, and P. J. W. Rayner, "Interpolation of missing data in image sequences," IEEE Trans. Image Process., vol. 4, no. 11, pp. 1509-1519, Nov. 1995.
30. X. Lee, Y.-Q. Zhang, and A. Leon-Garcia, "Information loss recovery for block-based image coding techniques - A fuzzy logic approach," IEEE Trans. Image Process., vol. 4, no. 3, pp. 259-273, Mar. 1995.
31. S. Mallat, A Wavelet Tour of Signal Processing. New York: Academic, 1998.
32. A. Papoulis, "A new algorithm in spectral analysis and band-limited extrapolation," IEEE Trans. Circuits Syst., vol. CAS-22, no. 6, pp. 735-742, Jun. 1975.
33. J. W. Park, J. W. Kim, and S. U. Lee, "DCT coefficients recovery-based error concealment technique and its application to the MPEG-2 bit stream error," IEEE Trans. Circuits Syst. Video Technol., vol. 7, no. 6, pp. 845-854, Dec. 1997.
34. J. Portilla and E. P. Simoncelli, "A parametric texture model based on joint statistics of complex wavelet coefficients," Int. J. Comput. Vis., vol. 40, pp. 49-71, Oct. 2000.
35. R. Schneider, Convex Bodies: The Brunn-Minkowski Theory. Cambridge, U.K.: Cambridge Univ. Press, Mar. 2003.
36. 1 Minimization in the Wavelet Domain. presented at Proc. IEEE Int. Conf. Image Processing. [Online]. Available: http://eeweb.poly.edu/~onur/online_pub.html
37. S. Shirani, F. Kossentini, and R. Ward, "Reconstruction of baseline JPEG coded images in error prone environments," IEEE Trans. Image Process., vol. 9, no. 7, pp. 1292-1299, Jul. 2000.
38. J. L. Starck, E. J. Candes, and D. L. Donoho, "The curvelet transform for image denoising," IEEE Trans. Image Process., vol. 11, no. 4, pp. 670-684, Apr.
39. H. Stark and J. W. Woods, Probability, Random Processes, and Estimation Theory for Engineers. Englewood Cliffs, NJ: Prentice-Hall, 1986.
40. H. Sun and W. Kwok, "Concealment of damaged block transform coded images using projections onto convex sets," IEEE Trans. Image Process., vol. 4, no. 4, pp. 470-477, Apr. 1995.
41. Y. Wang, S. Wenger, J. Wen, and A. K. Katsaggelos, "Error resilient video coding techniques," IEEE Signal Process. Mag., no. 7, pp. 61-82, Jul. 2000.
42. Y. Wang and Q.-F. Zhu, "Error control and concealment for video communication: A review," Proc. IEEE, vol. 86, no. 5, pp. 974-997, May 1998.
43. Y. Wang, Q.-F. Zhu, and L. Shaw, "Maximally smooth image recovery in transform coding," IEEE Trans. Commun., vol. 41, no. 10, pp. 1544-1551, Oct. 1993.