Reconstruction of nonuniformly sampled images in spline spaces

IEEE Transactions on Image Processing

Volumn 14, Issue 6, 2005, Pages 713-725

  Vázquez, Carlos ^a   Dubois, Eric ^b   Konrad, Janusz ^c  

^a Dept of Electrical and Computer Engineering   (Canada)

^b UNIVERSITY OF OTTAWA   (Canada)

^c Boston University   (United States)

Author keywords

Image interpolation; Image reconstruction; Motion compensated interpolation; Nonuniform sampling; Regularization; Scattered data approximation; Splines

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; IMAGE CODING; IMAGING SYSTEMS; INTERPOLATION; INVERSE PROBLEMS; LINEAR EQUATIONS; MATHEMATICAL TRANSFORMATIONS; MOTION COMPENSATION; VIDEO CAMERAS;

IMAGE INTERPOLATION; MOTION COMPENSATED INTERPOLATION; NONRECURSIVE VIDEO CODING; NONUNIFORMLY SAMPLED IMAGES; RECONSTRUCTION ALGORITHM; REGULARIZATION; SCATTERED DATA APPROXIMATION;

IMAGE RECONSTRUCTION;

ALGORITHM; ARTICLE; AUTOMATED PATTERN RECOGNITION; BIOLOGICAL MODEL; COMPARATIVE STUDY; COMPUTER ASSISTED DIAGNOSIS; COMPUTER SIMULATION; EVALUATION; IMAGE ENHANCEMENT; IMAGE SUBTRACTION; INFORMATION RETRIEVAL; MATHEMATICAL COMPUTING; METHODOLOGY; PHOTOGRAPHY; REPRODUCIBILITY; SAMPLE SIZE; SENSITIVITY AND SPECIFICITY; SIGNAL PROCESSING; STATISTICAL MODEL; THREE DIMENSIONAL IMAGING; VIDEORECORDING;

ALGORITHMS; COMPUTER SIMULATION; IMAGE ENHANCEMENT; IMAGE INTERPRETATION, COMPUTER-ASSISTED; IMAGING, THREE-DIMENSIONAL; INFORMATION STORAGE AND RETRIEVAL; MODELS, BIOLOGICAL; MODELS, STATISTICAL; NUMERICAL ANALYSIS, COMPUTER-ASSISTED; PATTERN RECOGNITION, AUTOMATED; PHOTOGRAPHY; REPRODUCIBILITY OF RESULTS; SAMPLE SIZE; SENSITIVITY AND SPECIFICITY; SIGNAL PROCESSING, COMPUTER-ASSISTED; SUBTRACTION TECHNIQUE; VIDEO RECORDING;

EID: 20444387180     PISSN: 10577149     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIP.2005.847297     Document Type: Article

References (36)

1. S. Cho and W. Pearlman, "A full-featured, error-resilient, scalable wavelet video codec based on the set partitioning in hierarchical trees (SPIHT) algorithm," IEEE Trans. Circuits Syst. Video Technol., vol. 12, no. 3, pp. 157-171, Mar. 2002.
2. A. Secker and D. Taubman, "Highly scalable video compression using a lifting-based 3-D wavelet transform with deformable mesh motion compensation," in Proc. IEEE Int. Conf. Image Processing, vol. 3, Rochester, NY, Sep. 2002, pp. 749-752.
3. J. Konrad, "Enhacement of viewer comfort in stereoscopic viewing: Parallax adjustment," in Proc. SPIE Stereoscopic Displays and Virtual Reality Systems, vol. 3639, San José, CA, Jan. 1999, pp. 179-190.
4. J. Konrad, "View reconstruction for 3-D video entertaiment: Issues, algorithms, and applications," in Proc. Int. Conf. Image Processing and Applications, Manchester, U.K., Jul. 1999, pp. 8-12.
5. H. Feichtinger and K. Gröchenig, "Theory and practice of irregular sampling," in Wavelet: Mathematics and Applications, J. Benedetto and M. Frazier, Eds. Boca Raton, FL: CRC, 1994, ch. 8, pp. 305-363.
6. Y. Liu, "Irregular sampling for spline wavelet," IEEE Trans. Inf. Theory, vol. 42, no. 2, pp. 623-627, Feb. 1996.
7. A. Aldroubi and K. Gröchenig, "Non-uniform sampling and reconstruction in shift-invariant spaces," in SIAM Rev., vol. 43, Oct. 2001, pp. 585-620.
8. A. Sharaf and F. Marvasti, "Motion compensation using spatial transformations with forward mapping," Signal Process.: Image Commun., vol. 14, no. 3, pp. 209-227, Jan. 1999.
9. A. Glassner, Principles of Digital Image Synthesis, 1st ed. San Mateo, CA: Morgan Kaufmann, 1995.
10. D. Watson, Contouring: A Guide to the Analysis and Display of Spatial Data, 1st ed. New York: Pergamon, 1992.
11. G. Turk and J. O'Brien, "Shape transformation using variational implicit functions," in Proc. ACM SIGGRAPH, Los Angeles, CA, Aug. 1999, pp. 335-342.
12. B. Morse, T. Yoo, P. Rheingans, D. Chen, and K. Subramanian, "Interpolating implicit surfaces from scattered data using compactly supported radial basis functions," in Proc. IEEE Int. Conf. Shape Modeling and Applications, Genoa, Italy, May 2001, pp. 89-98.
13. F. Chen and D. Suter, "Using fast multipole method for accelerating the evaluation of splines," IEEE Comput. Sci. Eng., vol. 5, no. 3, pp. 24-31, Jul. 1998.
14. A. Faul and M. Powel, "Proof of convergence of an iterative technique for thin plate spline interpolation in two dimensions," Adv. Comput. Math., vol. 11, no. 2, pp. 183-192, Jan. 1999.
15. K. Sauer and J. Allebach, "Iterative reconstruction of band-limited images from nonuniformly spaced samples," IEEE Trans. Circuits Syst., vol. 34, no. 12, pp. 1497-1506, Dec. 1987.
16. R. Stasiński and J. Konrad, "Improved POCS reconstruction of stereoscopic views," Signal Process.: Image Commun., vol. 17, no. 9, pp. 689-704, Oct. 2002.
17. R. Stasiński and J. Konrad, "Linear shift-variant filtering for POCS reconstruction of irregularly sampled images," in IEEE Int. Conf. Image Processing, Barcelona, Spain, Sep. 2003, pp. 689-692.
18. T. Strohmer, "Computationally attractive reconstruction of bandlimited images from irregular samples," IEEE Trans. Image Process., vol. 6, no. 4, pp. 540-548, Apr. 1997.
19. M. Unser, "Splines: A perfect fit for signal and image processing," IEEE Signal Process. Mag., vol. 16, no. 6, pp. 22-38, Jun. 1999.
20. D. Terzopoulos, "The computation of visible-surface representation," IEEE Trans. Pattern Anal. Mach. Intell., vol. 10, no. 4, pp. 417-438, Jul. 1988.
21. R. Szeliski, "Fast surface interpolation using hierarchical basis functions," IEEE Trans. Pattern Anal. Mach. Intell., vol. 12, no. 6, pp. 513-528, Jun. 1990.
22. S. Lee, G. Wolberg, and S. Shin, "Scattered data interpolation with multilevel B-splines," IEEE Trans. Vis. Comput. Graph., vol. 3, no. 3, pp. 228-244, Jul. 1997.
23. M. Arigovindan, M. Sühling, P. Hunziker, and M. Unser, "Multigrid image reconstruction from arbitrarily spaced samples," in Proc. IEEE Int. Conf. Image Processing, vol. III, Rochester, NY, Sep. 2002, pp. 381-384.
24. N. Nguyen and P. Milinfar, "A wavelet-based interpolation-restoration method for superresolution (wavelet superresolution)," Circuits Syst. Signal Process., vol. 19, no. 4, pp. 321-338, Jul. 2000.
25. H. Choi and R. Baraniuk, "Interpolation and denoising of nonuniformly sampled data using wavelet-domain processing," in Proc. IEEE Int. Conf. Acoustics Speech Signal Process., vol. III, Phoenix, AZ, Mar. 1999, pp. 1645-1648.
26. C. Bernard, "Wavelets and Ill Posed Problems: Optic Flow and Scattered Data Interpolation," Ph.D. dissertation, CMAP, École Polytechnique, Paris, France, Nov. 1999.
27. M. Unser, A. Aldroubi, and M. Eden, "B-spline signal processing: Parts - I and II," IEEE Trans. Signal Process., vol. 41, no. 2, pp. 821-848, Feb. 1993.
28. Y.-P. Wang, Y. Chen, and A. Amini, "Fast LV motion estimation using subspace approximation techniques," IEEE Trans. Med. Imag., vol. 20, no. 6, pp. 499-513, Jun. 2001.
29. C. Vázquez, "Reconstruction d'images à partir d'échantillons irrégulièrement espacés," Ph.D. dissertation, Institut national de la recherche scientifique (INRS)-Énergie, Matériaux et Télécommunications (EMT), Montréal, QC, Canada, 2003.
30. N. Nguyen, P. Milinfar, and G. Golub, "Efficient generalized cross-validation with applicatiions to parametric image restoration and resolution enhancement," IEEE Trans. Image Process., vol. 10, no. 9, pp. 1299-1308, Sep. 2001.
31. M. Belge, M. Kilmer, and E. Miller, "Wavelet domain image restoration with adaptive edge-preserving regularization," IEEE Trans. Image Process., vol. 9, no. 4, pp. 597-608, Apr. 2000.
32. T. Berger, J. Strömberg, and T. Eltoft, "Adaptive regularized constrained least squares image restoration," IEEE Trans. Image Process., vol. 8, no. 9, pp. 1191-1203, Sep. 1999.
33. C. Vázquez, E. Dubois, and J. Konrad, "Reconstruction of irregularly sampled images by regularization in spline spaces," in Proc. IEEE Int. Conf. Image Processing, vol. 3, Rochester, NY, Sep. 2002, pp. 405-408.
34. G. Golub and C. Van Loan, Matrix Computations, 3rd ed. Baltimore, MD: The Johns Hopkins Univ. Press, 1996.
35. P. Thévenaz, T. Blu, and M. Unser, "Interpolation revisited," IEEE Trans. Med. Imag., vol. 19, no. 7, pp. 739-758, Jul. 2000.
36. V. Finnerty, "Reconstruction d'images intermédiaires á partir d'une paire d'images stéréoscopiques," M.S. thesis, Institut national de la recherche scientifique (INRS)-Télécommunications, Montréal, QC, Canada, 2002.