# ITERATIVE IMAGE INTERPOLATION FOR IRREGULARLY SAMPLED IMAGE

### Jonghwa Lee, Chulhee Lee

#### Abstract

For irregularlyFor irregularly sampled color images, an iterative interpolation algorithm utilizing a wavelet shrinkage denoising technique is proposed. Exploiting the non-local information from neighboring blocks, the reconstruction performance converges as the iteration of the proposed algorithm is repeated. Experimental results show that the proposed algorithm outperforms the conventional algorithms in terms of subjective quality and objective measures. The proposed algorithm correctly reconstructs the edge and provides perceptually good performance with randomly chosen 25% pixels.

#### References

- Abma, R. and N. Kabir, "3D interpolation of irregular data with a POCS algorithm," Geophysics, vol. 71, pp. E91-E97, 2006.
- Barber, C. B., et al., "The Quickhull algorithm for convex hulls," ACM Trans. Mathematical Software, vol. 22, pp. 469-483, 1996.
- Buades, A., et al., "A non-local algorithm for image denoising," in IEEE Computer Vision and Pattern Recognition, pp. 60-65, 2005.
- Chambolle, A., et al., "Nonlinear wavelet image processing: variational problems, compression, and noise removal through wavelet shrinkage," IEEE Trans. Image Process., vol. 7, pp. 319-335, 1998.
- Chen, J. S., et al., "Fast Convolution with Laplacian-ofGaussian Masks," IEEE Trans. Patt. Anal. Mach. Intell., vol. PAMI-9, pp. 584-590, 1987.
- Dabov, K., et al., "Image Denoising by Sparse 3-D Transform-Domain Collaborative Filtering," IEEE Trans. Image Process., vol. 16, pp. 2080-2095, 2007.
- Delaunay, B., "Sur la sphÃ¨re vide, Izvestia Akademii Nauk SSSR, Otdelenie Matematicheskikh i Estestvennykh Nauk," vol. 7, pp. 793-800, 1934.
- Donoho, D. L. and I. M. Johnstone, "Adapting to Unknown Smoothness Via Wavelet Shrinkage," Journal of the American Statistical Association, vol. 90, 1995.
- Donoho, D. L., "Compressed sensing," IEEE Trans. Information Theory, vol. 52, pp. 1289-1306, 2006.
- Duijndam, A. J. W., et al., "Irregular and sparse sampling in exploration seismology," in Nonuniform sampling: theory and practice, F. Marvasti, Ed., ed: Kluwer Academic/Plenum, 2001.
- Guleryuz, O. G., "Nonlinear approximation based image recovery using adaptive sparse reconstructions and iterated denoising-part I: theory," IEEE Trans. Image Process., vol. 15, pp. 539-554, 2006.
- Guleryuz, O. G., "Nonlinear approximation based image recovery using adaptive sparse reconstructions and iterated denoising-part II: adaptive algorithms," IEEE Trans. Image Process., vol. 15, pp. 555-571, 2006.
- Herrmann, F. J. and G. Hennenfent, "Non-parametric seismic data recovery with curvelet frames," Geophsical Journal International, vol. 173, pp. 233- 248, 2008.
- Lertrattanapanich, S. and N. K. Bose, "High resolution image formation from low resolution frames using Delaunay triangulation," IEEE Trans. Image Process., vol. 11, pp. 1427-1441, 2002.
- Li ,X., "Patch-based image interpolation: algorithms and applications," presented at the Int'l Workshop on Local and Non-Local Approximation in Image Processing, 2008.
- Lustig, M., et al., "Compressed Sensing MRI," IEEE Signal Process. Mag., vol. 25, pp. 72-82, 2008.
- Lustig, M., et al., "Sparse MRI: The application of compressed sensing for rapid MR imaging," Magnetic Resonance in Medicine, vol. 58, pp. 1182-1195, 2007.
- Marvasti, F., "nonuniform sampling," in Advanced topics in Shannon sampling and interpolation theory R. J. M. II, Ed., ed: Springer-Verlag in NY, 1993.
- Marvasti, F., A unified approach to zero-crossings and nonuniform sampling of single and multi-dimensional signals and systems: Chicago, Ill., 1987.
- Sandberg, I. W., "On the Properties of Some Systems that Distort Signals-I," Bell Syst. Tech. J., pp. 2003-2046, 1963.
- Takeda, H. et al., "Kernel Regression for Image Processing and Reconstruction," IEEE Trans. Image Process., vol. 16, pp. 349-366, 2007.
- Takeda, H. et al., "Robust Kernel Regression for Restoration and Reconstruction of Images from Sparse Noisy Data," in IEEE Int'l Conf. Image Processing, pp. 1257-1260, 2006.
- Wang, Z. et al., "Image quality assessment: from error visibility to structural similarity," IEEE Trans. Image Process., vol. 13, pp. 600-612, 2004.
- Wiley, R., "Recovery of Bandlimited Signals from Unequally Spaced Samples," IEEE Trans. Commun., vol. 26, pp. 135-137, 1978.

#### Paper Citation

#### in Harvard Style

Lee J. and Lee C. (2012). **ITERATIVE IMAGE INTERPOLATION FOR IRREGULARLY SAMPLED IMAGE** . In *Proceedings of the International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP, (VISIGRAPP 2012)* ISBN 978-989-8565-03-7, pages 176-181. DOI: 10.5220/0003821701760181

#### in Bibtex Style

@conference{visapp12,

author={Jonghwa Lee and Chulhee Lee},

title={ITERATIVE IMAGE INTERPOLATION FOR IRREGULARLY SAMPLED IMAGE},

booktitle={Proceedings of the International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP, (VISIGRAPP 2012)},

year={2012},

pages={176-181},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0003821701760181},

isbn={978-989-8565-03-7},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP, (VISIGRAPP 2012)

TI - ITERATIVE IMAGE INTERPOLATION FOR IRREGULARLY SAMPLED IMAGE

SN - 978-989-8565-03-7

AU - Lee J.

AU - Lee C.

PY - 2012

SP - 176

EP - 181

DO - 10.5220/0003821701760181