Image Reconstruction Based on the TV and Mumford-Shah-Euler Model

Article Preview

Abstract:

In this paper, we firstly analyze some previous super-resolution models based on the TV model. Secondly, we propose two novel super-resolution models. One combines the TV model with the Mumford-Shah model, the other combines the TV model with the Mumford-Shah-Euler image model. Finally, we show some numerical experiments of our models based on convergence approximation. The results show that the TV-MSE model gives a well effect.

You might also be interested in these eBooks

Info:

Periodical:

Pages:

198-202

Citation:

Online since:

January 2011

Export:

Price:

Permissions CCC:

Permissions PLS:

Сopyright:

© 2011 Trans Tech Publications Ltd. All Rights Reserved

Share:

Citation:

[1] L. Ambrosio and V. Tortorelli, Approximation of functionals depending on jumps by elliptic functionals via convergence. Comm. Pure Appl. Math., 43, 1990, p.999–1036.

DOI: 10.1002/cpa.3160430805

Google Scholar

[2] L. Ambrosio and V. Tortorelli. On the approximation of free discontinuity problems. Boll. Un. Mat. Ital., 6-B, 1992, p.105–123.

Google Scholar

[3] N. Bose and K. Boo, High-resolution image reconstruction with multi-sensors, International Journal of Imaging Systems and Technology, 9, 1998, pp.294-304.

Google Scholar

[4] T. Chan, N. Ng, A. Yau and A. Yip, Super-resolution Image Reconstruction Using Fast Inpainting Algorithms, Applied and Computational Harmonic Analysis, 23, 2007, pp.3-24.

DOI: 10.1016/j.acha.2006.09.005

Google Scholar

[5] T. Chan and J. Shen. Morphologically invariant PDE inpaintings. UCLA CAM Report 2001-15 at: www. math. ucla. edu /˜imagers; submitted to IEEE Trans. Image Process., (2001).

Google Scholar

[6] T. Chan and J. Shen, Mathematical models for local non-texture inpainting, SIAM Journal on Applied Mathematical, 62, 2001, pp.1019-1043.

Google Scholar

[7] A. Love, A Treatise on the Mathematical Theory of Elasticity, Dover, New York, 4th ed. (1927).

Google Scholar

[8] D. Mumford, Elastica and computer vision, In C. L. Bajaj, editor, Algebraic Geometry and its Applications, Springer-Verlag, New York, 1994, pp.291-506.

DOI: 10.1007/978-1-4612-2628-4_31

Google Scholar

[9] D. Mumford and J. Shah, Optimal approximation by piecewise smooth functions and associated variational problems, Comm. Pure Applied Math., XLII, 1989, pp.577-685.

DOI: 10.1002/cpa.3160420503

Google Scholar

[10] N. Nguyen and M. Peyman, A wavelet-based interpolation-restoration method for super- -resolution (wavelet super-resolution), Circuits, Systems, and Signal Processing, 19, 2000, pp.321-338.

DOI: 10.1007/bf01200891

Google Scholar

[11] D. Rajan and S. Chaudhuri, An MRF-based approach to generation of super-resolution images from blurred observations, Journal of Mathematical Imaging and Vision, 16, 2002, pp.5-15.

Google Scholar