AM  Vol.9 No.10 , October 2018
Integer Wavelet-Based Image Interpolation in Lifting Structure for Image Resolution Enhancement
A floating-point wavelet-based and an integer wavelet-based image interpolations in lifting structures and polynomial curve fitting for image resolution enhancement are proposed in this paper. The proposed prediction methods estimate high-frequency wavelet coefficients of the original image based on the available low-frequency wavelet coefficients, so that the original image can be reconstructed by using the proposed prediction method. To further improve the reconstruction performance, we use polynomial curve fitting to build relationships between actual high-frequency wavelet coefficients and estimated high-frequency wavelet coefficients. Results of the proposed prediction algorithm for different wavelet transforms are compared to show the proposed prediction algorithm outperforms other methods.
Cite this paper: Chen, C.-Y., Guo, S.-M., Tsai, C.-H. and Tsai, J.S.-H.(2018) Integer Wavelet-Based Image Interpolation in Lifting Structure for Image Resolution Enhancement. Applied Mathematics, 9, 1156-1178. doi: 10.4236/am.2018.910077.

[1]   Lehmann, T.M., Gonner, C. and Spitzer, K. (1999) Survey: Interpolation Methods in Medical Image Processing. IEEE Transactions on Medical Imaging, 18, 1049-1075.

[2]   Keys, R.G. (1981) Cubic Convolution Interpolation for Digital Image Processing. IEEE Transactions on Acoustics, Speech and Signal Processing, 29, 1153-1160.

[3]   Guo, S.M., Hsu, C.Y., Shih, G.C. and Chen, C.W. (2011) Fast Pixel-Size-Based Large-Scale Enlargement and Reduction of image: Adaptive Combination of bilinear Interpolation and Discrete Cosine Transform. Journal of Electronic Imaging, 20, Article ID: 033005.

[4]   Carey, W.K., Chuang, D.B. and Hemami, S.S. (1999) Regularity-Preserving Image Interpolation. IEEE Transactions on Image Processing, 8, 1293-1297.

[5]   Temizel, A. and Vlachos, T. (2006) Wavelet Domain Image Resolution Enhancement. IEE Proceedings—Vision, Image and Signal Processing, 153, 25-30.

[6]   Piao, Y., Shin, I.H. and Park, H.W. (2007) Image Resolution Enhancement Using Inter-Subband Correlation in Wavelet Domain. IEEE International Conference on Image Processing, 1, 445-448.

[7]   Kinebuchi, K., Muresan, D.D. and Parks, T.W. (2001) Image Interpolation Using Wavelet-Based Hidden Markov Trees. IEEE International Conference on Acoustics, Speech, and Signal Processing, 3, 1957-1960.

[8]   Temizel, A. (2007) Image Resolution Enhancement Using Wavelet Domain Hidden Markov Tree and Coefficient Sign Estimation. IEEE International Conference on Image Processing, 5, 381-384.

[9]   Kim, S.S., Kim, Y.S. and Eom, I.K. (2009) Image Interpolation Using MLP Neural Network with Phase Compensation of Wavelet Coefficients. Neural Computing and Applications, 18, 967-977.

[10]   Lee, W.L., Yang, C.C., Wu, H.T. and Chen, M.J. (2009) Wavelet-Based Interpolation Scheme for Resolution Enhancement of Medical Images. Journal of Signal Processing Systems, 55, 251-265.

[11]   Guo, S.M., Lai, B.W., Chou, Y.C. and Yang, C.C. (2011) Novel Wavelet-Based IMAGE Interpolations in Lifting Structures for Image Resolution Enhancement. Journal of Electronic Imaging, 20, Article ID: 033007.

[12]   Demirel, H. and Anbarjafari, G. (2011) Discrete Wavelet Transform-Based Satellite Image Resolution Enhancement. IEEE Transactions on Geoscience and Remote Sensing, 49, 1997-2004.

[13]   Chavez-Roman, H., Ponomaryov, V. and Peralta-Fabi, R. (2012) Image Super Resolution Using Interpolation and Edge Extraction in Wavelet Transform Space. International Conference on Electrical Engineering, Computing Science and Automatic Control (CCE), Mexico City, 26-28 September 2012, 1-6.

[14]   Iqbal, M.Z., Ghafoor, A. and Siddiqui, A.M. (2013) Satellite Image Resolution Enhancement Using Dual-Tree Complex Wavelet Transform and Nonlocal Means. IEEE Geoscience and Remote Sensing Letters, 10, 451-455.

[15]   Demirel, H. and Anbarjafari, G. (2011) Image Resolution Enhancement by Using Discrete and Stationary Wavelet Decomposition. IEEE Transactions on Image Processing, 20, 1458-1460.

[16]   Divya Lakshmi, M.S. (2013) Robust Satellite Image Resolution Enhancement Based on Interpolation of Stationary Wavelet Transform. International Journal of Scientific and Engineering Research, 4, 1365-1369.

[17]   Calderbank, R.C., Daubechies, I., Sweldens, W. and Yeo, B.L. (1998) Wavelet Transforms That Map Integers to Integers. Applied and Computational Harmonic Analysis, 5, 332-369.

[18]   Bilgin, A., Zweig, G. and Marcellin, M.W. (2000) Three-Dimensional Image Compression with Integer Wavelet Transforms. Applied Optics, 39, 1799-1814.

[19]   Xiong, Z., Wu, X., Cheng, S. and Hua, J. (2003) Lossy-to-Lossless Compression of Medical Volumetric Data Using Three-Dimensional Integer Wavelet Transforms. IEEE Transactions on Medical Imaging, 22, 459-470.

[20]   Mallat, S.G. (1989) A Theory for Multiresolution Signal Decomposition: The Wavelet Representation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 11, 674-693.

[21]   Daubechies, I. and Sweldens, W. (1998) Factoring Wavelet Transforms into Lifting Steps. Journal of Fourier Analysis and Applications, 4, 247-269.

[22]   Test Images.