近年來，超解析影像技術變得日漸重要，如高清電視、衞星影像及高畫質視訊會議等都需要影像放大技術來滿足目前的需求，其原因不是因為照相機或攝影機無法拍攝出高畫質的影像，而是在實際應用中常常受到記憶體容量、傳輸頻寬、電子產品的續航力和拍攝設備的價格等等所限制。目前的影像放大技術可以在空間域或頻率域上完成，在操作上，這兩個領域都有其優點。在空間域上，我們可以偵測出影像和邊緣及紋理部份，針對它們在超解析過程中做特別處理；而在頻率域上，我們可以利用瀘波器的特性來幫我們建構出一張自然影像。這篇論文我們結合了空間域和頻率域上的優點，從而建構出高品質的影像，同時引入了遞迴投影技術來使得我們的結果快速收斂。對比起普遍的影像放大技術，我們的結果無論是在客觀上或主觀上都能突顯其優越性。此外，在實際硬體的考量上，輸入緩衝器的容量一向是一個廠商非常關心的議題，因為它牽涉到大量的製造成本，然而，對於在頻率域的超解析技術來說，要降低緩衝器的容量仍是一門嚴峻的課題。我們提出的方法既有包含頻率域的技術，其突破點在於它同時能完全符合降低緩衝器容量的需求。

Existing single image super-resolution techniques interpolate a low-resolution image either in spatial domain or in wavelet domain. Both domains exhibit their respective advantages. For instance, edge information in the spatial domain can be detected and enhanced to construct a sharp high-resolution image. In wavelet domain, we can exploit the support of filters to model the regularity of natural images. This paper combines the advantages of both spatial domain and wavelet domain algorithms. Still, we introduce the back-projection technique to minimize the reconstruction error with an efficient iterative procedure. Comparing with conventional image interpolation techniques, results show that the proposed method is considerably superior both in objective and subjective terms. Finally, for practical consideration, we propose an algorithm to reduce the scan lines in the input buffer which is an essential consideration for hardware implementation.

[1] J. Allebach and P. Wong, “Edge-directed interpolation,” IEEE International Conf. Image processing, vol. 3, pp. 707-710, 1996.
[2] M. Crouse, Nowak, R.D., and Baraniuk, “Wavelet-based statistical signal processing using hidden Markov models,” IEEE Trans. Signal Processing, vol. 46, no. 4, pp. 886, 1998.
[3] A. Cohen, I. Daubechies, and J.C. Feauveau, "Biorthogonal bases of compactly supported wavelets," Comm. Pure & Appl. Math., vol. 45, no. 5, pp. 485-560, 1992.
[4] S. Dai, Han, and Wu, "Bilateral Back-Projection for Single Image Super Resolution," IEEE International Conf. Multimedia and Expo., pp. 1039-1042, 2007.
[5] I. Daubechies, "Ten Lectures on wavelets ," SIAM 1992.
[6] S. Dai, M. Han, et al, “Soft edge smoothness prior for alpha channel super resolution,” IEEE International Conf. Computer Vision and Pattern Recognition, pp. 1-8, 2007.
[7] W. Dong, Zhang, Shi and Wu, "Nonlocal back-projection for adaptive image enlargement," IEEE International Conf. Image Processing, pp. 349-352, 2009.
[8] M. Irani and S. Peleg, “Motion analysis for image enhancement: resolution, occlusion and transparency,” J. Visual Commun. Image Represent., vol.4, pp. 324-335, Dec. 1993.
[9] J. Kim, Lee and Cho, “Bayesian Image Interpolation Based on the Learning and Estimation of Higher Bandwavelet Coefficients,” IEEE International Conf. Image Processing, pp. 685-688, 2006.
[10] R. Keys, "Cubic convolution interpolation for digital image processing," IEEE Trans. Signal Processing, Acoustics, Speech, and Signal Processing, vol. 29, no. 6, pp. 1153-1160, 1981.
[11] X. Li, M.T. Orchard, "New Edge-Directed Interpolation," IEEE Trans. Image Processing, vol. 10, no. 10, pp. 1521-1527, 2001.
[12] J. Tian, Yu, and Xie, “Wavelet-Based Image Interpolation Using a Three-Component Exponential Mixture Model,” IEEE Conf. Image and Signal Processing, vol. 4, pp. 129-132, 2008.
[13] R. Tsai and T. Huang, “Multiframe image restoration and registration,” Advances in Computer Vision and Image Processing, pp. 317-339, 1984.
[14] P. Tsai, T. Acharya, "Image Up-Sampling Using Discrete Wavelet Transform," 9th JCIS, 2006.
[15] A. Temizel, “Image resolution upscaling in the wavelet domain using directional cycle spinning,” IET J. Electronic Letters, vol. 41, no. 3, pp. 119-121, 2005.
[16] A. Temizel and T. Vlachos, "Wavelet domain image resolution enhancement," IEE Proc. Vision. Image Signal Processing, vol. 153, no. 1, pp. 25-30, 2006.
[17] A. Temizel, “Image Resoluton Enhancement using Wavelet Domain Hidden Markov Tree and Coefficient Sign Estimation,” IEEE International Conf. Image Processing, vol. 5, pp. 381-384, 2007.
[18] J. Tian, L. Ma and W. Yu, “Ant colony optimization for wavelet-based image interpolation using a three-component exponential mixture model,” Elsevier, Expert Systems with Applications, Vol. 38, no. 10, Sep.2011.
[19] D. Woo, K. Eom, and Y. Kim, “Image Interpolation based on inter-scale dependency in wavelet domain,” IEEE International Conf. Image Processing, vol. 3, pp. 1687-1690, 2004.
[20] J. Wang, Gong, "Fast image super-resolution using Connected Component Analysis," IEEE International Conf. Multimedia and Expo, pp. 157-160, 2008.
[21] X. Zhang and X. Wu, “Image Interpolation by Adaptive 2-D Autoregressive Modeling and Soft-Decision Estimation,” IEEE Trans. Image Processing, vol. 17, no. 6, pp. 887-896, 2008.
[22] “Image Data Compression: Recommended Standard for CCSDS 122.0-B-1,” The Consultative Committee for Space Data Systems, Blue Book, 2005.