Chinese Journal of Computers   Full Text
Title	Combining Variation and Wavelet Transform for Image Zooming
Authors	FENG Xiang-Chu1) JIANG Dong-Huan2) XU Guang-Bao2)
Address	1)(Department of Mathematics, Xidian University, Xi’an 710071) 2)(College of Information Science and Engineer, Shandong University of Science and Technology, Qingdao, Shandong 266510)
Year	2008
Issue	No.2(340—345)
Abstract &   Background	Abstract To improve the image resolution, a new algorithm for image zooming combining variation and wavelet transform is proposed. The zoomed image is found by minimizing the variational functional in the wavelet domain which uses the Besov norm to measure the regularity of the image. Because the high-frequency subband of the wavelet transform keeps most details, the image is reconstructed with high quality. The new algorithm has the advantage of high velocity with the use of wavelet transform. Unlike the traditional image zooming by interpolation, the variation model is incorporated in the new zooming algorithm. Both theoretical analysis and experimental results have verified that the algorithm can achieve the same effect as the interpolation by using spline. keywords image zoom; variational functional; wavelet transform background Image zooming is one of the most fundamental problems in the field of image processing. It is a kind of technology which interpolates an image to higher resolution. Zooming in and zooming out play an important role in many digital image processing. To adapt to a special situation or to obtain a better visual effect, for example, to stand out some details of an image, it is common to change the size of the image effectively and the zoomed image are still of high quality. Image interpolation techniques are often used to zoom an image, such as the duplication interpolation, the bilinear interpolation and the spline interpolation. The interpolation methods have shown superior properties for some classes of images. However, most of the interpolation methods have been introduced with no count on edges. Thus they bring up the smoothing effect in resulting images. Furthermore, when the image is zoomed by a large factor, the zoomed image looks blocky. Recently, some new nonlinear methods have been suggested to overcome the artifacts of linear methods. The new methods are respectively based on wavelet and partial differential equations. Guichard and Maltouyres suggest total variation based interpolation. They define an interpolation method by imposing the interpolation to be reversible, in the sense that the original image can be deduced from its interpolation by a sub-sampling.This imposes some constraints on the Fourier coefficients of the interpolated image. There exist many possible interpolations that satisfy these constraints. They choose the total variation of the image to be the most regular among all possibilities. In 2004, Chambolle gives the discrete algorithm of the image zooming based on total variation.Therefore, image zoom has become the focus of many researchers all over the world and lots of progress has been made. In this paper, a new algorithm for image zooming combining variation and wavelet transform is proposed. The authors find the zoomed image by minimizing the variational functional in the wavelet domain which uses the Besov norm to measure the regularity of the image. Because the high-frequency subband of the wavelet transform keeps most details, the image can be reconstructed with high quality. The new algorithm has the advantage of high velocity with the use of wavelet transform. Unlike the traditional image zooming by interpolation, the variation model is incorporated in the new zooming algorithm.