主 题: Sparse Approximation by Wavelet Frames and Applications
报告人: Prof. Bin Dong (Department of Mathematics, The University of Arizona)
时 间: 2012-06-18 14:00-15:00
地 点: 理科一号楼1560
Wavelet frames are known to be able to sparsely approximate piecewise smooth functions, which has recently been used for image restoration problems including image deblurring, inpainting and medical imaging. In the first half of this talk, I will start with a brief review of some wavelet frame based models. Then I will address their connections to variational models based on one of our recent theoretical studies [1], which granted geometric interpretations to the wavelet frame transform and enabled us to extend the applications of wavelet frames to some new problems [2, 3]. To further utilize the property of sparse approximation by wavelet frames, I will present a model (as well as some fast algorithms) that penalizes the 0-norm of the frame coefficients [4, 5], instead of the commonly used 1-norm. Numerical experiments show that using the 0-norm has advantages for some specific type of images. Finally, I will present our recent work on the application of wavelet frames to x-ray based CT image reconstruction with simultaneous Radon domain inpainting [6].
[1]. J. Cai, B. Dong, S. Osher and Z. Shen, Image restoration: total variation; wavelet frames; and beyond, to appear in Journal of American Mathematical Society, 2012.
[2]. B. Dong and Z. Shen, Wavelet frame based surface reconstruction from unorganized points, Journal of Computational Physics, 230 (22), 8247-8255, 2011.
[3]. B. Dong, A. Chien and Z. Shen, Frame based segmentation for medical images, Communications in Mathematical Sciences, 9 (2), 551-559, 2010.
[4]. Y. Zhang, B. Dong and Z. Lu, l0 minimization of wavelet frame based image restoration, to appear in Mathematics of Computation, 2012
[5]. B. Dong and Y. Zhang, An efficient algorithm for l0 minimization in wavelet frame based image restoration, to appear in Journal of Scientific Computing, 2012.
[6]. B. Dong, J. Li and Z. Shen, X-ray CT image reconstruction via wavelet frame based regularization and Radon domain inpainting, to appear in Journal of Scientific Computing, 2012.
