A 2-D Geometric Signal Compression Method Based on Compressed Sensing
-
摘要: 本文给出的压缩方法属于谱压缩方法. 谱压缩方法是一种常用的二维轮廓线模型压缩方法. 文章从压缩感知的角度解释了谱压缩方法, 并提出了基于压缩感知的二维轮廓线模型压缩方法. 首先利用二维轮廓线模型 Laplace 算子的特征向量构造了一组基. 二维轮廓线模型的几何结构在这组基下可以被稀疏表达. 利用随机矩阵对二维轮廓线模型的几何结构抽样, 完成压缩. 恢复过程中, 通过最优化1-范数, 实现几何信号的恢复. 实验结果表明, 该方法压缩速度快, 比例高, 恢复效果好, 适合对大型数据以及远距离数据进行压缩.Abstract: Spectral compression method is a commonly used compression method in the field of two-dimensional contour model compression. This paper explains the spectral compression method from the perspective of compressed sensing and provides a compression method of two-dimensional contour model based on compressed sensing. Constructing a basis using Laplace operator of the two-dimensional contour model, we get the sparse representation of the 2-D geometric signal based on this basis. We complete compressing the two-dimensional contour model by sampling the two-dimensional contour model geometry information based on a random matrix. In the recovery process, we reconstruct the 2-D geometric signal through optimizing 1-norm of the sparse signal. Experimental results show that the compression ratio of this method is high, the restore effect is good, and it is suitable for large-scale data compression.
-
Key words:
- Compressed sensing /
- geometric signal /
- random sampling /
- sparse representation
-
[1] Bhat P, Zitnick C L, Cohen M, Curless B. GradientShop: a gradient-domain optimization framework for image and video filtering. ACM Transactions on Graphics, 2010, 29(2):1-14[2] Zhou K, Gong M M, Huang X, Guo B N. Data-parallel oc-trees for surface reconstruction. IEEE Transactions on Vi-sualization and Computer Graphics, 2010, 17(5): 669-681[3] Marchesin S, Chen C K, Ho C, Ma K L. View-dependent streamlines for 3D vector fields. IEEE Transactions on Visu-alization and Computer Graphics, 2010, 16(6): 1578-1586[4] Zhou Kun. Digital Geometry Processing: Theory and Ap-plications [Ph. D. dissertation], Zhejiang University, China, 2002 (周昆. 数字几何处理: 理论与应用[博士学位论文], 浙江大学, 中 国, 2002)[5] Weinkauf T, Theisel H. Streak lines as tangent curves of a derived vector field. IEEE Transactions on Visualization and Computer Graphics, 2010, 16(6): 1225-1234[6] Farbman Z, Hoffer G, Lipman Y, Cohen-Or D, Lischinski D. Coordinates for instant image cloning. ACM Transactions on Graphics, 2009, 28(3): 1-9[7] Karni Z, Gotsman C. Spectral compression of mesh geome-try. In: Proceedings of the 27th annual conference on Com-puter graphics and interactive techniques. New York, NY, USA: ACM Press/Addison-Wesley Publishing Co, 2009. 279-286[8] Khodakovsky A, Schreder P, Sweldens W. Progressive ge-ometry compression. In: Proceedings of the 27th annual con-ference on Computer graphics and interactive techniques. New York, NY, USA: ACM Press/Addison-Wesley Publish-ing Co, 2000. 271-278[9] Gu X F, Gortler S J, Hoppe H. Geometry images. ACM Transactions on Graphics, 2002, 32(3): 355-361[10] Donoho D L. Compressed sensing. IEEE Transactions on Information Theory, 2006, 52(4): 1289-1306[11] Candues E J, Tao T. Near-optimal signal recovery from random projections: universal encoding strategies? IEEE Transactions on Information Theory, 2006, 52(12): 5406-5425[12] Mohimani H, Babie-Zadeh M, Jutten C. A fast approach for overcomplete sparse decomposition based on smoothed 0-norm. IEEE Transactions on Signal Processing, 2009, 57(1):289-301[13] Candμes E J, Wakin M B, Boyd S P. Enhancing sparsity by reweighted l1 minimization. Journal of Fourier Analysis and Applications, 2008, 14(5-6): 877-905[14] Rosanwo O, Petz C, Prohaska S, Hotz I, Hege H C. Dual streamline seeding. In: Proceedings of the 2009 IEEE Pa-cific Visualization Symposium. Beijing, China: IEEE, 2009.9-16[15] Candues E J, Romberg J, Tao T. Robust uncertainty prin-ciples: exact signal reconstruction from highly incomplete frequency information. IEEE Transactions on Information Theory, 2006, 52(2): 489-509
点击查看大图
计量
- 文章访问数: 1879
- HTML全文浏览量: 65
- PDF下载量: 1306
- 被引次数: 0