Abstract
We present High-dimensional Overdetermined Laplacian Partial Differential Equations (HD-ODETLAP), an algorithm and implementation for lossy compression of high-dimensional arrays of data. HD-ODETLAP exploits autocorrelations in the data in any dimension. It also adapts to regions in the data with varying value ranges, resulting in the maximum error being closer to the RMS error. HD-ODETLAP compresses a data array by iteratively selecting a representative set of points from the array. That set of points, efficiently coded, is the compressed dataset. The compressed dataset is uncompressed by solving an overdetermined sparse system of linear equations for an approximation to the original array. HD-ODETLAP uses NVIDIA CUDA called from MATLAB to exploit GPU parallel processing to achieve considerable speedup compared to execution on a CPU. In addition, HD-ODETLAP compresses much better than JPEG2000 and 3D-SPIHT, when fixing either the average or the maximum error. An application is to facilitate storage and transmission of voluminous datasets for better climatological and environmental analysis and prediction.
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References
Anagnostou, K., Atherton, T.J., Waterfall, A.E.: 4d volume rendering with the shear warp factorisation. In: Proceedings of the 2000 IEEE symposium on Volume Visualization, VVS ’00, pp. 129–137. ACM, New York, NY, USA (2000). DOI http://doi.acm.org/10.1145/353888.353909
Bell, N., Garland, M.: CUSP: Generic Parallel Algorithms for Sparse Matrix and Graph Computations. http://cusp-library.googlecode.com (2010). Version 0.1.0
Bjøke, J.T., Nilsen, S.: Efficient representation of digital terrain models: compression and spatial decorrelation techniques. Computers & Geosciences 28(4), 433–445 (2002). DOI DOI:10.1016/S0098-3004(01)00082-6
Franklin, W.R.: The RPI GeoStar project. In: 25th International Cartographic Conference. Paris (2011)
Franklin, W.R., Inanc, M., Xie, Z.: Two novel surface representation techniques. In: Autocarto 2006. Cartography and Geographic Information Society, Vancouver Washington (2006)
Franklin, W.R., Said, A.: Lossy compression of elevation data. In: Seventh International Symposium on Spatial Data Handling. Delft (1996)
Inanc, M.: Compressing terrain elevation datasets. Ph.D. thesis, Rensselaer Polytechnic Institute (2008)
Kidner, D.B., Smith, D.H.: Advances in the data compression of digital elevation models. Computers & Geosciences 29(8), 985–1002 (2003). DOI DOI:10.1016/S0098-3004(03) 00097-9
Kim, B.J., Pearlman, W.: An embedded wavelet video coder using three-dimensional set partitioning in hierarchical trees (SPIHT). In: Data Compression Conference, 1997. DCC ’97. Proceedings, pp. 251–260 (1997). DOI 10.1109/DCC.1997.582048
Lalgudi, H., Bilgin, A., Marcellin, M., Nadar, M.: Compression of fMRI and ultrasound images using 4D SPIHT. In: Image Processing, 2005. ICIP 2005. IEEE International Conference on, vol. 2, pp. II – 746–9 (2005). DOI 10.1109/ICIP.2005.1530163
Li, Y.: CUDA-accelerated HD-ODETLAP: a high dimensional geospatial data compression framework. Ph.D. thesis, Rensselaer Polytechnic Institute (2011)
Li, Y., Lau, T.Y., Stuetzle, C., Fox, P., Franklin, W.R.: 3D oceanographic data compression using 3D-ODETLAP. In: 18th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems (ACM SIGSPATIAL GIS 2010). San Jose, CA, USA (2010). (PhD Dissertation showcase)
Lloyd, S.: Least squares quantization in PCM. Information Theory, IEEE Transactions on 28(2), 129–137 (1982). DOI 10.1109/TIT.1982.1056489
Locarnini, R.A., Mishonov, A.V., Antonov, J.I., Boyer, T.P., Garcia, H.E., Baranova, O.K., Zweng, M.M., Johnson, D.R.: World ocean atlas 2009, volume 1: Temperature p. 184 (2010)
Lum, E.B., Ma, K.L., Clyne, J.: Texture hardware assisted rendering of time-varying volume data. In: VIS ’01: Proceedings of the conference on Visualization ’01, pp. 263–270. IEEE Computer Society, Washington, DC, USA (2001)
Mehlhorn, K., Näher, S.: LEDA: a platform for combinatorial and geometric computing. Commun. ACM 38(1), 96–102 (1995). http://www.mpi-sb.mpg.de/guide/staff/uhrig/leda.html
Menegaz, G., Thiran, J.P.: Lossy to lossless object-based coding of 3-d mri data. IEEE Transactions on Image Processing 11(9), 1053–1061 (2002). DOI 10.1109/TIP.2002. 802525
Muckell, J.: Evaluating and compressing hydrology on simplified terrain. Master’s thesis, Rensselaer Polytechnic Institute (2008)
NVIDIA: NVIDIA Corporation: Compute Unified Device Architecture Programming Guide. http://developer.nvidia.com/cuda (retrieved 1/11/2011)
Plaza, A., Plaza, J., Paz, A.: Improving the scalability of hyperspectral imaging applications on heterogeneous platforms using adaptive run-time data compression. Computers & Geosciences 36(10), 1283–1291 (2010). DOI DOI:10.1016/j.cageo.2010. 02.009
Sanchez, V., Nasiopoulos, P., Abugharbieh, R.: Lossless Compression of 4D Medical Images using H.264/AVC. In: 2006 IEEE International Conference on Acoustics, Speech and Signal Processing, 2006. ICASSP 2006 Proceedings, vol. 2, p. II (2006). DOI 10.1109/ICASSP.2006.1660543
Stookey, J.: Parallel terrain compression and reconstruction. Master’s thesis, Rensselaer Polytechnic Institute (2008)
Stookey, J., Xie, Z., Cutler, B., Franklin, W.R., Tracy, D.M., Andrade, M.V.: Parallel ODETLAP for terrain compression and reconstruction. In: W.G. Aref, et al. (eds.) 16th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems (ACM GIS 2008). Irvine CA (2008)
Taubman, D.S., Marcellin, M.W., Rabbani, M.: Jpeg2000: Image compression fundamentals, standards and practice. Journal of Electronic Imaging 11, 286 (2002). DOI doi:10.1117/1.1469618
Tracy, D.M.: Path planning and slope representation on compressed terrain. Ph.D. thesis, Rensselaer Polytechnic Institute (2009)
Xie, Z.: Representation, compression and progressive transmission of digital terrain data using over-determined laplacian partial differential equations. Master’s thesis, Rensselaer Polytechnic Institute (2008)
Yang, W., Lu, Y., Wu, F., Cai, J., Ngan, K., Li, S.: 4-D wavelet-based multiview video coding. IEEE Transactions on Circuits and Systems for Video Technology 16(11), 1385–1396 (2006)
Ziegler, G., Lensch, H., Magnor, M., Seidel, H.P.: Multi-video compression in texture space using 4d spiht. In: Multimedia Signal Processing, 2004 IEEE 6th Workshop on, pp. 39–42 (2004). DOI 10.1109/MMSP.2004.1436410
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This research was partially supported by NSF grants CMMI-0835762 and IIS-1117277.
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Franklin, W.R., Li, Y., Lau, TY., Fox, P. (2013). CUDA-Accelerated HD-ODETLAP: Lossy High Dimensional Gridded Data Compression. In: Shi, X., Kindratenko, V., Yang, C. (eds) Modern Accelerator Technologies for Geographic Information Science. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-8745-6_8
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