AUTHORS: Rodolfo A. Fiorini
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ABSTRACT: Contemporary approaches to data compression vary in time delay or impact on application performance as well as in the amount of compression and loss of data. The very best modern lossless data compression algorithms use standard approaches and are unable to match spacetime high end requirements for mission critical application, with full information conservation (a few pixels may vary by com/decom processing). Advanced instrumentation, dealing with nanoscale technology at the current edge of human scientific enquiry, like X-Ray CT, generates an enormous quantity of data from single experiment. In previous papers, we have already shown that traditional Q Arithmetic can be regarded as a highly sophisticated open logic, powerful and flexible bidirectional formal language of languages, according to “Computational Information Conservation Theory” (CICT). This new awareness can offer competitive approach to guide more convenient, spatiotemporal lossless compression algorithm development and application. To test practical implementation performance and effectiveness on biomedical imaging, this new technique has been benchmarked by normalized spatiotemporal key performance index, and compared to well-known, standard lossless compression techniques.
KEYWORDS: Lossless Compression, Arithmetic Geometry, Computed Tomography, X-rays, Biomedical Imaging, Compressed Sensing, Biomedical Cybernetics, Biomedical Engineering, Public Health, Healthcare
REFERENCES:
[1] N., Reims, T., Schoen, M., Boehnel, F., Sukowski, M., Firsching, Strategies for efficient scanning and reconstruction methods on very large objects with high-energy x-ray computed tomography, Proc. SPIE 9212, Developments in X-Ray Tomography IX, 921209, September 12, 2014; doi: 10.1117/12.
[2] K.J., Batenburg, J., Sijbers, DART: a practical reconstruction algorithm for discrete tomography, IEEE Transactions on Image Processing, Vol. 20, No. 9, 2011, pp. 2542- 2553.
[3] K.J., Batenburg, S., Bals, J., Sijbers, C., Kuebel, P.A., Midgley, J.C., Hernandez, U., Kaiser, .R., Encina, E.A., Coronado, G., Van Tendeloo, 3D imaging of nanomaterials by discrete tomography, Ultramicroscopy, Vol. 109, No. 6, 2009, pp. 730-740.
[4] M.H., Kryder, S.K., Chang, After Hard Drives – What Comes Next?, IEEE Transactions on Magnetics, Vol. 45, No. 10, October 2009, pp. 3406-3413.
[5] D.A., Koff, H., Shulman, An overview of digital compression of medical images: Can we use lossy image compression in radiology?, Canadian Association of Radiologists Journal, Vol. 57, 2006, pp. 211–217.
[6] M.J., Zukoski, T., Boult, T., Iyriboz, A novel approach to medical image compression, International Journal of Bioinformatic Research and Applications, 2006, pp. 89–103.
[7] T.J., Kim, K.H., Lee, B., Kim, E.J. Chun, V. Baipal, Y.H. Kim, S. Hahn, K.W. Lee, Regional variance of visually lossless threshold in compressed chest CT images: lung versus mediastinum and chest wall, European Journal of Radiology, Vol.69, No. 3, 2009, pp. 483– 488.
[8] A.H., Robinson, C., Cherry, Results of a prototype television bandwidth compression scheme, Proceedings of the IEEE, Vol. 55, No. 3, 1967, pp. 356–364.
[9] Recommendation T.45 (02/00), Run-length colour encoding, International Telecommunication Union, 2000. Available at:
[10] D., Huffman, A Method for the Construction of Minimum-Redundancy Codes, Proceedings of the IRE, Vol. 40, No. 9, 1952, pp. 1098–1101.
[11] Modified Huffman coding, Available at:
[12] J.S., Vitter, Design and Analysis of Dynamic Huffman Codes, Journal of the ACM, Vol. 34, No.4, October 1987, pp 825–845.
[13] J., Ziv, A., Lempel, A Universal Algorithm for Sequential Data Compression, IEEE Transactions on Information Theory, Vol. 23, No. 3, May 1977, pp. 337–343.
[14] J., Ziv, A., Lempel, Compression of Individual Sequences via Variable-Rate Coding, IEEE Transactions on Information Theory, Vol. 24, No. 5, September 1978, pp. 530–536.
[15] T., Welch, A Technique for High-Performance Data Compression, Computer, Vol. 17, No. 6, 1984, pp. 8–19.
[16] J.J., Rissanen, Generalized Kraft Inequality and Arithmetic Coding, IBM Journal of Research and Development, Vol. 20, No. 3, May 1976, pp. 198–203.
[17] J.J., Rissanen, G.G., Langdon, Jr., Arithmetic coding, IBM Journal of Research and Development, Vol. 23, No. 2, March 1979, pp. 149–162
[18] E.J., Candès, J.K., Romberg, T., Tao, Stable signal recovery from incomplete and inaccurate measurements, Communications on Pure and Applied Mathematics, Vol. 59, No. 8, 2006, pp. 1207–1223
[19] ., Nyquist, Certain topics in telegraph transmission theory, Transactions of AIEE, Vol.47, April 1928, pp. 617–644.
[20] J.C., Kieffer, E-H., Yang, Grammar-based codes: A new class of universal lossless source codes, IEEE Trans. Inform. Theory, Vol. 46, No. 3, 2000, 737–754.
[21] C.G., Nevill-Manning, Inferring sequential structure, Ph.D. thesis, Department of Computer Science, University of Waikato, New Zealand.
[22] C.G., Nevill-Manning, .H., Witten, Identifying Hierarchical Structure in Sequences: A lineartime algorithm, 1997, arXiv:cs/9709102. Available at:
[23] J., Kieffer, E-H., Yang, Structured grammarbased codes for universal lossless data compression, Communications in Information Systems, Vol. 2, No.1, 2002, pp.29-52. Available at:
[24] D., Li, D., O'Shaughnessy, Speech processing: a dynamic and optimization-oriented approach, Marcel Dekker, 2003, pp. 41–48.
[25] C., Chapin Cutler, Differential Quantization of Communication Signals, U.S. patent 2605361, filed June 29, 1950, issued July 29, 1952. Available at:
[26] H., Al –Mahmood, Z., Al-Rubaye, Lossless Image Compression based on Predictive Coding and Bit Plane Slicing, International Journal of Computer Applications (0975 – 8887), Vol. 93, No 1, May 2014, pp.1-6.
[27] K., Chen, T.V., Ramabadran, An improved hierarchical interpolation (HINT) method for the reversible compression of grayscale images, Proceedings. Data Compression Conference, Snowbird, UT, USA, 1991, pp. 436-439.
[28] The DICOM standard, (2009). Available at:
[29] ISO/IEC 15444 (2007). Available at:
[30] Wikipedia, Jpeg2000 (2017). Available at:
[31] C.E., Shannon, Bell Systems Technical Journal, Vol. 27, No.3, July/October 1948, 379.
[32] A., Schrijver, 2017, A Course in Combinatorial Optimization. Available at:
[33] K.L., Hoffman, T.K., Ralphs, Integer and Combinatorial Optimization, Encyclopedia of Operations Research and Management Science, 2012. Available at:
[34] L. Fortnow, The status of the P versus NP problem, Communications of the ACM, Vol. 52, No. 9, 2009, p. 78–86.
[35] R.A. Fiorini, Computational Information Conservation Theory: An Introduction, Proceedings of the 8th International Conference on Applied Mathematics, Simulation, Modelling (ASM '14), in N.E. Mastorakis, M. Demiralp, N. Mukhopadhyay, F. Mainardi, Eds., Mathematics and Computers in Science and Engineering Series, No.34, NAUN Conferences, WSEAS Press, November 22-24, 2014, Florence, Italy, pp.385-394.
[36] R.A. Fiorini, GSI & CICT as coupled resource for multi-scale system biology and biomedical engineering modeling, International Journal of Systems Applications, Engineering and Development, Vol. 9, pp. 93-97 (2015). Available at:
[37] R.A. Fiorini, How Random is Your Tomographic Noise? A Number Theoretic Transform (NTT) Approach, Fundamenta Informaticae, Vol. 135, Nos 1-2, 2014, pp.135- 170.
[38] R.A. Fiorini, G. Laguteta, in V. Mladenov, Ed., Proceedings of the 19th International Conference on Systems, Zakynthos Island, Greece, 2015, pp. 648-655.
[39] E.W. Weisstein, (1999-2012). Available at:
[40] R.A. Fiorini, G. Laguteta, Discrete Tomography Data Footprint Reduction by Information Conservation, Fundamenta Informaticae, Vol. 125, Nos 3-4, pp. 261-272.
[41] D.M. Young, R.T. Gregory, A Survey of Numerical Mathematics, vol.I and II, Addison Wesley, Reading, Mass., USA, 1973.
[42] W.R. Hamilton, Memorandum respecting a new System of Roots of Unity, Philosophical Magazine, 12, 1856, pp. 446.
[43] B. Chandler, W. Magnus, The History of Combinatorial Group Theory: A Case Study in the History of Ideas, Studies in the History of Mathematics and Physical Sciences, Springer, 234, 1st ed., December 1, 1982.
[44] W. von Dyck, Gruppentheoretische Studien, Math. Ann., Vol. 20, No. 1, 1882, p.1-45.
[45] J. Stillwell, Mathematics and its history, Springer, 2002.
[46] C.W. Curtis, Pioneers of Representation Theory: Frobenius, Burnside, Schur, and Brauer, History of Mathematics, American Mathematical Society,(Providence, RI, USA, 2003.
[47] The New Test Images for Image Compression Benchmark (Jan 2008). Available at:
[48] M. J., Weinberger, G. Seroussi, G. Sapiro, The LOCO-I Lossless Image Compression Algorithm: Principles and Standardization into JPEG-LS, IEEE Trans. Image Processing, Vol. 9, No. 8, Aug. 2000, pp. 1309-1324. Available at:
[49] W. Sun, Y. Lu, W. Feng, L. Shipeng, Level Embedded Medical Image Compression Based on Value of Interest, IEEE, ICIP, 2009, pp. 1749-1752. Available at:
