Skip to main content
SpringerLink
Log in

Evaluation and performance analysis of Chinese remainder theorem and its application to lossless image compression

  • Original Research
  • Published:
Journal of Ambient Intelligence and Humanized Computing Aims and scope Submit manuscript

Abstract

Chinese remainder theorem (CRT) is widely utilized in many cryptographic applications and additionally the reversible nature of CRT is employed in compression of images. This paper mainly focuses on the suitability of CRT for lossless image compression and the analysis is carried out for the number and range of primes to be chosen. With respect to the analysis is carried out for the number of primes to be chosen (i.e., 2, 3, 4, 5, and 6), it is found that CRT suits well only for the chosen number of primes 2 with good compression ratio. For the remaining prime numbers, it provides negligible or even negative CR based on the chosen number of prime numbers. Also, CRT based lossless compression (CRTLC) reduces the size of the image based on the number of primes chosen. Further, it can achieve substantial compression of the original image. Using different test images, CRT is compared with recent lossless compression methods and against the standard set of lossless compression techniques (i.e., JPEG 2000, JPEG-LS, and CALIC). From these comparisons, it is inferred that CRT scores (maximum achieved CR is 1.8823) better than the recent and standard algorithms.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  • Ahmad I, Lee B, Shin S (2020) Analysis of Chinese remainder theorem for data compression. In: 2020 International conference on information networking (ICOIN), IEEE, pp 634–636

  • Ammar A, Al Kabbany A, Youssef M, Amam A (2001) A secure image coding scheme using residue number system. In: Proceedings of the eighteenth national radio science conference, NRSC’2001 (IEEE Cat. No. 01EX462), IEEE, vol 2, pp 399–405

  • Arazi B (1977) A generalization of the Chinese remainder theorem. Pac J Math 70(2):289–296

    Article  MathSciNet  MATH  Google Scholar 

  • Brindha M, Gounden NA (2016) A chaos based image encryption and lossless compression algorithm using hash table and Chinese remainder theorem. Appl Soft Comput 40:379–390

    Article  Google Scholar 

  • Burrows M, Wheeler D (1994) A block-sorting lossless data compression algorithm. In: Digital SRC research report, Citeseer

  • Chen Y, Zhao X, Zhang L, Kang JW (2016) Multiview and 3d video compression using neighboring block based disparity vectors. IEEE Trans Multimed 18(4):576–589

    Article  Google Scholar 

  • David T, Marcellin M (2012) Jpeg2000 image compression fundamentals, standards and practice: image compression fundamentals, standards and practice, vol 642. Springer Science & Business Media

  • Ghobaei-Arani M, Souri A (2019) LP-WSC: a linear programming approach for web service composition in geographically distributed cloud environments. J Supercomput 75(5):2603–2628

    Article  Google Scholar 

  • Ghobaei-Arani M, Rahmanian AA, Aslanpour MS, Dashti SE (2018a) CSA-WSC: cuckoo search algorithm for web service composition in cloud environments. Soft Comput 22(24):8353–8378

    Article  Google Scholar 

  • Ghobaei-Arani M, Rahmanian AA, Souri A, Rahmani AM (2018b) A moth-flame optimization algorithm for web service composition in cloud computing: simulation and verification. Softw Pract Exp 48(10):1865–1892

    Google Scholar 

  • Ghobaei-Arani M, Souri A, Baker T, Hussien A (2019) Controcity: an autonomous approach for controlling elasticity using buffer management in cloud computing environment. IEEE Access 7:106912–106924

    Article  Google Scholar 

  • Hernandez-Cabronero M, Marcellin MW, Blanes I, Serra-Sagrista J (2017) Lossless compression of color filter array mosaic images with visualization via JPEG 2000. IEEE Trans Multimed 20(2):257–270

    Article  Google Scholar 

  • Hidayat T, Zakaria MH, Pee ANC (2020) Survey of performance measurement indicators for lossless compression technique based on the objectives. In: 2020 3rd International conference on information and communications technology (ICOIACT), IEEE, pp 170–175

  • Howard PG, Vitter J (1994) Fast and e cient lossless image compression. In: Proc. data compression conference, JA Storer and M. Cohn, eds, Citeseer, pp 351–360

  • Jagannathan V, Mahadevan A, Hariharan R, Srinivasan E (2007) Number theory based image compression encryption and application to image multiplexing. In: 2007 International conference on signal processing, communications and networking, IEEE, pp 59–64

  • JTC I (2000) Information technology-JPEG2000 image coding system part 1: core coding system. ISO/IEC 15444-1

  • Kalluri M, Jiang M, Ling N, Zheng J, Zhang P (2018) Adaptive RD optimal sparse coding with quantization for image compression. IEEE Trans Multimed 21(1):39–50

    Article  Google Scholar 

  • Kasban H, Hashima S (2019) Adaptive radiographic image compression technique using hierarchical vector quantization and Huffman encoding. J Ambient Intell Humaniz Comput 10(7):2855–2867

    Article  Google Scholar 

  • Khan A, Khan A, Khan M, Uzair M (2017) Lossless image compression: application of bi-level burrows wheeler compression algorithm (BBWCA) to 2-D data. Multimed Tools Appl 76(10):12391–12416

    Article  Google Scholar 

  • Khelifi F, Bouridane A, Kurugollu F (2008) Joined spectral trees for scalable SPIHT-based multispectral image compression. IEEE Trans Multimed 10(3):316–329

    Article  Google Scholar 

  • Kim S, Cho NI (2013) Hierarchical prediction and context adaptive coding for lossless color image compression. IEEE Trans Image Process 23(1):445–449

    Article  MathSciNet  MATH  Google Scholar 

  • Kuo HC, Lin YL (2012) A hybrid algorithm for effective lossless compression of video display frames. IEEE Trans Multimed 14(3):500–509

    Article  Google Scholar 

  • Li P, Lo KT (2017) A content-adaptive joint image compression and encryption scheme. IEEE Trans Multimed 20(8):1960–1972

    Article  Google Scholar 

  • Li C, Liu Y, Zhang LY, Wong KW (2014) Cryptanalyzing a class of image encryption schemes based on Chinese remainder theorem. Signal Process Image Commun 29(8):914–920

    Article  Google Scholar 

  • Li S, Xu M, Ren Y, Wang Z (2017) Closed-form optimization on saliency-guided image compression for HEVC-MSP. IEEE Trans Multimed 20(1):155–170

    Article  Google Scholar 

  • Lucas LF, Rodrigues NM, da Silva Cruz LA, de Faria SM (2017) Lossless compression of medical images using 3-D predictors. IEEE Trans Med Imaging 36(11):2250–2260

    Article  Google Scholar 

  • McClellen JH, Rader CM (1979) Number theory in digital signal processing. Prentice Hall Professional Technical Reference

  • Ouni T, Lassoued A, Abid M (2015) Lossless image compression using gradient based space filling curves (G-SFC). Signal Image Video Process 9(2):277–293

    Article  Google Scholar 

  • Pei D, Salomaa A, Ding C (1996) Chinese remainder theorem: applications in computing, coding, cryptography. World Scientific, Singapore

    MATH  Google Scholar 

  • Pennebaker WB, Mitchell JL (1992) JPEG: still image data compression standard. Springer Science & Business Media, Berlin

    Google Scholar 

  • SECTOR S, ITU O (1998) Information technology–lossless and near-lossless compression of continuous-tone still images–baseline

  • Shen H, Pan WD, Wu D (2016) Predictive lossless compression of regions of interest in hyperspectral images with no-data regions. IEEE Trans Geosci Remote Sens 55(1):173–182

    Article  Google Scholar 

  • UmaMaheswari S, SrinivasaRaghavan V (2021) Lossless medical image compression algorithm using tetrolet transformation. J Ambient Intell Humaniz Comput 12(3):4127–4135

    Article  Google Scholar 

  • Venugopal D, Mohan S, Raja S (2016) An efficient block based lossless compression of medical images. Optik 127(2):754–758

    Article  Google Scholar 

  • Wang W, Swamy M, Ahmad MO (2004) RNS application for digital image processing. In: 4th IEEE international workshop on system-on-chip for real-time applications, IEEE, pp 77–80

  • Wang P, Dai R, Akyildiz IF (2010) Collaborative data compression using clustered source coding for wireless multimedia sensor networks. In: 2010 Proceedings IEEE INFOCOM, IEEE, pp 1–9

  • Weinberger MJ (2000) Senior member, IEEE, Gadiel Seroussi, fellow, IEEE, and Guillermo Sapiro, member, IEEE, the LOCO-I lossless image compression algorithm: principles and standardization into JPEG-LS in image processing. IEEE Trans 9:1309–1324

    Google Scholar 

  • Wiegand T, Schwarz H (2011) Source coding: part I of fundamentals of source and video coding. Now Publishers Inc, Norwell

    MATH  Google Scholar 

  • Wu X, Memon N (1996) CALIC-a context based adaptive lossless image codec. In: 1996 IEEE international conference on acoustics, speech, and signal processing conference proceedings, IEEE, vol 4, pp 1890–1893

  • Yang J, Chang C, Lin C (2010) Residue number system oriented image encoding schemes. Imaging Sci J 58(1):3–11

    Article  Google Scholar 

  • Yang F, Mou J, Sun K, Chu R (2020) Lossless image compression-encryption algorithm based on bp neural network and chaotic system. Multimed Tools Appl 79(27):19963–19992

    Article  Google Scholar 

  • Zhang Y, Adjeroh DA (2008) Prediction by partial approximate matching for lossless image compression. IEEE Trans Image Process 17(6):924–935

    Article  MathSciNet  Google Scholar 

  • Zhang H, Xq Wang, Yj Sun, Xy Wang (2020) A novel method for lossless image compression and encryption based on LWT, SPIHT and cellular automata. Signal Process Image Commun 84(115):829

    Google Scholar 

  • Zhu H, Zhao C, Zhang X (2013) A novel image encryption-compression scheme using hyper-chaos and Chinese remainder theorem. Signal Process Image Commun 28(6):670–680

    Article  Google Scholar 

  • Zhu S, Li M, Chen C, Liu S, Zeng B (2017) Cross-space distortion directed color image compression. IEEE Trans Multimed 20(3):525–538

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Computer Science and Engineering, Department of IOT, Vellore Institute of Technology, Vellore, India

    R. Vidhya

  2. Department of Computer Science and Engineering, National Institute of Technology, Tiruchirappalli, Tamil Nadu, India

    M. Brindha

Authors
  1. R. Vidhya
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Brindha
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Brindha.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Vidhya, R., Brindha, M. Evaluation and performance analysis of Chinese remainder theorem and its application to lossless image compression. J Ambient Intell Human Comput 14, 6645–6660 (2023). https://doi.org/10.1007/s12652-021-03532-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12652-021-03532-y

Keywords

Search

Navigation