Improved Binary Tree Coding for Image Compression using Modified Singular Value Decomposition

Naveen Kumar, B. N. Jagadale, J. S. Bhat

Abstract


Reducing the transmission cost while maintaining the quality of image data is the most challenging part in data transmission. In this paper, we report the possibility of improving the quality of image reconstruction by using modified singular value decomposition (SVD) and binary tree coding with adaptive scanning order (BTCA) for grayscale image compression. This method uses modified rank one updated SVD as a pre-processing step for binary tree coding to increase the quality of the reconstructed image. The high energy compaction in SVD process offers high image quality with less compression and is requires more number of bits for reconstruction. BTCA compression, also gives high image quality by coding more significant coefficients using adaptive scanning order from bottom to top with high compression rate. The proposed method uses both SVD and BTC for image compression and is tested with several test images and results are compared with those of SPIHT, JPEG, JPEG2000 and BTCA. The results show significant improvement in PSNR at high bitrates as compared to other methods.

Keywords


Image compression; Modified singular value decomposition; Binary tree coding

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References


K. Ahmadi, A.Y. Javid and E. Salari, An efficient compression scheme based on adaptive thresholding in wavelet domain using particle swarm optimization, Journal of Signal Processing: Image Communication 32 (2012), 33 – 39.

H.F. Ates and E. Tamer, Hierarchical quantization indexing for wavelet and wavelet packet image coding, IEEE Trans. Image Process. 25 (2) (2010), 111 – 120.

H.F. Ates and M.T. Orchard, Spherical coding algorithm for wavelet image compression, IEEE Trans. Image process., Geosci. Remote Sens. 18 (5) (2009), 1015 – 1024.

M. Brand, Fast low-rank modifications of the thin singular value decomposition, J. Linear Algebra, and its Applications 415 (2006), 20 – 30.

C.-C. Chang, P. Tsai and C.-C. Lin, SVD-based digital image watermarking scheme, Pattern Recog. Lett. 26 (2005), 1577 – 86.

C.-C. Chang, Y.-S. Hu and C.-C. Lin, A digital watermarking scheme based on singular value decomposition, in B. Chen, M. Paterson, G. Zhang (editors), Combinatorics, Algorithms, Probabilistic and Experimental Methodologies, Berlin — Heidelberg, Springer, pp. 82 – 93 (2007).

J. Chen, Image compression with SVD, ECS 29K, Scientific Computation, URL: http://fourier.eng.hmc.edu/e161/lectures/svdcompression.html#Aase99 (December 13, 2000).

F. Garcia-Vilchez, J. Munoz-Mari, M. Zortea, I. Blanes, V. Gonzalez-Ruiz, G. Camps-Valls, A. Plaza and J. Serra-Sagrista, On the impact of lossy compression on hyperspectral image classification and unmixing, IEEE Geosci. Remote Sens. Lett. 8 (2011), 253 – 257.

S.T. Hsiang and J.W. Woods, Embedded image coding using Zero block of subband/wavelet coefficients and context modeling, in Proc. Data compress. Conf., Washington, DC, pp. 83 – 92 (2001).

K.-K. Huang and D.-Q. Dai, A new on-board image codec based on binary tree with adaptive scanning order in scan-based mode, IEEE Trans. on Geosci. and Remote Sens. 50 (10) (2012), 3737 – 3750.

N. Jayant and P. Noll, Digital Coding of Waveforms: Principles and Applications to Speech and Video, Englewood Cliffs, NJ: Prentice-Hall (1984).

N. Jayant, J. Johnston and R. Safranek, Signal compression based on models of human perception, Proc. IEEE 81 (1993), 1385 – 1422.

S.K. Jha and R.D.S. Yadava, Denoising by singular value decomposition and its application to electronic nose data processing, IEEE Sensor Journal 11 (1) (2011), 35 – 44.

R. Kumar, A. Kumar and G.K. Singh, A hybrid method based on singular value decomposition and embedded zero tree wavelet technique for ECG signal compression, J. Computer Methods, and Programs in Biomedicine 129 (2016), 135 – 148.

C.-C. Lai, A digital watermarking scheme based on singular value decomposition and tiny genetic algorithm, Digital Signal Process 21 (2006), 522 – 527.

R. Neelamani, R. de Queiroz, Z. Fan, S. Dash and R.G. Baraniuk, Jpeg compression history estimation for color images, IEEE Trans. on Image Processing 15 (6) (2006), 1365 – 1378.

A. Plaza, J.M. Bioucas-Dias, A. Simic and W.J. Blackwell, Foreword to the Special Issue on Hyperspectral Image and Signal Processing, IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing 5 (2) (2012), 347 – 353.

G.H. Polub and C.F. Van Loan, Matrix Computations, 3rd edition, John Hopkins University Press (1996).

M. Rabbani and R. Joshi, An overview of JPEG2000 still image compression standard, J. Signal Processing: Image Communication 17 (2002), 3 – 48.

A.M. Rufai and G.A.H. Demirel, Lossy image compression using singular value decomposition and Wavelet difference reduction, J. Digital Signal Processing 24 (2014), 117 – 123.

A. Said and W.A. Perlman, New, fast, and efficient image codec based on set partitioning in hierarchical tree, IEEE Trans. Circuit and Systems for Video Technology 6 (3) (1996), 243 – 250.

M. Shaou-Gang, K. Fu-Sheng and C. Shu-Ching, A lossless compression method for medical image sequences using jpeg-ls and interframe coding, IEEE Transactions on Information Technology in Biomedicine 13 (2009), 818 – 821.

Taubman, High-performance scalable image compression with EBCOT, IEEE Trans. Image Processing 9 (7) (2000), 1158 – 1170.

C. Tzong-Jer and C. Keh-Shih, A pseudo lossless image Compression Method, Image and Signal Processing (CISP), 3rd International Congress, Vol. 2, pp. 610 – 615 (2010).

B.E. Usevith, A tutorial on modern lossy wavelet image compression: a foundation of JPEG 2000, IEEE Signal Processing. Mag. 22 – 35 (2001).

P. Waldemar and T.A. Ramstad, Hybrid KLT-SVD image compression, IEEE International Conference on Acoustics, Speech, and Signal Processing 4 (1997), 2713 – 2716.

F.W. Wheeler andW.A. Pearlman, SPIHT image compression without list, in Proc. ICASSP Istanbul, Turkey, pp. 2047 – 2050 (2000).




DOI: http://dx.doi.org/10.26713%2Fjims.v10i1-2.498

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