Open Access Open Access  Restricted Access Subscription Access

Image Compression via Non-separable Discrete Fractional Fourier Transform

Kritika Mittal

Abstract


The main idea behind image compression is to reduce the bandwidth for transmission and required space for storage. Thus, image compression is of great importance. In this paper we present the image compression technique using Non-Separable Discrete Fractional Fourier Transform (NSDFrFT). Numerical simulation results suggested that image compression method using NSDFrFT as transform technique gives better performance for images when compression ratio is high in comparison to DFrFT and JPEG. Different image quality measurement methods such as Gradient Magnitude Similarity Deviation (GMSD), Mean Structural Similarity Index Measure (MSSIM), Mean Squared Error (MSE) and Peak Signal to Noise Ratio (PSNR) are used to determine the performance.

Cite this Article
Kritika Mittal. Image Compression via Non-Separable Discrete Fractional Fourier Transform. Research & Reviews: Discrete Mathematical Structures. 2015; 2(3): 1–9p.




Keywords


Image Compression, NSDFrFT, GMSD, MSSIM, MSE

Full Text:

PDF

References


McIntyre KA. Dynamic Bandwidth Adaptive Image Compression/ Decompression Scheme. U.S. Patent 7024045. 2006.

Yng T L B, Lee BG, Yoo H. A Low Complexity and Lossless Frame Memory Compression for Display Devices. IEEE Trans. Consumer Electronics. 2008; 54 (3):1453–1458p.

Shukla J, Alwani M, Tiwari AK. A Survey on Lossless Image Compression Methods. Proc. 2nd International Conference on Computer Engineering and Technology (ICCET). 2010; 6: 136–141p.

Jayaraman S, Esakkirajan S, Veerakumar T. Digital Image Processing. Tata McGraw-Hill Education. 2011.

Gonzalez RC, Woods RE. Digital Image Processing. 3rd edition. 2008.

Thyagarajan KS. Still Image and Video Compression with MATLAB. John Wiley & Sons, Inc. Hoboken, New Jersey. 2011.

Skodras A, Christopoulos C, Ebrahimi T. The JPEG 2000 still Image Compression Standard. IEEE Trans. Signal Processing. 2001; 18 (5): 36–58p.

Watson AB. Image Compression using the Discrete Cosine Transform. Mathematica Journal. 1994; 4 (1): 81–88p.

Jindal N, Singh K. Image and Video Processing using Discrete Fractional Transforms. Signal, Image and Video Processing. 2012; DOI: 10.1007/s11760-012-0391-4.

Singh K. Performance of Discrete Fractional Fourier Transform Classes in Signal Processing Applications. Ph.D. Thesis, Department of Electronics and Communication Engineering, Thapar University, Patiala, India. 2005.

Grgic S, Grgic M, Cihlar BZ. Performance Analysis of Image Compression using wavelets. IEEE Trans. Industrial Electronics. 2001; 48 (3): 682–695p.

Namias V. The Fractional Order Fourier Transform and its Applications to Quantum Mechanics. IMA Journal of Applied Mathematics. 1980; 25 (3): 241–265p.

Cariolario G, Ersrghe T, Kraniauskas P, Laurenti N. A unified framework for the fractional fourier transform. IEEE Trans. Signal Processing. 1998; 46 (12): 3206–3212p.

Santhanam B, McClellan JH. The DFRFT-A Rotation in Time Frequency Space. Proc. 20th International Conference of Acoustics, Speech Signal Processing. 1995; 2: 921–924p.

Pei SC, Yeh MH. Discrete Fractional Fourier Transform. Proc. IEEE International Symposium on Circuits and Systems. 1996; 2: 536–539p.

Koc A, Ozaktas HM, Hesselink L. Fast and accurate computation of two-dimensional non-separable quadratic-phase integrals. Journal of the Optical Society of America A. 2010; 27: 1288–1302p.

Ding JJ, Pei SC. Heisenberg’s uncertainty principles for the 2-D nonseparable linear canonical transforms. Signal Processing; 2013; 93: 1027–1043p.

Ozaktas HM, Zalevsky Z, Kutay MA. The fractional Fourier Transform with Applications in Optics and Signal processing. John Wiley & Sons Ltd., New York. 2000.

Almeida BL. The fractional Fourier transform and time–frequency representations. IEEE Trans. Signal Processing. 1994; 42: 3084–3091p.

Sahin A, Kutay MA, Ozaktus HM. Nonseparable two-dimensional fractional Fourier transform. Journal of the Optical Society of America A. 1998; 37 (23): 5444–5453p.

Richardson IEG. H.264and MPEG-4 Video Compression, John Wiley & Sons. Inc. West Sussex, England. 2003.

Xue W, Zhang L, Mou X, Bovik AC. Gradeint Magnitude Similarity Deviation: An Highly Efficient Perceptual Image Quality Index. IEEE Trans. Image Processing. 2014; 23 (2): 684–695p.

Whang Z, Bovik AC, Sheikh HR, Simoncelli EP. Image Quality Assessment: From Error Visibility to Structural Similarity. IEEE Trans. Image Processing. 2004; 13 (4): 600–612p.

Parker JA, Kenyon RV, Troxel DE. Comparison of Interpolating Methods for Image Resampling. IEEE Trans. Medical Imaging. 1983; MI-2 (1): 31–39p.

Jindal N. Performance of Fractional Transforms in Image and Video Processing. Ph.D Thesis, Department of Electronics and Communication Engineering, Thapar University, Patiala, India. 2015.

Chen CC. On the selection of image compression algorithms. Proc. IEEE 14th International Conference on Pattern Recognition (ICPR’98). 1988: 1–5p.


Refbacks

  • There are currently no refbacks.


This site has been shifted to https://stmcomputers.stmjournals.com/