Applicability of fractional transforms in image processing - review, technical challenges and future trends

Fractional transforms not only enhance the overall signal processing applications but also improved the efficacy of systems. In this paper, we focus to present several image processing techniques using fractional transforms under one umbrella. The primary motive of this paper is to study the image related literature survey, formats, noises, performance parameters, websites and open issues to encourage further research in this area. The paper first describes fractional transforms and in the second part, we provide comprehensive and exhaustive details on the use of these transforms in image processing. Specific topics include image compression, encryption, enhancement, rotation, watermarking etc. Some technical image processing challenges like thresholding, CPU time etc., are also discussed with a future scope.

[1]  Valero Laparra,et al.  End-to-end Optimized Image Compression , 2016, ICLR.

[2]  Luming Zhang,et al.  Action2Activity: Recognizing Complex Activities from Sensor Data , 2015, IJCAI.

[3]  D. Sharma,et al.  Image Encryption Using Discrete Fourier Transform and Fractional Fourier Transform , 2013 .

[4]  Batuhan Hangun,et al.  Performance Comparison Between OpenCV Built in CPU and GPU Functions on Image Processing Operations , 2017 .

[5]  Almas Abbasi,et al.  Robust Image Watermarking using Fractional Sinc Transformation , 2016 .

[6]  Nanrun Zhou,et al.  Image encryption algorithm by using the logistic map and discrete fractional angular transform , 2017 .

[7]  N. Wiener.  Hermitian Polynomials and Fourier Analysis , 1929 .

[8]  Madhusudan Joshi,et al.  Color image encryption and decryption using fractional Fourier transform , 2007 .

[9]  瑞华 曹,et al.  傅里叶变换及其应用 The Fourier Transform and Its Application , 2014 .

[10]  Hoon Yoo,et al.  A low complexity and lossless frame memory compression for display devices , 2008, IEEE Transactions on Consumer Electronics.

[11]  J García,et al.  Fractional wavelet transform. , 1997, Applied optics.

[12]  Xue Mei Li.  Image enhancement in the fractional Fourier domain , 2013, 2013 6th International Congress on Image and Signal Processing (CISP).

[13]  Shishir Kumar,et al.  Mathematical transforms and image compression: A review , 2010 .

[14]  Naveen K. Nishchal,et al.  Image encryption and authentication verification using fractional nonconventional joint transform correlator , 2012 .

[15]  E. Condon,et al.  Immersion of the Fourier Transform in a Continuous Group of Functional Transformations. , 1937, Proceedings of the National Academy of Sciences of the United States of America.

[16]  Martin Reisslein,et al.  Performance evaluation of the fractional wavelet filter: A low-memory image wavelet transform for multimedia sensor networks , 2011, Ad Hoc Networks.

[17]  M. Alper Kutay,et al.  Optimal image restoration with the fractional Fourier transform , 1998 .

[18]  Ingemar J. Cox,et al.  Secure spread spectrum watermarking for images, audio and video , 1996, Proceedings of 3rd IEEE International Conference on Image Processing.

[19]  Zou Xuecheng,et al.  Blurred defocused image restoration based on FRFT , 2007 .

[20]  Kehar Singh,et al.  Image encryption using fractional Mellin transform, structured phase filters, and phase retrieval , 2014 .

[21]  Mamta Sharma,et al.  Compression Using Huffman Coding , 2010 .

[22]  Chien-Cheng Tseng,et al.  Discrete fractional Fourier transform based on orthogonal projections , 1999, IEEE Trans. Signal Process..

[24]  Bing-Zhao Li,et al.  Image Watermarking in the Linear Canonical Transform Domain , 2014 .

[25]  Naveen K. Nishchal.  Optical image watermarking using fractional Fourier transform , 2009 .

[26]  K. Thanushkodi,et al.  A Secure Fast 2D-Discrete Fractional Fourier Transform Based Medical Image Compression Using SPIHT Algorithm with Huffman Encoder , 2013 .

[27]  Rajiv Saxena,et al.  Hybrid Encryption-Compression Scheme Based on Multiple Parameter Discrete Fractional Fourier Transform with Eigen Vector Decomposition Algorithm , 2014 .

[28]  Mislav Grgic,et al.  Performance analysis of image compression using wavelets , 2001, IEEE Trans. Ind. Electron..

[29]  B. Jadhav,et al.  Analysis of various change detection techniques using satellite images , 2015, 2015 International Conference on Information Processing (ICIP).

[30]  Rajesh Kumar,et al.  A Semi-Blind Reference Watermarking Scheme Using DWT-SVD for Copyright Protection , 2011 .

[31]  Sanjay Kumar,et al.  Fractional Fourier Transform and Fractional-Order Calculus-Based Image Edge Detection , 2017, Circuits Syst. Signal Process..

[32]  Di Wang,et al.  Image compression and encryption scheme based on 2D compressive sensing and fractional Mellin transform , 2015 .

[33]  Feng Zhang,et al.  Image restoration method based on fractional variable order differential , 2018, Multidimens. Syst. Signal Process..

[34]  Neeru Jindal,et al.  Image and video processing using discrete fractional transforms , 2014, Signal Image Video Process..

[35]  Anil K. Jain.  Fundamentals of Digital Image Processing , 2018, Control of Color Imaging Systems.

[36]  R. Hudec,et al.  The comparison of CPU time consumption for image processing algorithm in Matlab and OpenCV , 2012, 2012 ELEKTRO.

[37]  Zeev Zalevsky,et al.  Some important fractional transformations for signal processing , 1996 .

[38]  Kulbir Singh,et al.  Image Change Detection using Discrete Fractional Fourier Transform along with Intensity Normalization and Thresholding , 2015 .

[39]  Rajiv Saxena,et al.  Image Compression Based On Multiple Parameter Discrete Fractional Fourier Transform for Satellite and Medical Images , 2014 .

[40]  Kulbir Singh,et al.  Image Change Detection by Means of Discrete Fractional Fourier Transform , 2013 .

[41]  Kulbir Singh,et al.  Image Compression by Using Fractional Transforms , 2009, 2009 International Conference on Advances in Recent Technologies in Communication and Computing.

[42]  Aloka Sinha,et al.  Image encryption by using fractional fourier transform and jigsaw transform in image bit planes , 2005 .

[43]  Angshul Majumdar.  Image compression by sparse PCA coding in curvelet domain , 2009, Signal Image Video Process..

[44]  Roberto Mecca,et al.  Fractional-order diffusion for image reconstruction , 2012, 2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[45]  Manoj Alwani,et al.  A survey on lossless image compression methods , 2010, 2010 2nd International Conference on Computer Engineering and Technology.

[46]  Vivek Arya,et al.  Image Compression Algorithm Using Two Dimensional Discrete Cosine Transform , 2016 .

[47]  Amr M. Youssef,et al.  On the security of image encryption schemes based on Multiple Parameters Transforms , 2010, The 10th IEEE International Symposium on Signal Processing and Information Technology.

[48]  M. El-Kordy,et al.  Target Image Enhancement in Radar Imaging Using Fractional Fourier Transform , 2012 .

[49]  Rafael C. González,et al.  Digital image processing, 3rd Edition , 2008 .

[50]  Sanjay J. Bagul,et al.  Color Image Compression Using Discrete Fractional Fourier Transform , 2014 .

[51]  Imam Samil Yetik,et al.  Continuous and discrete fractional Fourier domain decomposition , 2000, 2000 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.00CH37100).

[52]  Khaled Sahnoun,et al.  SATELLITE IMAGE COMPRESSION ALGORITHM BASED ON THE FFT , 2014 .

[53]  Ingemar J. Cox,et al.  Secure spread spectrum watermarking for multimedia , 1997, IEEE Trans. Image Process..

[54]  Ran Tao,et al.  Research progress of the fractional Fourier transform in signal processing , 2006, Science in China Series F.

[55]  H. Kober.  WURZELN AUS DER HANKEL-, FOURIER-UND AUS ANDEREN STETIGEN TRANSFORMATIONEN , 1939 .

[56]  Luming Zhang,et al.  Fortune Teller: Predicting Your Career Path , 2016, AAAI.

[57]  Z. Zalevsky,et al.  The Fractional Fourier Transform: with Applications in Optics and Signal Processing , 2001 .

[58]  S. Suresh Raja,et al.  A Review on Different Image Encryption Techniques for Secure Image Transmission , 2014 .

[59]  John T. Sheridan,et al.  Optical image encryption by random shifting in fractional Fourier domains. , 2003, Optics letters.

[60]  Kulbir Singh,et al.  Transform domain robust image-adaptive watermarking: Prevalent techniques and their evaluation , 2015, International Conference on Computing, Communication & Automation.

[61]  Lakhwinder Kaur,et al.  A novel robust logo watermarking scheme using fractional M-band wavelet transform , 2014 .

[62]  S. Ganorkar,et al.  Color Image Enhancement using Discrete Wavelet Transform , 2012 .

[63]  M. Alper Kutay,et al.  Image representation and compression with the fractional Fourier transform , 2001 .

[64]  John T. Sheridan,et al.  Fractional Fourier transform-based image encryption: phase retrieval algorithm , 2003 .

[65]  C. Vijaya,et al.  Signal compression using discrete fractional Fourier transform and set partitioning in hierarchical tree , 2006, Signal Process..

[66]  Naveen K. Nishchal,et al.  Digital Fresnel hologram watermarking , 2010, 2010 9th Euro-American Workshop on Information Optics.

[67]  Manish Kumar,et al.  Color image encoding using fractional Fourier transformation associated with wavelet transformation , 2012 .

[68]  Parvinder Kaur.  Image Compression Using Fractional Fourier Transform , 2007 .

[69]  Levent Onural,et al.  Optimal filtering in fractional Fourier domains , 1997, IEEE Trans. Signal Process..

[70]  Kulbir Singh,et al.  Fractional M-band dual tree complex wavelet transform for digital watermarking , 2014 .

[71]  Hamid A. Jalab,et al.  Liver CT enhancement using Fractional Differentiation and Integration , 2016 .

[72]  Jiawang Yi,et al.  Optical compression and encryption system combining multiple measurement matrices with fractional Fourier transform. , 2015, Applied optics.

[73]  Cagatay Candan,et al.  The discrete fractional Fourier transform , 2000, IEEE Trans. Signal Process..

[74]  X. Li,et al.  A novel method of image enhancement based on the fractional Fourier transform , 2014, 2014 7th International Congress on Image and Signal Processing.

[75]  Soo-Chang Pei,et al.  The discrete fractional cosine and sine transforms , 2001, IEEE Trans. Signal Process..

[76]  V. Namias.  The Fractional Order Fourier Transform and its Application to Quantum Mechanics , 1980 .

[77]  Andrew B. Watson,et al.  Image Compression Using the Discrete Cosine Transform , 1994 .

[78]  Lin Wei,et al.  SAR Image Enhancement Based On Fractional Fourier Transform , 2015 .

[79]  Ioannis Pitas,et al.  Protecting Digital-Image Copyrights: A Framework , 1999, IEEE Computer Graphics and Applications.

[80]  Lei Xu,et al.  Image Encryption Based on the Iterative Fractional Fourier Transform and a Novel Pixel Scrambling Technique , 2015 .

[81]  Ammar Sameer Anaz,et al.  Comparison between Open CV and MATLAB Performance in Real Time Applications , 2015 .

[82]  Jiasong Wu,et al.  Fractional Krawtchouk Transform With an Application to Image Watermarking , 2017, IEEE Transactions on Signal Processing.

[83]  Indu Saini,et al.  Optical image encryption in the fractional Hartley domain, using Arnold transform and singular value decomposition , 2017 .

[84]  Dinesh Goyal,et al.  Improved Digital Image Watermarking Algorithm Based on Hybrid DWT-FFT and SVD Techniques , 2017 .

[85]  Billur Barshan,et al.  Signal recovery from partial fractional Fourier domain information and its applications , 2008 .

[86]  Hong Liu,et al.  Image restoration based on the discrete fraction Fourier transform , 2001, International Symposium on Multispectral Image Processing and Pattern Recognition.

[87]  Narendra Singh,et al.  Optical image encryption using fractional Fourier transform and chaos , 2008 .

[88]  Mahendra Kumar,et al.  Digital image watermarking using fractional fourier transform via image compression , 2013, 2013 IEEE International Conference on Computational Intelligence and Computing Research.

[89]  Prerana Sharma,et al.  Efficient image encryption and decryption using discrete wavelet transform and fractional Fourier transform , 2012, SIN '12.

[90]  Manish Jain,et al.  Digital Image Watermarking using 3-Level DWT and FFT via Image Compression , 2015 .

[91]  Kamalesh Kumar Sharma,et al.  Investigations on use of fractional Fourier transform for image restoration in the Wiener and geometric mean filters , 2013, Other Conferences.

[92]  Naveen K. Nishchal,et al.  Three-Dimensional Image Watermarking Using Fractional Fourier Transform , 2009 .

[93]  Cesar Torres,et al.  Image encryption using the fractional wavelet transform , 2011 .

[94]  Ioannis Pitas,et al.  Digital watermarking in the fractional Fourier transformation domain , 2001, J. Netw. Comput. Appl..

[95]  Chaur-Chin Chen.  On the selection of image compression algorithms , 1998, Proceedings. Fourteenth International Conference on Pattern Recognition (Cat. No.98EX170).

[96]  Rajinder Kumar,et al.  Satellite Image Compression using Fractional Fourier Transform , 2012 .

[97]  Mauro Barni,et al.  A DCT-domain system for robust image watermarking , 1998, Signal Process..

[98]  Sanjay Kumar,et al.  Security and Privacy in Cloud Computing with Vision Trends and Challenges , 2017 .

[99]  S. Arivazhagan,et al.  Multiple Image Encryption using Fractional Multiresolution Transforms , 2015 .

[100]  M. Tech Scholar,et al.  An efficient image compression algorithm with reduced complexity , 2013 .

[101]  I P Skirnevskiy,et al.  Digital image processing using parallel computing based on CUDA technology , 2017 .

[102]  Soo-Chang Pei,et al.  Closed-form discrete fractional and affine Fourier transforms , 2000, IEEE Trans. Signal Process..

[103]  Ke Chen,et al.  A Total Fractional-Order Variation Model for Image Restoration with Nonhomogeneous Boundary Conditions and Its Numerical Solution , 2015, SIAM J. Imaging Sci..

[104]  David S. Rosenblum,et al.  From action to activity: Sensor-based activity recognition , 2016, Neurocomputing.

[105]  R. Saxena,et al.  Robust Image Encryption Using Discrete Fractional Fourier Transform with Eigen Vector Decomposition Algorithm , 2013 .

[106]  Eunsung Lee,et al.  Wavelet-domain color image enhancement using filtered directional bases and frequency-adaptive shrinkage , 2010, IEEE Transactions on Consumer Electronics.

[107]  Rajiv Saxena,et al.  A Novel Image Encryption Scheme based on Multiple Parameter Discrete Fractional Fourier Transform , 2014 .

[108]  James H. McClellan,et al.  The discrete rotational Fourier transform , 1996, IEEE Trans. Signal Process..

[109]  N VijayaKumarC,et al.  Performance Analysis of Image Compression Using Discrete Wavelet Transform , 2017 .

[110]  Madalina Barbu,et al.  Sonar signal enhancement using fractional Fourier transform , 2005, SPIE Defense + Commercial Sensing.

[111]  Kulbir Singh,et al.  Robust image-adaptive watermarking using an adjustable dynamic strength factor , 2015, Signal Image Video Process..

[112]  Touradj Ebrahimi,et al.  The JPEG 2000 still image compression standard , 2001, IEEE Signal Process. Mag..

[113]  Kulbir Singh,et al.  Joint image compression–encryption using discrete fractional transforms , 2014 .