Multiscale Transforms with Application to Image Processing (eBook)

Aparna Vyas was born in Allahabad, India in 1983. She received B.Sc. degree in Science and M.Sc. degree in Mathematics from the University of Allahabad, Allahabad, India in 2004 and 2006, respectively. She received a Ph.D. degree in Mathematics from the University of Allahabad, Allahabad, India in 2010. She was an Assistant Professor, Department of Mathematics, School of Basic Sciences, SHIATS, Deemed University, Allahabad, India, since 2006 to 2013. In 2014, She joined Manav Rachna University, Faridabad, India as an Assistant Professor. She was a Post-Doctoral Fellow at Soongsil University from August 2016 to September 2016. Currently, She is a post-doctoral Fellow in Chung-Ang University under BK21 Plus project. She has more than 10 years of teaching and research experience. She is also a life member of the Indian Mathematical Society and Ramanujan Mathematical Society. Her research interests includes Wavelet Analysis and Image Processing.Soohwan Yu was born in Incheon, Korea, in 1988. He received the B.S. degree in information and communication engineering from Suwon University, Korea, in 2013. He received the M.S degree in image engineering from Chung-Ang University, Korea, in 2016, where he is currently pursuing the Ph.D. degree in image engineering. His research interests include image enhancement, super-resolution, and image restoration.Joonki Paik was born in Seoul, Korea in 1960. He received a B.S. degree in control and instrumentation engineering from Seoul National University in 1984. He received an M.S. and a Ph.D. degrees in electrical engineering and computer science from Northwestern University in 1987 and 1990, respectively. From 1990 to 1993, he worked at Samsung Electronics, where he designed image stabilization chip sets for consumer camcorders. Since 1993, he has been a faculty member at Chung-Ang University, Seoul, South Korea. Currently, he is a professor in the Graduate School of Advanced Imaging Science, Multimedia and Film. From 1999 to 2002, he was a visiting professor in the Department of Electrical and Computer Engineering at the University of Tennessee, Knoxville. Dr. Paik was a recipient of the Chester-Sall Award from the IEEE Consumer Electronics Society, the Academic Award from the Institute of Electronic Engineers of Korea, and the Best Research Professor Award from Chung-Ang University. He has served the Consumer Electronics Society of IEEE as a member of the editorial board. Since 2005 he has been the head of the National Research Laboratory in the eld of image processing and intelligent systems. In 2008 he worked as a full time technical consultant for the System LSI Division at Samsung Electronics, where he developed various computational photographic techniques including an extended depth-of- eld (EDoF) system. From 2005 to 2007, he served as Dean of the Graduate School of Advanced Imaging Science, Multimedia, and Film. From 2005 to 2007, he was Director of the Seoul Future Contents Convergence (SFCC) Cluster established by the Seoul Research and Business Development (R&BD) Program. Dr. Paik is currently serving as a member of the Presidential Advisory Board for Scienti c/Technical Policy for the Korean government and as a technical consultant for the Korean Supreme Prosecutors Office for computational forensics.

I Introduction to Image Processing. 1 Fundamentals of Digital Image Processing. 1.1 Image Acquisition of Digital Camera. 1.1.1 Introduction. 1.2 Sampling. References.II Multiscale Transform.2 Fourier Analysis and Fourier Transform. 2.1 Overview. 2.2 Fourier Series. 2.2.1 Periodic Functions. 2.2.2 Frequency and Amplitude. 2.2.3 Phase. 2.2.4 Fourier Series of Periodic Functions. 2.2.5 Complex form of Fourier Series. 2.3 Fourier Transform. 2.3.1 2D-Fourier Transform. 2.3.2 Properties of Fourier Transform. 2.4 Discrete Fourier Transform. 2.4.1 1D-Discrete Fourier Transform. 2.4.2 Inverse 1D-Discrete Fourier Transform. 2.4.3 2D-Discrete Fourier Transform and 2D-Inverse Discrete Fourier Transform. 2.4.4 Properties of 2D-Discrete Fourier transform. 2.5 Fast Fourier Transform. 2.6 The Discrete Cosine Transform. 2.6.1 1D-Discrete Cosine Transform. 2.6.2 2D-Discrete Cosine Transform. 2.7 Heisenberg Uncertainty Principle. 2.8 Windowed Fourier Transform or Short-Time Fourier Transform. 2.8.1 1D and 2D Short-Time Fourier Transform. 2.8.2 Drawback of Short-Time Fourier Transform. 2.9 Other Spectral Transforms. References 3 Wavelets and Wavelet Transform. 3.1 Overview. 3.2 Wavelets. 3.3 Multiresolution Analysis. 3.4 Wavelet Transform. 3.4.1 The Wavelet Series Expansions. 3.4.2 Discrete Wavelet Transform. 3.4.3 Motivation: From MRA to Discrete Wavelet Transform. 3.4.4 The Quadrature Mirror Filter Conditions. 3.5 The Fast Wavelet Transform. 3.6 Why Use Wavelet. Transforms. 3.7 Two-Dimensional Wavelets. 3.8 2D-discrete Wavelet Transform. 3.9 Continuous Wavelet Transform. 3.9.1 1D Continuous Wavelet Transform. 3.9.2 2D Continuous Wavelet Transform. 3.10 Undecimated Wavelet Transform or Stationary Wavelet Transform. 3.11 Biorthogonal Wavelet Transform. 3.11.1 Linear Independence and Biorthogonality. 3.11.2 Dual MRA. 3.11.3 Discrete Transform for Biorthogonal Wavelets. 3.12 Scarcity of Wavelet Transform. 3.13 Complex Wavelet Transform. 3.14 Dual-Tree Complex Wavelet Transform. 3.15 Quaternion Wavelet and Quaternion Wavelet. Transform. 3.15.1 2D Hilbert Trnasform 3.15.2 Quaternion Algebra. 3.15.3 Quaternion Multiresolution Analysis. References.4 New Multiscale Constructions. 4.1 Overview. 4.2 Ridgelet Transform. 4.2.1 The Continuous Ridgelet Transform. 4.2.2 Discrete Ridgelet Transform. 4.2.3 The Orthonormal Finite Ridgelet Transform. 4.2.4 The Fast Slant Stack Ridgelet Transform. 4.2.5 Local Ridgelet Transform. 4.2.6 Sparse Representation by Ridgelets. 4.3 Curvelets. 4.3.1 The First Generation Curvelet Transform .4.3.2 Sparse Representation by First Generation Curvelets. 4.3.3 The Second-Generation Curvelet Transform. 4.3.4 Sparse Representation by Second Generation Curvelets. 4.4 Contourlet. 4.5 Contourlet Transform. 4.5.1 Multiscale Decomposition. 4.5.2 Directional Decomposition. 4.5.3 The Discrete Contourlet Transform. 4.6 Shearlet. 4.7 Shearlet Transform. 4.7.1 Continuous Shearlet Transform. 4.7.2 Discrete Shearlet Transform. 4.7.3 Cone-Adapted Continuous Shearlet Transform. 4.7.4 Cone-Adapted Discrete Shearlet Transform. 4.7.5 Compactly Supported Shearlets. 4.7.6 Sparse Representation by Shearlets. References. III Application of Multiscale transforms to Image Processing5 Image Restoration. 5.1 Model of image degradation and restoration process. 5.2 Image Quality Assessments Metrics. 5.3 Image Denoising. 5.4 Noise Models. 5.4.1 Additive Noise Model. 5.4.2 Multiplicative Noise Model. 5.5 Types of Noise. 5.5.1 Amplier(Gaussian) Noise. 5.5.2 Rayleigh Noise. 5.5.3 Uniform Noise. 5.5.4 Impulsive(Salt and Pepper) Noise. 5.5.5 Exponential Noise. 5.5.6 Speckle Noise. 5.6 Image Deblurring. 5.6.1 Gaussian Blur. 5.6.2 Motion Blur. 5.6.3 Rectangular Blur. 5.6.4 Defocus Blur. 5.7 Superresolution. 5.8 Classication of Image Restoration Algorithms. 5.8.1 Spatial Filtering. 5.8.2 Frequency Domain Filtering. 5.8.3 Direct Inverse Filtering. 5.8.4 Constraint Least-Square Filter. 5.8.5 IBD (Iterative Blind Deconvolution). 5.8.6 NAS-RIF (Nonnegative and Support Constraints Recursive InverseFiltering). 5.8.7 Superresolution Restoration Algorithm Based on Gradient Adaptive Interpolation. 5.8.8 Deconvolution Using a Sparse Prior. 5.8.9 Block-matching. 5.8.10 LPA-ICI algorithm. 5.8.11 Deconvolution using Regularized Filter (DRF). 5.8.12 Lucy-Richardson Algorithm. 5.8.13 Neural Network Approach. 5.9 Application of Multiscale Transform in Image Restoration. 5.9.1 Image Restoration using Wavelet Transform. 5.9.2 Image Restoration using Complex Wavelet Transform. 5.9.3 Image Restoration using Quaternion Wavelet Transform. 5.9.4 Image Restoration using Ridgelet Transform. 5.9.5 Image Restoration using Curvelet Transform. 5.9.6 Image Restoration using Contourlet Transform. 5.9.7 Image Restoration using Shearlet Transform. References.6 Image Enhancement. 6.1 Overview. 6.2 Spatial Domain Image Enhancement Techniques. 6.2.1 Gray Level Transformation. 6.2.2 Piecewise-Linear Transformation Functions. 6.2.3 Histogram Processing. 6.2.4 Spatial Filtering. 6.3 Frequency Domain Image Enhancement Techniques. 6.3.1 Smoothing Filters. 6.3.2 Sharpening Filters. 6.3.3 Homomorphic Filtering. 6.4 Colour Image Enhancement. 6.5 Application of Multiscale Transforms in Image Enhancement. 6.5.1 Image Enhancement using Fourier Transform. 6.5.2 Image Enhancement using Wavelet Transform. 6.5.3 Image Enhancement using Complex Wavelet Transform. 6.5.4 Image Enhancement using Curvelet transform. 6.5.5 Image Enhancement using Contourlet transform. 6.5.6 Image Enhancement using Shearlet transform. References.Appendix A Real and Complex Number System.Appendix B Vector Space.Appendix C Linear Transformation, Matrices.Appendix D Inner Product Space and Orthonormal Basis.Appendix E Functions and Convergence. E.1 Functions. E.2 Convergence of Functions.Index.