Digital Image Denoising in MATLAB provides a comprehensive treatment of digital image denoising, containing a variety of techniques with applications in high-quality photo enhancement as well as multi-dimensional signal processing problems such as array signal processing, radar signal estimation and detection, and more. Offering systematic guidance on image denoising in theories and in practice through MATLAB, this hands-on guide includes practical examples, chapter summaries, analytical and programming problems, computer simulations, and source codes for all algorithms discussed in the book.
The book explains denoising algorithms including linear and nonlinear filtering, Wiener filtering, spatially adaptive and multi-channel processing, transform and wavelet domains processing, singular value decomposition, and various low variance optimization and low rank processing techniques. Throughout the text, the authors address the theory, analysis, and implementation of the denoising algorithms to help readers solve their image processing problems and develop their own solutions. - Explains how the quality of an image can be quantified in MATLAB - Discusses what constitutes a “naturally looking” image in subjective and analytical terms - Presents denoising techniques for a wide range of digital image processing applications - Describes the use of denoising as a pre-processing tool for various signal processing applications or big data analysis - Requires only a fundamental knowledge of digital signal processing - Includes access to a companion website with source codes, exercises, and additional resources
Digital Image Denoising in MATLAB is an excellent textbook for undergraduate courses in digital image processing, recognition, and statistical signal processing, and a highly useful reference for researchers and engineers working with digital images, digital video, and other applications requiring denoising techniques.
Table of Contents
Preface vi
Acknowledgments viii
Authors x
Nomenclature xi
1 Digital Image 1
1.1 Color Image 3
1.1.1 Color Filter Array and Demosaicing 5
1.1.2 Perceptual Color Space 5
1.1.3 Grayscale Image 7
1.2 Alternate Domain Image Representation 8
1.3 Digital Imaging in MATLAB 9
1.4 Current Pixel and Neighboring Pixels 10
1.4.1 Boundary Extension 11
1.5 Digital Image Noise 12
1.5.1 Random Noise 13
1.5.2 Gaussian Noise 14
1.5.3 Salt and Pepper Noise 18
1.6 Mixed Noise 19
1.7 Performance Evaluation 21
1.8 Image Quality Measure 22
1.8.1 Mean Squares Error 23
1.8.2 Peak Signal-to-Noise Ratio 25
1.8.3 Texture and Flat PSNR 26
1.8.4 Texture Area Classification 28
1.9 Structural Similarity 30
1.10 Brightness Normalization 33
1.11 Summary 33
1.12 Exercises 34
2 Filtering 36
2.1 Mean Filter 37
2.1.1 Gaussian Smoothing 42
2.2 Wiener Filter 44
2.3 Transform Thresholding 46
2.3.1 Overlapped Block 49
2.4 Median Filter 50
2.4.1 Noise Reduction Performance 52
2.4.2 Adaptive Median Filter 53
2.4.3 Median Filter with Predefined Mask 55
2.4.4 Median of Median 56
2.5 Summary 58
2.6 Exercises 58
3 Wavelet 60
3.1 2D Wavelet Transform 60
3.2 Noise Estimation 62
3.3 Wavelet Denoise 64
3.4 Thresholding 65
3.4.1 Threshold function 66
3.5 Threshold Value 68
3.5.1 Universal Threshold (Donoho Threshold) 68
3.6 Wavelet Wiener 75
3.7 Cycle Spinning 76
3.8 Fusion 80
3.8.1 Baseband Image Fusion 81
3.8.2 Detail Images Fusion 82
3.9 Which Wavelets to Use 85
3.10 Summary 86
3.11 Exercises 87
4 Rank Minimization 88
4.1 Singular Value Decomposition (SVD) 88
4.2 Threshold Denoising through AWGN Analysis 90
4.2.1 Noise Estimation 92
4.2.2 Denoising Performance 93
4.3 Blocked SVD 94
4.4 The Randomized Algorithm 97
4.4.1 Iterative Adjustment 98
4.5 Summary 100
4.6 Exercises 101
5 Variational Method 103
5.1 Total Variation 103
5.1.1 Rudin-Osher-Fatemi (ROF) Model 104
5.1.2 Le-Chartrand-Asaki (LCA) Model 104
5.1.3 Aubert-Aujol (AA) Model 105
5.2 Gradient Descent ROF TV Algorithm 105
5.2.1 Finite Difference Method 106
5.3 Staircase Noise Artifacts 109
5.4 Summary 110
5.5 Exercises 111
6 Nonlocal Means 112
6.1 NonLocal Means 112
6.1.1 Hard Threshold 118
6.2 Adaptive Window Size 120
6.2.1 Patch Window Size Adaptation 121
6.2.2 Search Window Size Adaptation 123
6.3 Summary 125
6.4 Exercises 126
7 Random Sampling 127
7.1 Averaging Multiple Copies of Noisy Images 128
7.2 Missing Pixels and Inpainting 130
7.3 Singular Value Thresholding Inpainting 131
7.4 Wavelet Image Fusion 133
7.5 Summary 135
7.6 Exercises 135
Bibliography 141
Index 142
