Digital Image Denoising in MATLAB

Chi-Wah Kok is the Founder and Executive Director of Canaan Semiconductor Pty Ltd, South Australia, Australia. He has worked with leading semiconductor companies, multimedia signal processing companies, research institutions, and universities including AT&T Labs Research, SONY Research Labs, Stanford University, and Hong Kong University of Science and Technology. Dr. Kok’s research interests include the application of signal processing methods in multimedia signal processing problems, solid state circuit design and modeling problems, and other real world problems. Wing-Shan Tam is the Founder and Engineering Manager of Canaan Semiconductor Pty Ltd, South Australia, Australia, where she works on advanced CMOS sensor design and high-power device structure and process development. Dr Tam’s research interests include mixed-signal integrated circuit design and image interpolation and color enhancement algorithm development.

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