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List of Figures

Page No.

1.1 Time-Frequency Resolution 11

2.1 Ridgelet Transform flow graph 20

2.2 Flow graph of curvelet transform 31

2.3 Overview of organization of the curvelet transform 34

2.4 Spatial decomposition of a single subband 35

2.5 Big Mac image and stages of curvelet analysis 35

2.6 Curvelet coefficients and stages of curvelet synthesis 37

2.7 Representation of a few curvelets at two different scales 41

2.8 Curvelet Coefficients Analysis(Image-1) 46

2.9 Curvelet Coefficients Analysis(Image-2) 46

2.10 Curvelet Coefficients Analysis(Image-3) 46

3.1 A Transform coding 48

3.2 Existing Quantizer 51

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3.3 Proposed Quantizer with K=0.6 and M=0.5 53

3.4 Proposed Quantizer with K=0.7 and M=0.4 54

3.5 Proposed Quantizer with K=0.8 and M=0.3 54

3.6 Barbara Image for Compression Ratio of 1:20 59

3.7 PSNR Vs Compression Ratio Plot(Barbara image) 60

3.8 Bit rate Vs PSNR Plot(Barbara image) 60

3.9 Building image for compression ratio of 1:100 62

3.10 PSNR Vs Compression Ratio Plot(Building image) 63

3.11 Bit rate Vs PSNR Plot(Building image) 63

3.12 Textured image for compression ratio of 1:100 65

3.13 PSNR Vs Compression Ratio Plot(Textured image) 66

3.14 Bit rate Vs PSNR Plot(Textured image) 66

4.1 Denoising system using transform techniques 69

4.2 Problem formulation and proposed method for denoising 72

4.3 Thresholding for the Gaussian prior 80

4.4 Thresholding for the Laplacian prior 82

4.5 Thresholding for the Generalized Gaussian prior 84

4.6 Lenna image added with different types of noises 91

4.7 Standard deviation Vs PSNR plot(Lenna image) 92

4.8 Building image added with different types of noises 94

4.9 Standard deviation Vs PSNR plot(Building image) 95

4.10 Textured image added with different types of noises 97

4.11 Standard deviation Vs PSNR plot(Textured image) 98

5.1 Fingerprint images corresponding to SD of 0.3 103

5.2 Comparative plots of PSNR vs SD 104

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6.1 Problem formulation and proposed method for denoising 107

6.2 Lenna image added with different types of noises 111

6.3 Standard deviation Vs PSNR plot(Lenna image) 112

6.4 Building image added with different types of noises 115

6.5 Standard deviation Vs PSNR plot(Building image) 116

6.6 Textured image added with different types of noises 119

6.7 Standard deviation Vs PSNR plot(Textured image) 120

List of Tables

Page No.

3.1 PSNR Vs Compression ratio for various algorithms

w.r.t. Barbara image. 61

3.2 PSNR Vs Compression ratio for various algorithms

w.r.t. Building image. 64

3.3 PSNR Vs Compression ratio for various algorithms

w.r.t. Textured image. 67

4.1 Comparison of PSNR w.r.t SD for Lenna image. 93

4.2 Comparison of PSNR w.r.t SD for Building image. 96

4.3 Comparison of PSNR w.r.t SD for Textured image. 99

5.1 PSNR for different types of noise. 102

6.1a Comparison of PSNR w.r.t SD for Gaussian noise

(Lenna image). 113

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6.1b Comparison of PSNR w.r.t SD for Speckle noise

(Lenna image). 113

6.1c Comparison of PSNR w.r.t SD for Salt & Pepper noise

(Lenna image).

114

6.2a Comparison of PSNR w.r.t SD for Gaussian noise

(Building image). 117

6.2b Comparison of PSNR w.r.t SD for Speckle noise

(Building image). 117

6.2c Comparison of PSNR w.r.t SD for Salt & Pepper noise

(Building image). 118

6.3a Comparison of PSNR w.r.t SD for Gaussian noise

(Textured image). 121

6.3b Comparison of PSNR w.r.t SD for Speckle noise

(Textured image). 121

6.3c Comparison of PSNR w.r.t SD for Salt & Pepper noise

(Textured image). 122

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