Dcblurrinq Images Matrices, Spectra, and Filtering

by Newebug 28. February 2010 01:18

Dcblurrinq Images Matrices, Spectra, and Filtering


Preface ix
How to Get the Software xii
1 The Image Deblurring Problem 1
1.1 How Images Become Arrays of Numbers 2
1.2 A Blurred Picture and a Simple Linear Model 4
1.3 A First Attempt at Deblurring 5
1.4 Deblurring Using a General Linear Model 7
2 Manipulating Images in MATLAB 13
2.1 Image Basics 13
2.2 Reading, Displaying, and Writing Images 14
2.3 Performing Arithmetic on Images 16
2.4 Displaying and Writing Revisited 18
3 The Blurring Function 21
3.1 Taking Bad Pictures 21
3.2 The Matrix in the Mathematical Model 22
3.3 Obtaining the PSF 24
3.4 Noise 28
3.5 Boundary Conditions 29
4 Structured Matrix Computations 33
4.1 Basic Structures 34
4.1.1 One-Dimensional Problems 34
4.1.2 Two-Dimensional Problems 37
4.1.3 Separable Two-Dimensional Blurs 38
4.2 BCCB Matrices 40
4.2.1 Spectral Decomposition of a BCCB Matrix 41
4.2.2 Computations with BCCB Matrices 43
4.3 BTTB + BTHB+BHTB + BHHB Matrices 44
4.4 Kronecker Product Matrices 48
4.4.1 Constructing the Kronecker Product from the PSF . . . . 48
4.4.2 Matrix Computations with Kronecker Products 49
4.5 Summary of Fast Algorithms 51
4.6 Creating Realistic Test Data 52
5 SVD and Spectral Analysis 55
5.1 Introduction to Spectral Filtering 55
5.2 Incorporating Boundary Conditions 57
5.3 SVDAnalysis 58
5.4 The SVD Basis for Image Reconstruction 61
5.5 The DFT and DCT Bases 63
5.6 The Discrete Picard Condition 67
6 Regularization by Spectral Filtering 71
6.1 Two Important Methods 71
6.2 Implementation of Filtering Methods 74
6.3 Regularization Errors and Perturbation Errors 77
6.4 Parameter Choice Methods 79
6.5 Implementation of GCV 82
6.6 Estimating Noise Levels 84
7 Color Images, Smoothing Norms, and Other Topics 87
7.1 A Blurring Model for Color Images 87
7.2 Tikhonov Regularization Revisited 90
7.3 Working with Partial Derivatives 92
7.4 Working with Other Smoothing Norms 96
7.5 Total Variation Deblurring 97
7.6 Blind Deconvolution 99
7.7 When Spectral Methods Cannot Be Applied 100

Appendix: MATLAB Functions 103
1. TSVD Regularization Methods 103
  Periodic Boundary Conditions 103
  Reflexive Boundary Conditions 104
  Separable Two-Dimensional Blur 106
  Choosing Regularization Parameters 107
2. Tikhonov Regularization Methods 108
  Periodic Boundary Conditions 108
  Reflexive Boundary Conditions 109
  Separable Two-Dimensional Blur Ill
  Choosing Regularization Parameters 112
3. Auxiliary Functions 113
  Bibliography 121
Index 127

Dcblurrinq Images Matrices, Spectra, and Filtering 下载:

Deblurring-Images-Matrices-Spectra-and-Filtering-Fundamentals-of-Algorithms.rar (6.34 MB)


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