sparse image representation via combined transforms - Convex ...
sparse image representation via combined transforms - Convex ... sparse image representation via combined transforms - Convex ...
xviii
List of Tables 3.1 Comparison of transforms and the image features that they are good at processing. The third column lists the order of computational complexity for their discrete fast algorithms. .......................... 26 3.2 DefinitionsoffourtypesofDCTs. ....................... 39 3.3 Number of multiplications and additions for various fast one-D DCT/IDCT algorithms. The number in {·}is the value when N is equal to 8. . . . . 42 3.4 Decomposition of covariance matrix that can be diagonalized by different typesofDCT. .................................. 50 6.1 Table of Running Times . . . .......................... 127 A.1 Percentages of edgelet coefficients being used in the reconstructions. . . . . 137 A.2 Order of edgelets within a square. . . ...................... 145 B.1 Pairsoftransformsandtheiradjoint...................... 160 xix
- Page 1 and 2: SPARSE IMAGE REPRESENTATION VIA COM
- Page 3: I certify that I have read this dis
- Page 7 and 8: To find a sparse image representati
- Page 9: Abstract We consider sparse image d
- Page 12 and 13: xii
- Page 14 and 15: 2.3 Discussion.....................
- Page 16 and 17: 6 Simulations 119 6.1 Dictionary...
- Page 21 and 22: List of Figures 2.1 Shannon’s sch
- Page 23 and 24: A.3 Edgelet transform of the wood g
- Page 25 and 26: Nomenclature Special sets N .......
- Page 27 and 28: List of Abbreviations BCR .........
- Page 29 and 30: Chapter 1 Introduction 1.1 Overview
- Page 31 and 32: Chapter 2 Sparsity in Image Coding
- Page 33 and 34: 2.1. IMAGE CODING 5 INFORMATION SOU
- Page 35 and 36: 2.1. IMAGE CODING 7 2.1.2 Source an
- Page 37 and 38: 2.1. IMAGE CODING 9 x ✲ T y ERROR
- Page 39 and 40: 2.1. IMAGE CODING 11 where Q stands
- Page 41 and 42: 2.2. SPARSITY AND COMPRESSION 13 Pr
- Page 43 and 44: 2.2. SPARSITY AND COMPRESSION 15 av
- Page 45 and 46: 2.2. SPARSITY AND COMPRESSION 17 wi
- Page 47 and 48: 2.2. SPARSITY AND COMPRESSION 19 lo
- Page 49 and 50: 2.3. DISCUSSION 21 tail compact. Th
- Page 51 and 52: 2.4. PROOF 23 The index l does not
- Page 53 and 54: Chapter 3 Image Transforms and Imag
- Page 55 and 56: 27 Some of the figures show the bas
- Page 57 and 58: 3.1. DCT AND HOMOGENEOUS COMPONENTS
- Page 59 and 60: 3.1. DCT AND HOMOGENEOUS COMPONENTS
- Page 61 and 62: 3.1. DCT AND HOMOGENEOUS COMPONENTS
- Page 63 and 64: 3.1. DCT AND HOMOGENEOUS COMPONENTS
- Page 65 and 66: 3.1. DCT AND HOMOGENEOUS COMPONENTS
- Page 67 and 68: 3.1. DCT AND HOMOGENEOUS COMPONENTS
xviii