A FAST AND ROBUST FRAMEWORK FOR IMAGE FUSION AND ...

More documents

Recommendations

Info

a b c Figure 1.3: Super-resolution experiment on real world data. A set of 26 low quality images were fused resulting in a higher quality image. One captured image is shown in (a). The red square section of (a) is zoomed in (b). Super-resolved image in (c) is the high quality output image. However, we shall see that in general, super resolution is a computationally complex and numer- ically ill-posed problem 2 . All this makes super-resolution one of the most appealing research areas in image processing. 1.1 Super-Resolution as an Inverse Problem Super-resolution algorithms attempt to extract the high resolution image corrupted by the limitations of an optical imaging system. This type of problem is an example of an inverse problem, wherein the source of information (high resolution image) is estimated from the observed data (low resolution image or images). Solving an inverse problem in general requires first constructing a forward model. By far, the most common forward model for the 2 Let ϖ : φ1 −→ φ2, Y = ϖ(X) is said to be well-posed [9] if 1. for Y ∈ φ2 there exists X ∈ φ1, called a solution, for which Y = ϖ(X) holds. 2. the solution X is unique. 3. the solution is stable with respect to perturbations in Y . This means that if Y = ϖ(X)and ˘ Y = ϖ( ˇ X) then X → ˇX whenever Y → ˇY . A problem that is not well-posed is said to be ill-posed. 5
problem of super-resolution is linear in form Y = MX + V , (1.1) where Y is the measured data (single or collection of images), X is the unknown high resolution image or images, V is the random noise inherent to any imaging system.We use the underscore notation such as X to indicate a vector. In this formulation, the image is represented in vector form by scanning the 2-D image in a raster or any other scanning format 3 to 1-D. The matrix M in the above forward model represents the imaging system, consisting of several processes that affect the quality of the estimated images. The simplest form of M is the identity matrix, which simplifies the problem at hand to a simple denoising problem. More interesting (and harder to solve) problems can be defined by considering more complex models for M. For example, to define the grey-scale super-resolution problem in Chapter 2, we consider an imaging system that consists of the blur, warp, and down-sampling processes. Moreover, addition of the color filtering process to the later model, enables us to solve for the multi-frame demosaicing problem defined in Chapter 3. Aside from some special cases where the imaging system can be physically measured on the scene, we are bound to estimate the system matrix M from the data. In the first few chapters of this thesis (Chapters 2-4), we assume that M is given or estimated in a separate process. However, we acknowledge that such estimation is prone to errors, and design our methods considering this fact. We will discuss this in detail in the next chapter. Armed with a forward model, a clean but practically naive solution to (1.1) can be achieved via the direct pseudo-inverse technique: X = � M T M � −1 M T Y . (1.2) Unfortunately, the dimensions of the matrix M (as explicitly defined in the next chapters) is so large that even storing (putting aside inverting) the matrix M T M is computationally impracti- cal. 3 Note that this conversion is semantic and bares no loss in the description of the relation between measurements and ideal signal. 6
Page 1 and 2: UNIVERSITY OF CALIFORNIA SANTA CRUZ
Page 3 and 4: Contents List of Figures vi List of
Page 5 and 6: Appendix F Appendix: Affine Motion
Page 7 and 8: 2.3 Effect of upsampling D T matrix
Page 9 and 10: 3.11 Multi-frame color super-resolu
Page 11 and 12: 4.5 A sequence of 250 low-resolutio
Page 13 and 14: List of Tables 2.1 The true motion
Page 15 and 16: show that using such constraints wi
Page 17 and 18: I thank all the handsome gentlemen
Page 19 and 20: It’s the robustness, stupid! xix
Page 21 and 22: quality. We develop the theory and
Page 23: That is, ⎧ ⎪⎨ ⎪⎩ y1 = h1.
Page 27 and 28: accomplished by way of Lagrangian t
Page 29 and 30: which addresses the artifacts resul
Page 31 and 32: noise and Y is the resulting discre
Page 33 and 34: ods, where the regularization-like
Page 35 and 36: 2.2 Robust Super-Resolution 2.2.1 R
Page 37 and 38: and horizontal directions and subsa
Page 39 and 40: Note that if p =2then (2.8) will be
Page 41 and 42: Figure 2.3: Effect of upsampling D
Page 43 and 44: where λ, the regularization parame
Page 45 and 46: Although a relatively large regular
Page 47 and 48: image(X). Figure 2.5(b) is the corr
Page 49 and 50: of high-resolution frame � Xn. Bl
Page 51 and 52: as conjugate gradient is not a stra
Page 53 and 54: of minimization problem (2.23) can
Page 55 and 56: norm is not robust to motion error,
Page 57 and 58: e one. Figure 2.12(f) is the result
Page 59 and 60: 50 100 150 200 250 300 350 50 100 1
Page 61 and 62: a: One of 8 LR Frames b: Cubic Spli
Page 63 and 64: a: Frame 1 of 55 LR Frames b: Frame
Page 65 and 66: Chapter 3 Multi-Frame Demosaicing a
Page 67 and 68: chrominance layers are separated fr
Page 69 and 70: Other examples of popular demosaici
Page 71 and 72: a: Original b: Down-sampled c: Blur
Page 73 and 74: 3.3 Mathematical Model and Solution
Page 75 and 76:
epresents the down-sampling operato
Page 77 and 78:
image (Spatial Luminance Penalty Te
Page 79 and 80:
Acquire a Set of LR Color Filtered
Page 81 and 82:
espect to the other color channels.
Page 83 and 84:
in different color bands. Our propo
Page 85 and 86:
the robust super-resolution method
Page 87 and 88:
We used the method described in [48
Page 89 and 90:
the color artifacts of a set of low
Page 91 and 92:
a: Reconst. with lumin. regul. b: R
Page 93 and 94:
a: Reconst. with all terms. Figure
Page 95 and 96:
a: LR b: Shift-and-Add c: SR [4] on
Page 97 and 98:
a b c d e f Figure 3.14: Multi-fram
Page 99 and 100:
a b c d Figure 3.16: Multi-frame co
Page 101 and 102:
a b c d e f Figure 3.18: Multi-fram
Page 103 and 104:
ates from them in several important
Page 105 and 106:
order. The current image X(t) is of
Page 107 and 108:
With this alternative definition of
Page 109 and 110:
GS a 0 0 0 b 0 0 0 c D T GSD =⇒
Page 111 and 112:
Figure 4.2: Block diagram represent
Page 113 and 114:
ˆZ(t), necessitating a further joi
Page 115 and 116:
Figure 4.3: Block diagram represent
Page 117 and 118:
4.3 Simultaneous Deblurring and Int
Page 119 and 120:
Y (t) Input CFA Data Y R (t) Y G (t
Page 121 and 122:
4.5(b) & 4.5(f) show frames #50 and
Page 123 and 124:
a b c d e f g h Figure 4.6: A seque
Page 125 and 126:
dB 24 22 20 18 16 14 12 10 8 0 50 1
Page 127 and 128:
a b c d e f g h Figure 4.10: A sequ
Page 129 and 130:
Chapter 5 Constrained, Globally Opt
Page 131 and 132:
In this chapter, we study such prio
Page 133 and 134:
(a) (b) Figure 5.2: The consistent
Page 135 and 136:
vector field δi,j is spatially con
Page 137 and 138:
5.3.3 Robust Multi-Frame Registrati
Page 139 and 140:
MSE 10 −1 10 −2 10 −3 10 0 10
Page 141 and 142:
(a) (b) (c) (d) Figure 5.6: Experim
Page 143 and 144:
we advocated the use of the L1 norm
Page 145 and 146:
y the user. - The user is able to s
Page 147 and 148:
There is need for more research on
Page 149 and 150:
than the corresponding single-frame
Page 151 and 152:
In [111], Elad proved that such fil
Page 153 and 154:
all iterations, which means estimat
Page 155 and 156:
Appendix C Noise Modeling Based on
Page 157 and 158:
Appendix D Error Modeling Experimen
Page 159 and 160:
Appendix E Derivation of the Inter-
Page 161 and 162:
Appendix F Appendix: Affine Motion
Page 163 and 164:
Bibliography [1] A. Zomet, A. Rav-A
Page 165 and 166:
[26] H. Ur and D. Gross, “Improve
Page 167 and 168:
[55] K. Hirakawa and T. Parks, “A
Page 169 and 170:
[84] S. Farsiu, D. Robinson, M. Ela
Page 171:
[112] S. M. Kay, Fundamentals of st
show all

A FAST AND ROBUST FRAMEWORK FOR IMAGE FUSION AND ...

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?