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

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function looks like ΥBTV (X) = P� l,m=−P α |m|+|l| �X − S l xS m y X�1, (2.16) where S l x and S m y are the operators corresponding to shifting the image represented by X by l pixels in the horizontal direction and m pixels in the vertical direction, respectively. This cost function in effect computes derivatives across multiple scales of resolution (as determined by the parameter P ). The scalar weight 0
Although a relatively large regularization factor (λ =4.5) was chosen for this reconstruction which resulted in the loss of sharp edges, the noise has not been removed effectively. The result of using TV prior (P =1, λ =0.009) for denoising is shown in Figure 2.4(d). Figure 2.4(e) shows the result of applying BTV prior (P =3, λ =0.009) 6 . Notice the effect of each reconstruction method on the pixel indicated by an arrow in Figure 2.4(a). As this pixel is surrounded by non-similar pixels, TV prior considers it as a heavily noisy pixel, and uses the value of immediate neighboring pixels to estimate its original value. On the other hand, BTV considers a larger neighborhood. By bridging over immediate neighboring pixels, the value of similar pixels are also considered in graylevel estimation of this pixel, therefore the smoothing effect in Figure 2.4(e) is much less than Figure 2.4(d). Figure 2.4(f) compares the performance of TV and BTV denoising methods in estimating graylevel value of the arrow indicated pixel. Unlike BTV regularization, increasing the number of iterations in Tikhonov and TV regularization will result in more undesired smoothing. This example demonstrates the tendency of other regularization functionals to remove point like details from the image. The proposed regularization not only produces sharp edges but also retains point like details. To compare the performance of our regularization method to the Tikhonov regularization method, we set up another experiment. We corrupted an image by blurring it with a Gaussian blur kernel followed by adding Gaussian additive noise. We reconstructed the image using Tikhonov and our proposed regularization terms (this scenario can be thought of as a super-resolution problem with resolution factor of one). If X and Y represent the original and corrupted images and H represents the matrix form of the blur kernel then following (2.14), we minimized � �X 2 = ArgMin �Y − HX�2 + λΥ(X) X � (2.20) 6 The criteria for parameter selection in this example (and other examples discussed in this thesis) was to choose parameters which produce visually most appealing results. Therefore to ensure fairness, each experiment was repeated several times with different parameters and the best result of each experiment was chosen as the outcome of each method. Figure 2.4(c) is an exception where we show that Tikhonov regularization fails to effectively remove noise even with a very large regularization factor. 26
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 and 24: That is, ⎧ ⎪⎨ ⎪⎩ y1 = h1.
Page 25 and 26: problem of super-resolution is line
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: where λ, the regularization parame
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
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4.5(b) & 4.5(f) show frames #50 and
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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
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In this chapter, we study such prio
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(a) (b) Figure 5.2: The consistent
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vector field δi,j is spatially con
Page 137 and 138:
5.3.3 Robust Multi-Frame Registrati
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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
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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
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A FAST AND ROBUST FRAMEWORK FOR IMAGE FUSION AND ...

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