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

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a: Original b: Blurred and Noisy c: Best Tikhonov Regularization d: Proposed Regularization Figure 2.5: Simulation results of deblurring using different regularization methods. The Mean Square Error (MSE) of reconstructed image using Tikhonov regularization (c) was 313. The MSE of reconstructed image using BTV (d) was 215. The matrices F , H, D, S and their transposes can be exactly interpreted as direct image operators such as shift, blur, and decimation [47] [4]. Noting and implementing the effects of these matrices as a sequence of operators spares us from explicitly constructing them as matrices. This property helps our method to be implemented in an extremely fast and memory efficient way. Figure 2.6 is the block diagram representation of (2.22). There, each low-resolution measurement Y (k) will be compared to the warped, blurred and decimated current estimate 29
of high-resolution frame � Xn. Block Gk represents the gradient back projection operator that compares the k th low-resolution image to the estimate of the high-resolution image in the n th steepest descent iteration. Block Rm,l represents the gradient of the regularization term, where the high-resolution estimate in the n th steepest descent iteration is compared to its shifted ver- sion (l pixel shift in horizontal and m pixel shift in vertical directions). Details of the blocks Gk and Rm,l are defined in Figures 2.7(a) and 2.7(b). Block T (PSF) in Figure 2.7(a) replaces the matrix H T (k) with a simple convolution. Function T flips the columns of PSF kernel in the left-right direction (that is, about the vertical axis), and then flips the rows of PSF kernel in the up-down direction (that is, about the horizontal axis) 8 . The D T (k) up-sampling block in Figure 2.7(a) can be easily implemented by filling r − 1 zeros both in vertical and horizontal directions around each pixel (Figure 2.3). And finally the F T (k) shift-back block in Figure 2.7(a), is implemented by inverting the translational motion in the reverse direction. Note that even for the more general affine motion model a similar inverting property (though more complicated) is still valid. Parallel processing potential of this method, which significantly increases the overall speed of implementation, can be easily interpreted from Figure 2.6, where the computation of each Gk or Rl,m blocks may be assigned to a separate processor. Our robust super-resolution approach also has an advantage in the computational as- pects over other methods including the one proposed in [1]. In our method, an inherently robust cost function has been proposed, for which a number of computationally efficient numerical minimization methods 9 are applicable. On the contrary, [1] uses steepest descent method to minimize the non-robust L2 norm cost function, and robustness is achieved by modifying the steepest descent method, where the median operator is used in place of summation operator in computing the gradient term of (2.12). Implementing the same scheme of substituting the summation operator with the median operator in computationally more efficient methods such 8 If the PSF kernel has even dimensions, one extra row or column of zeros will be added to it, to make it odd size (zero columns and rows have no effect in convolution process). 9 Such as Conjugate Gradient (CG), Preconditioned Conjugate Gradient (PCG), Jacobi, and many others. 30
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 and 44: where λ, the regularization parame
Page 45 and 46: Although a relatively large regular
Page 47: image(X). Figure 2.5(b) is the corr
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
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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
Page 131 and 132:
In this chapter, we study such prio
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(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
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