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

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3. apply a method for fusing the information from multiple images which is (a) robust to inaccuracies in the forward model and the noise in the estimated data. (b) computationally efficient. In the last two decades, many papers have been published, proposing a variety of solutions to different multi-frame image restoration related inverse problems. These methods are usually very sensitive to their assumed model of data and noise, which limits their utility. This thesis reviews some of these methods and addresses their shortcomings. We use the statistical signal processing approach to propose efficient robust image reconstruction methods to deal with different data and noise models. 1.2 Organization of this thesis In what follows in this thesis, we study several important multi-frame image fusion/reconstruction problems under a general framework that helps us provide fast and robust solutions. • In Chapter 2, we study the “multi-frame super-resolution” problem for grayscale images. To solve this problem, first we review the main concepts of robust estimation techniques. We justify the use of the L1 norm to minimize the data penalty term, and propose a robust regularization technique called Bilateral Total-Variation, with many applications in diverse image processing problems. We will also justify a simple but effective image fusion technique called Shift-and-Add, which is not only very fast to implement but also gives insight to more complex image fusion problems. Finally, we propose a fast super- resolution technique for fusing grayscale images, which is robust to errors in motion and blur estimation and results in images with sharp edges. • In Chapter 3, we focus on color images and search for an efficient method for remov- ing color artifacts in digital images. We study the single frame “demosaicing” problem, 9
which addresses the artifacts resulting from the color-filtering process in digital cameras. A closer look at demosaicing and super-resolution problems reveals the relation between them, and as conventional color digital cameras suffer from both low-spatial resolution and color-filtering, we optimally address them in a unified context. We propose a fast and robust hybrid method of super-resolution and demosaicing, based on a MAP estimation technique by minimizing a multi-term cost function. • In Chapter 4, unlike previous chapters in which the final output was a single high- resolution image, we focus on producing high-resolution videos. The memory and com- putational requirements for practical implementation of this problem, which we call “dy- namic super-resolution”, are so taxing that require highly efficient algorithms. For the case of translational motion and common space-invariant blur, we propose such a method, based on a very fast and memory efficient approximation of the Kalman Filter, applicable to both grayscale and color(filtered) images. • In Chapter 5, we address the problem of estimating the relative motion between the frames of a video sequence. In contrast to the commonly applied pairwise image registration methods, we consider global consistency conditions for the overall multi-frame motion estimation problem, which is more accurate. We review the recent work on this subject and propose an optimal framework, which can apply the consistency conditions as both hard constraints in the estimation problem, or as soft constraints in the form of stochastic (Bayesian) priors. The proposed MAP framework is applicable to virtually any motion model and enables us to develop a robust approach, which is resilient against the effects of outliers and noise. 10
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: accomplished by way of Lagrangian t
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
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Acquire a Set of LR Color Filtered
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espect to the other color channels.
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in different color bands. Our propo
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the robust super-resolution method
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We used the method described in [48
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the color artifacts of a set of low
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a: Reconst. with lumin. regul. b: R
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a: Reconst. with all terms. Figure
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a: LR b: Shift-and-Add c: SR [4] on
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a b c d e f Figure 3.14: Multi-fram
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a b c d Figure 3.16: Multi-frame co
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a b c d e f Figure 3.18: Multi-fram
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ates from them in several important
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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 =⇒
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Figure 4.2: Block diagram represent
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ˆZ(t), necessitating a further joi
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Figure 4.3: Block diagram represent
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4.3 Simultaneous Deblurring and Int
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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
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dB 24 22 20 18 16 14 12 10 8 0 50 1
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a b c d e f g h Figure 4.10: A sequ
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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
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5.3.3 Robust Multi-Frame Registrati
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MSE 10 −1 10 −2 10 −3 10 0 10
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(a) (b) (c) (d) Figure 5.6: Experim
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we advocated the use of the L1 norm
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y the user. - The user is able to s
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There is need for more research on
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than the corresponding single-frame
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In [111], Elad proved that such fil
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all iterations, which means estimat
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Appendix C Noise Modeling Based on
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Appendix D Error Modeling Experimen
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Appendix E Derivation of the Inter-
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Appendix F Appendix: Affine Motion
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Bibliography [1] A. Zomet, A. Rav-A
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[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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