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Unformatted text preview: problem (but of course you must explain how you did it); in particular, you do not need to
use the SDP formulation found in part (b).
42 5.6 Total variation image interpolation. A grayscale image is represented as an m × n matrix of
orig
intensities U orig . You are given the values Uij , for (i, j ) ∈ K, where K ⊂ {1, . . . , m} × {1, . . . , n}.
Your job is to interpolate the image, by guessing the missing values. The reconstructed image
orig
will be represented by U ∈ Rm×n , where U satisﬁes the interpolation conditions Uij = Uij for
(i, j ) ∈ K.
The reconstruction is found by minimizing a roughness measure subject to the interpolation conditions. One common roughness measure is the ℓ2 variation (squared),
m m n n (Uij − Ui,j −1 )2 . 2 (Uij − Ui−1,j ) + i=2 j =1 i=1 j =2 Another method minimizes instead the total variation,
m m n i=2 j =1 Uij − Ui−1,j  + n i=1 j =2 Uij − Ui,j −1 . Evidently both methods lead to convex optimization problems.
Carry out ℓ2 and total...
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This note was uploaded on 09/10/2013 for the course C 231 taught by Professor F.borrelli during the Fall '13 term at University of California, Berkeley.
 Fall '13
 F.Borrelli
 The Aeneid

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