58 least squares tting with convex splines a cubic

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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.

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