This problem is about graph signal inpainting via total variation regularization. Signal in- painting is the process of estimating missing signal values from available noisy measurements. Assume that the observed graph signal is y = [ y T1 y T2 ] T , where y 1 ? R M × 1 is known and y 2 = 0 ? R ( N ? M ) × 1 is missing or unknown. Now two cases are possible: the known part of the signal y 1 may be noisy or noiseless.
(a)
(b)
Hint: Use the method of Lagrange multipliers.
Note: The problem in the book has a small error. Above is the corrected version.
(a) Weight matrix–based framework
(b) Weight matrix–based framework
To satisfy the constraint, we can put
f1=y1 in the above expression and then take derivative
with respect to f2
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