Problem 1: 1-D signal restoration via dynamic programming. You are given a 1-D noisy signal I of length n. It can be found in the file hw5data.mat. The goal is to find the corresponding clean signal J. Assume J(α) ∈ {0, 1, 2, …, 255}. You will use dynamic programming to find J such that the Ising energy E(I, J) is minimized. E(I, J) = c X α (I(α) − J(α))2 + X α∼β (J(α) − J(β))2 , = c Xn α=1 (I(α) − J(α))2 + nX−1 α=1 (J(α + 1) − J(α))2 . where c > 0 is a real constant and α ∼ β means α and β are adjacent pixels. (a) Decide the value of c by experiments. Explain the effects of different values of c on the final results. (b) Plot the signal J on top of signal I and attach all Matlab codes used for this problem. To plot two signals on top of each other, you may use the Matlab command “hold on”.

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