rameter λdepends on the noise level of the input data; the noisier the data, the larger the value of λshould be. Fig. 11 shows how λin?uences the reconstructed results given the same noiseless input image. The larger λ, the smoother the result image texture gets. This is obvious by formulating Eq. 8 into Maximum a Posterior (MAP) problem: α?=argmax P ( α) · P (? y | α, ? D ) . (27) where P ( α)= 1 2 b exp( ??α? 1 b ) P (? y | α, ? D )= 1 2 σ 2 exp( ? 1 2 σ 2 ?? Dα?? y ? 2 2 ) , (28) where bis the variance of the Laplacian prior on α, and σ 2 is the variance of the noise assumed on the data ? y. Taking the negative log likelihood in Eq. 27, we get the exact optimization problem in Eq. 8, with λ= σ 2 /b. Suppose the Laplacian variance bis ?xed, the more noisy of the data ( σ 2is larger),
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