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Fig. 7 | EURASIP Journal on Image and Video Processing

Fig. 7

From: Directional global three-part image decomposition

Fig. 7

The comparison of ALM (ai) and QPM (jq) for the DG3PD model with the same parameters and 20 iterations: \(\protect \phantom {\dot {i}\!}\beta _{4} = 0.025 \,, \theta = 0.9 \,, c_{1} = 10 \,, c_{2} = 1.3 \,, {c_{{\mu }_{1}}} = {c_{{\mu }_{2}}} = 0.03 \,, \gamma = 1 \,, S = L = 32 \,, \delta = 5\). We observe that the error image of QPM still contains geometry and texture information; see after 20 iterations in p and after 60 in q. Using QPM for constrained minimization is similar to decomposing the original image into four parts, namely cartoon (j), texture (k), residual (m), and error (p). The amount of information in the error image by QPM strongly depends on the choice of parameters (β 1,β 2,β 3,β 4). However, for ALM, the updated Lagrange multipliers (λ 1 ,λ 2,λ 3,λ 4) compensate for the choice of (β 1,β 2,β 3,β 4). Thus, the error numerically tends to 0 as the number of iterations increases, see the error image after 20 iterations in h and after 60 iterations in i

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