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. Author manuscript; available in PMC: 2016 Sep 7.
Published in final edited form as: SIAM J Imaging Sci. 2015 May 5;8(2):1030–1069. doi: 10.1137/140984002

Figure 2.

Figure 2

Trend of the absolute value of the eigenvalues Λii, i = 1, …, 8192, of the reduced Hessian ℋh for plain H2-regularization (γ = 0; left) and the Stokes regularization scheme (γ = 1; H1-regularization; right) for β ∈ {0, 1E–2, 1E6} (as indicated in the legend of the plots). We report the trend of the entire set of 8192 eigenvalues. The test problem is the UT images (see section 5.1 for details on the construction of this synthetic registration problem; nx = (64, 64)⊤ and nc = 1). The Hessian is computed at the true solution vh, ★ to ensure that ℋh ≻ 0 (this statement is confirmed by the values reported in Table 3). The eigenvalues (absolute value) are sorted in descending order for the unregularized problem (i.e., for β = 0) and in ascending order otherwise (i.e., for β = 1E–3 and β = 1E6).