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Proximal Methods for Hierarchical Sparse Coding

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Figure 1: Example of a tree Twe have when p = 6. With the rule we consider for the nonzero patterns, if α ̸5= 0, we must also have α ̸k= 0 for k in ancestors(5) = {1,3,5}.
Figure 2: Left: example of a tree-structured set of groups G (dashed contours in red), correspondingto a tree T with p = 6 nodes represented by black circles
Figure 3: Benchmark for solving a least-squares regression problem regularized by the hierarchicalnorm Ω
Table 1: Top part of the tables: Average PSNR measured for the denoising of 12 standard im-ages, when the wavelets are Haar or Daubechies3 wavelets (see Mallat, 1999), for two nonconvexapproaches (ℓ0 and ℓtree0 ) and three different convex regularizations—
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