Fig. 2

The top subplots show the Haar wavelet basis for \(T=16\). The bottom subplot shows the corresponding wavelet tree. In the tree layout induced by the lifting scheme, the position of a coefficient equals that of the central discontinuity of its associated Haar wavelet. For instance, \({\varvec{\psi }} _{2,0}\) has positive support on \(\mathbf{y }[0], \mathbf{y }[1]\), and negative support on \(\mathbf{y }[2], \mathbf{y }[3]\), with \(b^+_{2,0}=0\), \(b^\pm _{2,0}=2\) and \(b^-_{2,0}=4\). In this example, nodes for which \(\left|{} d_{j,k} \right| >\lambda\) are shown in black, i. e. \(\left|{} d_{1,0} \right| >\lambda\), inducing block boundaries at 0, 1 and 2, and \(\left|{} d_{1,7} \right| >\lambda\), inducing block boundaries at 14, 15 and 16 (indicated by thin solid vertical lines), creating 5 blocks in total. The wavelet tree data structure is subcompressive, as it induces additional breakpoints. \(s_{i,k}\) denotes the maximum of all \(\left|{} d_{j',k'} \right|\) in the subtree. Nodes in gray indicate the case where \(\left|{} d_{j,k} \right| <\lambda\), yet \(s_{i,k}>\lambda\), hence inducing additional block boundaries, indicated here by dotted lines, at 2, 4, 8, 12 an 14. This yields a total of 8 blocks