10 20 30 40 SO 60
Figure 3.4: Process variation and its sparse wavelet transform for a typical circuit in
power framework.
3.3 Fast tomography by compressive sensing
As discussed in Section 2.2, sparse vectors can be acquired using very few mea-
surements. In this section, first, we introduce fast tomography for chips with
gates located on regular grids. Then, we extend this approach for cases with
gates located on irregular grids.
3.3.1 Sparse representation
The spatial correlation in the variations provides some redundancies in the varia-
tion values. The spatial correlation suggests that variations can be sparsely rep-
resented in an appropriate basis. In this section, we use wavelet basis to sparsely
represent the process variations. Specifically, we assume d = IV-1s, where W is
30
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