coefficient for both irregular wavelet transformation and our fine-grid wavelet
transformation in the C880 circuit. The wavelet coefficients of the of the proposed
fine-grid method decay much faster than irregular grid transformation. The main
reason is that the gate placement is not completely irregular. The standard gate
sizes are integer multiplicand of a specific value. Moreover, the placement tools
assume irregularity in just one dimension.
3.4 Tomography using spatial constraints
(TUSC)
In this section, we directly use the spatial correlation to improve the estimation
error of power variations. In Section 3.2, we just used power (leakage) mea-
surements in Equation 3.3 to estimate the variations. Representing variations in
sparse domain in Section 3.3 is based on the spatial correlation in the variations.
Here, we reformulate the variation estimation problem such that the spatial cor-
relation explicitly appears in the optimization problem.
3.4.1 Adding spatial constraints
Adding spatial constraints directly to the optimization problem improves the
estimation performance. The spatial correlation implies that nearby gates should
have approximately similar scaling factors. As the distance between two gates
35
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