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Note that Gaussian random variables describe variations in the dimensions
of gates (or equivalently gate delays), i.e.,
du = d%l + ψu where is nominal
dimension of the gate.

2.2.2 Compressive sensing β

The compressive sensing concepts, that enable us to reconstruct a sparse vector
by partial measurement, are explained here (see [10,15,24]). A vector is called
s-sparse when it has only
s non-zero elements. Assume X is an s-sparse N × 1
vector. Assume
Y is described based on the following equation

Y = UX + e.                        (2.2)

Vector X is the unknown sparse vector; U is a known K×N measurement matrix
and e is measurement noise. Note that not only are the values of the non-zero
components of
X are not known, neither which components are zero. The vector
Y is our observation (measurement). The goal is to estimate the sparse vector X
using the measurement vector Y. To retrieve the vector Xf one might choose a
vector that minimizes ∣∣V — tλX^∣∣2∙ Because of the measurement noise and small
number of measurements, this procedure usually leads to a non-sparse signal.
However, solving the following optimization problem finds an sparse solution

min ∣∣X∣∣0 + α∣∣e∣∣2                           (2.3)

such that Y = UX + e,

20



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