The name is absent

where σ = minimum eigen value of AA^τ. For a = 0.05, will be 591.13. It is
clearly far from the optimal regularization factor, λ_opt (Figure 4.5).

Tb understand the behavior of the best λ, we study optimal point curves of
й the problem. For each λ ∈ [λo,∞), let xχ be the solution of the problem in
¥

Equation 4.13. Define

s(ʌ) = lkλ∣∣ι

t(λ) = ∣∣Ar_λ - b∣∣₂.                         (4.15)

(s(λ),i(λ)) defines a curve in s-t plane. A number of these curves are shown in
Figure 4.6. These curves are for different noise levels. The points that are shown
by star on each curve represent the optimal regularization factor, (s(λ_opt), s(λ_opt));
we call these point optimal points. It suggests that the optimal points are approx-
imately on a horizontal line. Thus, we use following optimization formulation to
estimate the variation.

min ∣∣Ar — 6∣∣₂

such that ∣∣τ∣∣ι ≤ c

where c is a constant number. We assume c = 0-E(∣∣τ∣∣ι); where θ ∈ [1.5,2].

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