The name is absent

0.07

0.065

0.06

0.055

0.05

0.045

0.04-------------^,-------------'-------------¹-------?-----^,-------------¹~

0       5      10      15      20      25

Regularization coefficient λ

30

Figure 4.5: The variation estimation error for various regularization factors λ.

4.4 Determining the regularization coefficient λ

Consider ^-regularization problem,

min ∣∣τ∣∣ι + λ∣∣Aa? — fe∣∣2∙                         (4-13)

When λ is very small, λ∣∣Ax — b∖∣2 would be small compared to the ^ɪ-norm term,
∣∣x∣∣ι and does not affect objective function dramatically. Thus, norm-one term
H:r∣∣ι is the main component that determines the solution of the regularization
problem; the solution tends to be sparse. In the other hand, when λ is very large,
λ∣∣√Lr — fe∣∣2 would be large compared to the norm-one term, ∣∣x∣∣ι, and small
changes in ∣∣√4τ — b∣∣2 result in large changes in objective function. In general, λ
balances between sparsity (Д-norm term) and fitting to measurements (∕⅛-norm
term).

Measurement noise and sparsity of the vector x are two major components

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