JSDA introduces the jointly sparse regular term (i.e. L2,1-norms term) to the criterion.
In these methods, some schemes of approximation that have to do with the non-smooth norm term are usually employed.
Tunable parameters β and λ are used to control the contributions of the L2 norm term and log determinant term in the cost function, respectively.
The operator S 1/ρ is also known as the proximity operator for the ℓ 1-norm term in the augmented Lagrangian L ρ.
For the MAP eigenphone method, σ -2) denotes the inverse prior variance for the eigenphone, i.e., the weighting factor λ2 of the squared l2 norm term.
Similar to the TV term in Equation 1 and the ℓ 1-norm term in Equation 2, the ℓ 1-norm term in Equation 3 promotes sparsity in the chosen transform domain and is defined as the sum of the absolute values.
The ℓ1-norm term in (11) can be equivalently expressed as an extra LS error term for the extra measurement 0 = 2 λ x k T 1 + u k, where u k is zero-mean noise with unit-variance.
The quadratic (l2-norm) error term 1 2 | | Φx − y | | 2 2 in Equation 9 is a convex function, but the convex region of the approximate l0-norm term F σ x = ∑ i = 1 N [ 1 − exp − x i 2 2 σ 2 ] depends on parameter is σ.
Sparse group lasso looks very similar to the elastic net regularizer but differs in that the column-wise l2 norm term is not squared, which makes it not differentiable at 0. However, we will show in Section 4 that within each nonzero group (i.e., eigenphone) it gives an 'adaptive' elastic net fit.
When p = 2, Eq. (5) is converted into the following minimization problem: where λ>0 is a properly chosen regularization parameter and controls the weight given to the minimization of the regularization penalty term relative to the minimization of the residual norm term.
