Algorithm 1.

Path-following optimization. It solves the problem (2.1) using a decreasing sequence of regularization parameters ${\{{\lambda }_K\}}_{K=0}^N$. More specifically, λ₀ = ‖ℒ(0)‖_∞ yields an all zero output solution θ̂^{0} = 0. For K = 1, …, N, we set λ_K = ηλ_{K − 1}, where η ∈ (0, 1). We solve (2.1) for λ_K with θ̂^{{K − 1}} as an initial solution. Note that AISTA is the computational algorithm for obtaining θ̂^{K + 1} using θ̂^K as the initial solution. L_min and ${\{{\hat{L}}^{\{K\}}\}}_{K=0}^N$ are corresponding step size parameters. More technical details on AISTA are presented are Algorithm 3.

Algorithm: ${\{{\hat{\mathit{\theta }}}^{(K)}\}}_{K=0}^N\leftarrow \mathtt{\text{APISTA}}({\{{\lambda }_K\}}_{K=0}^N)$

Parameter: η, Lmin

Initialize: λ0 = ‖∇ℒ(0)‖∞, θ̂{0} ← 0, L̂{0} ← Lmin

For: K = 0, …., N − 1

λK+1 ← ηλK, {θ̂{K+1}, L̂{K+1}} ← AISTA(λK+1, θ̂{K}, L̂{K})

End for

Output: ${\{{\hat{\mathit{\theta }}}^{(K)}\}}_{K=0}^N$