Table 10 SL0 steps

● Initialization:

1. Set ${\widehat{\mathbf{s}}}_0$ equal to the minimum ℓ₂-norm solution of A s=x, obtained by pseudo-inverse of A.

2. Choose a suitable decreasing sequence for σ, $[{\sigma }_1,\dots ,{\sigma }_K]$.

● For $i=1,\dots ,K$:

1. Set σ=σ _i ,

2. Maximize the function F _σ on the feasible set $\mathcal{S}=\left\{\mathbf{s}\right|\mathbf{A}\mathbf{s}=\mathbf{x}\}$ using L iterations of the steepest ascent algorithm (followed by projection onto the feasible set):

−Initialization: $\mathbf{s}={\widehat{\mathbf{s}}}_{i-1}$.

−for $j=1,\dots ,L$ (loop L times):

(a) Let: $\Delta \mathbf{s}={[s_1{e}^{-\frac{s_1^2}{2{\sigma }^2}},\dots ,s_n{e}^{-\frac{s_n^2}{2{\sigma }^2}}]}^T$.

(b) Set s ← s − μΔ s (where μ is a small positive constant).

(c) Project s back onto the feasible set $\mathcal{S}$:

$\begin{array}{c}\mathbf{s}\leftarrow \mathbf{s}-{\mathbf{A}}^T{\left(\mathbf{A}{\mathbf{A}}^T\right)}^{-1}\left(\mathbf{A}\mathbf{s}-\mathbf{x}\right)\end{array}$

3. Set ${\widehat{\mathbf{s}}}_i=\mathbf{s}$.

● Final answer is $\widehat{\mathbf{s}}={\widehat{\mathbf{s}}}_K$