Algorithm 6 Fast Negentropy + Weighted ${\mathit{\ell }}_1$ Norm

1: Input: measurement matrix $D$, measurement signal $x$.

2: Initialization: choose proper $\eta$, $\lambda$, $c$, $p$ and $\delta$, ${\theta }_1={\mathsf{\alpha }}_0=0,k=0,t_1=1$

3: Main iteration: increment $k$ by 1

4: ${\beta }_i^{k-1}={\theta }_i^{k-1}-\eta \nabla f({\theta }_i^{k-1})$

5: ${\mathsf{\alpha }}_i^k=\mathrm{sign}({\beta }_i^{k-1})\max (0,|{\beta }_i^{k-1}|-\lambda \eta w_i^{k-1})$

6: $t_{k+1}=\frac{1+\sqrt{1+4t_k^2}}{2}$

7: ${\mathsf{\theta }}_{k+1}={\mathsf{\alpha }}_k+\left(\frac{t_k-1}{t_{k+1}}\right)({\mathsf{\alpha }}_k-{\mathsf{\alpha }}_{k-1})$

8: Stopping rule: stop if ${\mathsf{\alpha }}_k$ has converged

9: Output: sparse signal $\mathsf{\alpha }$