Algorithm 7 Fast Negentropy + ${\mathsf{\ell }}_{0.5}$ Norm

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

2: Initialization: choose proper $\eta$, $\lambda$, $c$,

3: ${\theta }_1={\mathsf{\alpha }}_0=0,k=0,t_1=1$

4: Main iteration: increment $k$ by 1

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

6: ${\alpha }_i^k=\frac{2}{3}x(1+\cos (\frac{2}{3}{\cos }^{-1}(-\frac{3^{3/2}}{4}\lambda \eta |x{|}^{-3/2})))\mathrm{sign}(\max (0,|{\beta }_i^{k-1}|-\frac{3}{2}\lambda {\eta }^{\frac{2}{3}}))$

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

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

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

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