Algorithm 4 Negentropy + ${\mathit{\ell }}_{0.5}$ Norm

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

2: Initialization: choose proper $\eta ,\lambda ,c,{\mathsf{\alpha }}_0=0,k=0$

3: Main iteration: increment $k$ by 1

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

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

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

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