Table 1 Summary of the K-cluster-valued CoSaMP algorithm

- Output: S-sparse approximation $\widehat{\mathit{x}}$ of target image x.

- Initialization: ${\widehat{\mathit{x}}}^0=0$, r= y and i = 1.

  While halting criterion = true

     1 z ← Φ*r{Compute the proxy of residual}

     2 Ω ← supp(z_2K) {Identify the largest 2K components of the proxy}

     3 $\mathit{T}\leftarrow \mathbf{\Omega }\cup supp\left({\widehat{\mathit{x}}}^{\left(i-1\right)}\right)$ {Merge supports}

     4 $\mathit{b}{|}_{\mathit{T}}\leftarrow {\mathbf{\Phi }}_{\mathit{T}}^{†}\mathit{y}$ and $\mathit{b}{|}_{{\mathit{T}}^C}\leftarrow 0${Estimate the image by least-squares solution}

     5 ${\widehat{\mathit{x}}}^i\leftarrow {\mathit{b}}_K$ {Prune to obtain the image approximation for the next iteration or output}

       While ${\sum }_{n=1}^N{\sum }_{k=1}^K{r}_{nk}\parallel {\widehat{x}}_n^i-{\mu }_k^i{\parallel }_2<threshold$

          6 For each n = 1, 2,..., N, {Assign intensity values of each pixel to the closest intensity cluster}

                $r_{nk}^i=\left\{\begin{array}{cc}\hfill 1\hfill & \hfill ifk=arg{min}_j\parallel {\widehat{x}}_n^i-{\mu }_k^i{\parallel }_{2}and{\widehat{x}}_n^i\ne 0\hfill \\ \hfill 0\hfill & \hfill otherwise\hfill \end{array}\right.$

          7 For each $n=1,2,\dots ,N,{\mu }_k^i=\frac{{\Sigma }_{n=1}^N{r}_{nk}^i{\widehat{x}}_n^i}{{\Sigma }_{n=1}^N{r}_{nk}^i}$. {Obtain the K cluster centres}

       End

   8 For n = 1, 2,..., N, if r _nk = 1, then ${\widehat{x}}_n^i={\mu }_k^i$ {Optimize the estimated image with K-cluster intensities}

   9 $\mathit{r}=\mathit{y}-\mathbf{\Phi }{\widehat{\mathit{x}}}^i$ {Update the measurement residual for the next iteration}

   10 i = i + 1 {Update the iteration number}

  End

  return $\widehat{\mathit{x}}$${\widehat{\mathit{x}}}^i$