Computation procedure of SpaRSA for a B-scan on one GPU

Input:
${\mathbf{y}}_u^1,\dots ,{\mathbf{y}}_u^L$	# under-sampled data for each A-scan
I or Fu	# sampling mask or the sensing matrix
η	# stopping iteration number
τ	# CS regulation parameter
Output:
(x1)η,...,(xL)η	# (xi)j is the j-th iterate of the i-th A-scan
1: Initialization: set (α1)0,...,(αL)0, (x1)0,...,(xL)0
2: copy ${\mathbf{y}}_u^1,\dots ,{\mathbf{y}}_u^L$, I or Fu to GPU
3: p ← 0
4: for all j ∈ [1,...,L] do in parallel
5:      ${({\mathbf{r}}^j)}^0={\mathbf{F}}_u{({\mathbf{x}}^j)}^0-{\mathbf{y}}_u^j$
6: end for
7: while p ≠ η do
8:     for all j ∈ [1,...,L] do in parallel
9:      ${({\mathbf{u}}^j)}^p={({\mathbf{x}}^j)}^p-(1/{({\alpha }^j)}^p){\mathbf{F}}_u^T{({\mathbf{r}}^j)}^p$
10:     end for
11:     for all i ∈ [0,...,N − 1] and j ∈ [1,... L] do in parallel
12:        ${\left(x_i^j\right)}^{p+1}=\text{soft}\left({\left(u_i^j\right)}^p,\tau /{({\alpha }^j)}^p\right)$	# $x_i^j$ is the i-th component of xj
13:     end for
14:     for all j ∈ [1,...,L] do in parallel
15:       (sj)p+1 = (xj)p+1 − (xj)p
16:        ${({\mathbf{r}}^j)}^{p+1}={\mathbf{F}}_u{({\mathbf{x}}^j)}^{p+1}-{\mathbf{y}}_u^j$
17:       (αj)p+1 = ‖(rj)p+1 − (rj)p‖2/‖(sj)p+1‖2
18:     end for
19:     p ← p + 1
20: end while
21: Finish: copy (x1)η,...,(xL)η to the host memory