Table 1 Simultaneous Orthogonal Matching Pursuit (SOMP) algorithm

(1): Input: training sample matrix $A$, testing sample matrix $Y$

(2): Output: Row-wise sparse solution $\widehat{X}$

(3): Initialization: residual $R_0=Y$, ${\widehat{X}}_0=0$, non-zero rows $\text{Ω}=\varnothing$, i = 0

(4): While stopping criterion false do

1). Find a new atom from matrix A to best approximate the current residual based on q-norm: $w=\text{arg }\underset{k\in \text{Ω}}{\text{max}}{∥a_k^T{R}_{i-1}∥}_q$

2). Update the non-zero row support $\text{Ω}=\text{Ω}\cup \left\{w\right\}$.

3). Update the signal estimation ${\widehat{X}}_i={\left(A_{\text{Ω}}^T{A}_{\text{Ω}}\right)}^{+}{A}_{\text{Ω}}^{T}Y$, where $A_{\text{Ω}}$ denotes the sub-matrix of A consisting of the atoms from matrix A, and the residual: $R_i=Y-A_{\text{Ω}}{\widehat{X}}_i$.

4).i = i + 1.

(5): End while

(6): Return: $\widehat{X}={\widehat{X}}_i$