Algorithm 1. Resonance-based sparse signal decomposition (RSSD).

Input: The raw signal of ship radiated noise $x\left(t\right)$. Output: The high-oscillatory signal ${\widehat{x}}_h$ and the low-oscillatory signal ${\widehat{x}}_l$.

Initialize: Set the suitable $\alpha$ and $\beta$. 1: Calculate $Q_h$, $r_h$ and $J_h$ for high-oscillatory channel and $Q_l$, $r_l$ and $J_l$ for low-oscillatory channel; 2: Construct the wavelet bases ${\mathsf{\Psi }}_h$ and ${\mathsf{\Psi }}_l$ by TQWT based on the above selected parameters; 3: Choose the benefitting weight parameters ${\lambda }_{l,j}$ and ${\lambda }_{h,j}$ at each level according to Equation (13) and observation of noise corruption intensity; 4: Work out the objected optimization Function (12) using the SALSA method and obtain the wavelet coefficient matrices $w_l^{\ast }$ and $w_h^{\ast }$; 5: Estimate high-oscillatory and low-oscillatory components ${\widehat{x}}_h$ and ${\widehat{x}}_l$ according to Equation (14).