Algorithm 1: The proposed algorithm for one-dimensional signal processing.

Input: A column vector of length N: b ∈ ℂN × 1 Number of sinusoid components: s A column vector for coarse estimation: $\widehat{b}$∈ ℂk× 1, s < k < N IDFT matrix: $W_N^{-1}$ Points number added each time: δ Extraction rate: β (β << 1) Output: Spectral peak positions ẑ = [z1,…, zs]T Initialize: Coarse spectral peak positions ẑc = zeros(s, 1) 1: /* Coarse estimation stage */ 2: Set $\widehat{b}$ = b(1: k) 3: Calculate tempValue = sort(FFT($\widehat{b}$)) 4: Generate ẑc = tempValue(k-s + 1: k) 5:        /* Iteration stage */ 6: For j from 1 to s THEN 7:        For h from k + 1 to N STEP δ THEN 8:        Set $\widehat{b}$(h: h + δ −1) = b(h: h + δ-1) 9:        Calculate n= β × h 10:      Obtain bn by randomly extracting n rows from $\widehat{b}$ 11:      Obtain $W_n^{-1}$ by correspondingly extracting n rows of $W_N^{-1}$ 12:      IF h == k + 1 THEN 13:                       Obtain $z=\max \left\{\langle W_{n({\widehat{z}}_c(j)-1)}^{-1},b_n\rangle ,\langle W_{n({\widehat{z}}_c(j))}^{-1},b_n\rangle ,\langle W_{n({\widehat{z}}_c(j)+1)}^{-1},b_n\rangle \right\}$ 14:      Else 15:                       Obtain $z=\max \left\{\langle W_{n(z-1)}^{-1},b_n\rangle ,\langle W_{n(z)}^{-1},b_n\rangle ,\langle W_{n(z+1)}^{-1},b_n\rangle \right\}$ 16:      End IF 17:      END FOR 18:      Set zj = z 19: END FOR 20: Return ẑ