An Efficient CS-Based Spectral Peak Search Method

. 2022 Sep 16;22(18):7025. doi: 10.3390/s22187025

Algorithm 2: The proposed method for two-dimensional signal processing.

Input: A two-dimensional signal: B∈ ℂ^N ^{× M}
Number of estimated spectral peaks: s
A matrix for coarse estimation:

\hat{B}

∈ ℂ^N ^{× k}, s < k < M
Input column vector of the second dimensional transformation:

{\hat{B}}_{x}

Columns number added each time: δ
IDFT matrix:

W_{N}^{- 1}

Extraction rate: β (β<<1)
Output: Spectral peak positions: Ẑ = [Z₁,…, Z_s]^T
Initialize: Coarse spectral peak positions: Ẑ_c = zeros (s, 1)
1: /* Coarse estimation stage */
2: Set

\hat{B}

= B (:, 1: k)
3: For i from 1 to k THEN
4: Calculate

b_{i}^{\max}

= max (FFT(

\hat{B}

(:, i)))
5: Obtain

{\hat{B}}_{x}

(j) =

b_{i}^{\max}

6: END FOR
6: Perform tempValue = sort (FFT(

{\hat{B}}_{x}

))
6: Generate Ẑ_c = tempValue ((k-s): k)
5:          /* Iteration stage */
6: For j from 1 to s THEN
7:          For h from (k + 1) to M STEP δ THEN
8:          Generate

\hat{B}

(:, h: h + δ-1) = B (:, h: h + δ-1)
3: For i from h to (h + δ-1) THEN
4: Calculate

b_{i}^{\max}

= max (FFT(

\hat{B}

(:, i)))
4: Set

{\hat{B}}_{x}

(i) =

b_{i}^{\max}

5:                       END FOR
9:          Calculate n = β × h
10:        Obtain b_n by randomly extracting n rows from

{\hat{B}}_{x}

11: Obtain

W_{n}^{- 1}

by correspondingly extracting n rows of

W_{N}^{- 1}

12: IF h == k + 1 THEN
13: Obtain

z = \max {〈 W_{n ({\hat{z}}_{c} (j) - 1)}^{- 1}, b_{n} 〉, 〈 W_{n ({\hat{z}}_{c} (j))}^{- 1}, b_{n} 〉, 〈 W_{n ({\hat{z}}_{c} (j) + 1)}^{- 1}, b_{n} 〉}

14: Else
15: Obtain

z = \max {〈 W_{n (z - 1)}^{- 1}, b_{n} 〉, 〈 W_{n (z)}^{- 1}, b_{n} 〉, 〈 W_{n (z + 1)}^{- 1}, b_{n} 〉}

16:        End IF
17:        END FOR
18:        Set z_j = z
19: END FOR
20: Return ẑ