Sparse Signal Recovery via ECME Thresholding Pursuits

Algorithm 2

EMTP-𝛽 algorithm.

Input: Measurement matrix 𝐴, measurements 𝑦, thresholding parameter 𝛽

Output: The reconstructed signal 𝑥

(1)  Initialization:

(2)  𝑡=1 //iteration number

(3)  𝑥⁽⁰⁾=𝟎 //initial signal

(4)  𝑟⁽⁰⁾=𝑦 //initial residual

(5)  𝐼⁽⁰⁾=∅ //initial support set

(6)  while  halting criterion false do

(7) 𝑥^(𝑡)=𝑥^(𝑡−1)+𝐴^†𝑟^(𝑡−1)

(8) 𝐼^(𝑡)={𝑖∶|𝑥^𝑖(𝑡)|>𝛽^𝑡max|𝑥|}

(9) 𝑥^𝐼(𝑡)_(𝑡)=𝐴^†𝐼_(𝑡)𝑦

(10) 𝑥^{(𝑡)[1,𝑛]⧵𝐼}_(𝑡)=0

(11) 𝑟^(𝑡)=𝑦−𝐴𝑥^(𝑡)

(12) 𝑡=𝑡+1

(13)  end while

(14)  return  𝑥