Performance of 2D Compressive Sensing on Wide-Beam Through-the-Wall Imaging

Algorithm 1

OMP algorithm description. Adapted from [26].

Inputs:

     (i) measured incomplete signal 𝑦 and matrix Θ, populated with simulated wall or point-target model data

      (ii) maximum number of iterations 𝐾

Output: reconstructed scene vector 𝜎

(1) Initialize residual 𝑟₀ to the measured signal vector 𝑦 and secondary matrix Θ^† to zero

    𝑟₀=𝑦,Θ^†=0

(2) Increase 𝑘. Find the column-vector of Θ that provides highest correlation with the residual

 𝑐_𝑘=argmax𝑟_𝑘−1,Θ_𝑛

(3) Add column 𝑐_𝑘 of Θ to Θ^† and zero 𝑐_𝑘 from Θ

(4) Solve

 𝜎=argmin_𝜎‖𝜎‖₂s.t.𝑦=Θ^†𝜎

   and update residual with Θ

             𝑟_𝑘=𝑦−Θ𝜎

(5) Go to step 2 until 𝑘 reaches stop condition (𝑘=𝐾)