CMB Map Restoration

Algorithm 1

(1) Initialization: set the number of iterations 𝐼_max, the step size 𝛾=min_𝑘𝜎²_𝑘, and the starting point 𝑥⁰.

(2) Main loop: apply iteratively the following steps at each iteration 𝑘:

 (a) Forward step of the FPS:

𝑢=𝑥^𝑘+2𝛾𝚺⁻¹(𝑦−𝑥^𝑘)

 (b) Backward step of the FPS:

𝑥^𝑘+1=ℱ^𝐻(𝐼+2𝛾𝐂⁻¹)⁻¹ℱ𝑢

(3) Stop when 𝑘=𝐼_max.