Nonlocal Regularized Algebraic Reconstruction Techniques for MRI: An Experimental Study

Algorithm 1

Nonlocal regularized ART (NR-ART).

Input: measurement data 𝐹_𝑘, 𝑘-space location (𝑥_𝑘,𝑦_𝑘), and

density compensation function 𝑤_𝑘;

Output: reconstructed image 𝑓_𝑛

(i) Initialization: set 𝑓_𝑛⁽⁰⁾ to be the output of TV-regularized

ART;

(ii) Main loop: for 𝑡=1,…,𝑡_max, set the threshold

𝑇_𝑡=𝑇₀−(𝑡−1)Δ

  (a) Projection onto the regularization constraint set:

𝑓_𝑛^(𝑡+1/2)=𝑃_reg𝑓_𝑛^(𝑡) where 𝑃_reg refers to a nonlocal regularized

filter in (3) or (4);

  (b) Projection onto the observation constraint set:

𝑓_𝑛^𝑡+1=𝑃^(𝑟)_obs𝑓_𝑛^𝑡+1/2 where 𝑃_obs refers to the ART iteration (2);