Robust dynamic myocardial perfusion CT deconvolution for accurate residue function estimation via adaptive-weighted tensor total variation regularization: A preclinical study

. Author manuscript; available in PMC: 2017 Nov 21.

Published in final edited form as: Phys Med Biol. 2016 Oct 26;61(22):8135–8156. doi: 10.1088/0031-9155/61/22/8135

1:Initial: K̅⁽¹⁾ = K⁽⁰⁾ = 0, m⁽¹⁾ = 1;

2:Initial: η = 1.0×10⁻³, δ;

3: For n = 1, 2, …, J;

K_s = K̅⁽ⁿ⁾ − r⁽ⁿ⁺¹⁾ A^T (AK̅⁽ⁿ⁾ − C),

w_{i, i + 1, j, j, t, t} = exp [- {(\frac{K_{s (i, j, t)} - K_{s (i + 1, j, t)}}{δ})}^{2}],

w_{i, i, j, j + 1, t, t} = exp [- {(\frac{K_{s (i, j, t)} - K_{s (i, j + 1, t)}}{δ})}^{2}],

w_{i, i, j, j, t, t + 1} = exp [- {(\frac{K_{s (i, j, t)} - K_{s (i, j, t + 1)}}{δ})}^{2}],

For d = 1, 2, ⋯, D;

If d == 1;

K^{(n - 1) + d} = K_{s} - {‖ K_{s} - K^{(n - 1)} ‖}^{2} \cdot η \cdot \frac{\nabla {‖ K_{s} ‖}_{A w T T V}}{‖ \nabla {‖ K_{s} ‖}_{A w T T V} ‖};

Else

K^{(n - 1) + d} = K^{(n - 1) + (d - 1)} - {‖ K_{s} - K^{(n - 1)} ‖}^{2} \cdot η \cdot \frac{\nabla {‖ K^{(n - 1) + (d - 1)} ‖}_{A w T T V}}{‖ \nabla {‖ K^{(n - 1) + (d - 1)} ‖}_{A w T T V} ‖};

10:

End If ;

11:

End For;

12:

K⁽ⁿ⁾ = K^(n−1)+D;

13:

m^{(n + 1)} = \frac{1 + \sqrt{1 + 4 {(m^{(n)})}^{2}}}{2};

14:

K̅⁽ⁿ⁺¹⁾ = K⁽ⁿ⁾ + ((m⁽ⁿ⁾ − 1) / m⁽ⁿ⁺¹⁾)(K⁽ⁿ⁾ − K⁽ⁿ⁻¹⁾);

15:

η = 0.995* η;

16: End For;

17: K̂ = K^(N);

18: Return K̂.