Table 1 The Gaussian diffusion sinogram inpainting MAR algorithm

Initialize k = 0, η = 1×10⁻⁴, μ = 1, δ = 4, t ⁰ = 1.

Do {

Step 1. \(t^{k + 1} = \left( {1/2} \right)\left( {1 + \sqrt {1 + 4\left( {t^{k} } \right)^{2} } } \right).\)

Step 2. \(\bar{x} = x^{k} + \left( {t^{k} - 1} \right)/t^{k + 1} \left( {x^{k} - x^{k - 1} } \right).\)

Step 3. \(\tilde{x} = \bar{x} - \lambda {\nabla }^{T} f\left( {\left\| {{\nabla }x_{p} } \right\|} \right){\nabla }\left( {x^{k} - x_{p} } \right).\)

Step 4. \(x^{k + 1} = \tilde{x} + H\left( {x_{ori} - \tilde{x}} \right).\)

Step 5. k = k+1.}

While \(\left( {\left\| {x^{k + 1} - x^{k} } \right\|/\left\| {x^{k} } \right\| > \eta } \right){.}\)