Table 1.

Training algorithm: De(.), En(.), and Di(.) stands for the Decoder, Encoder, and Discriminator, respectively. First two lines belong to the accuracy phase of the training process and the remaining lines belong to the correction phase.

Algorithm 1 Minibatch stochastic gradient descent training of adversarial autoencoder network.

For number of training iterations do:   • Sample minibatch of m motion corrupted examples $\{{\text{x}}^1,{\text{x}}^2\dots {\text{x}}^{\mathrm{m}}\}$ from motion-corrupted set $\mathrm{X}$.   • Update the Encoder and the Decoder by ascending its stochastic gradient:     ${\nabla }_{{{\theta }_{En},\varnothing }_{De}}\frac{1}{m}\sum _{i=1}^m{\left|x^i-De(En\left(x^i\right))\right|}_1$   • Sample minibatch of m motion corrupted examples $\{{\text{x}}^1,{\text{x}}^2\dots {\text{x}}^{\mathrm{m}}\}$ from motion-corrupted set $\mathrm{X}$.   • Sample minibatch of m breath-hold examples $\{{\text{y}}^1,{\text{y}}^2\dots {\text{y}}^{\mathrm{m}}\}$ from motion-free set $\mathrm{Y}$.   • Update the discriminator by ascending its stochastic gradient:     ${\nabla }_{{\vartheta }_{Di}}\frac{1}{m}\sum _{i=1}^m\lceil logDi\left(y^i\right)+\mathrm{l}\mathrm{o}\mathrm{g}(1-Di\left(En\left(x^i\right)\right))\rceil$   • Sample minibatch of m motion corrupted examples $\{{\text{x}}^1,{\text{x}}^2\dots {\text{x}}^{\mathrm{m}}\}$ from motion-corrupted set $\mathrm{X}$.   • Update the Encoder by descending its stochastic gradient:     ${\nabla }_{{\theta }_{En}}\frac{1}{m}\sum _{i=1}^m\left[\mathrm{l}\mathrm{o}\mathrm{g}(1-Di\left(En\left(x^i\right)\right))\right]$