Least Squares Generative Adversarial Networks

Mao, Xudong; Li, Qing; Xie, Haoran; Lau, Raymond Y. K.; Wang, Zhen; Smolley, Stephen Paul

doi:10.1109/iccv.2017.304

Cited by 4,382 publications

(2,641 citation statements)

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“…Effectively, this is allowing the discriminator to learn its own domain knowledge, and then provide feedback to update the main model. For this study, we utilized the Least Squares GAN (LSGAN) formulation:

\begin{matrix} \underset{θ_{N_{D}}}{arg truemin} & L_{A D V_{D}} = \frac{1}{2} {(||, N_{D} ()(, y_{italictrue}) - b)}_{2}^{2} + \frac{1}{2} {(||, N_{D} ()(, N_{G} ()(, x)) - a)}_{2}^{2} \end{matrix}

\begin{matrix} \underset{θ_{N_{G}}}{arg truemin} & L_{A D V_{G}} = \frac{1}{2} {(||, N_{D} ()(, N_{G} ()(, x)) - c)}_{2}^{2} \end{matrix}

where

θ_{N_{D}}

and

θ_{N_{G}}

are the trainable weights parameterizing the discriminator network, N D , and generator network, N G , respectively.

L_{A D V_{D}}

and

L_{A D V_{G}}

are the loss functions to be minimized with respect to

θ_{N_{D}}

and

θ_{N_{G}}

.…”

Section: Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Incorporating human and learned domain knowledge into training deep neural networks: A differentiable dose‐volume histogram and adversarial inspired framework for generating Pareto optimal dose distributions in radiation therapy

et al. 2019

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Purpose We propose a novel domain‐specific loss, which is a differentiable loss function based on the dose‐volume histogram (DVH), and combine it with an adversarial loss for the training of deep neural networks. In this study, we trained a neural network for generating Pareto optimal dose distributions, and evaluate the effects of the domain‐specific loss on the model performance. Methods In this study, three loss functions — mean squared error (MSE) loss, DVH loss, and adversarial (ADV) loss — were used to train and compare four instances of the neural network model: (a) MSE, (b) MSE + ADV, (c) MSE + DVH, and (d) MSE + DVH+ADV. The data for 70 prostate patients, including the planning target volume (PTV), and the organs at risk (OAR) were acquired as 96 × 96 × 24 dimension arrays at 5 mm3 voxel size. The dose influence arrays were calculated for 70 prostate patients, using a 7 equidistant coplanar beam setup. Using a scalarized multicriteria optimization for intensity‐modulated radiation therapy, 1200 Pareto surface plans per patient were generated by pseudo‐randomizing the PTV and OAR tradeoff weights. With 70 patients, the total number of plans generated was 84 000 plans. We divided the data into 54 training, 6 validation, and 10 testing patients. Each model was trained for a total of 100,000 iterations, with a batch size of 2. All models used the Adam optimizer, with a learning rate of 1 × 10−3. Results Training for 100 000 iterations took 1.5 days (MSE), 3.5 days (MSE+ADV), 2.3 days (MSE+DVH), and 3.8 days (MSE+DVH+ADV). After training, the prediction time of each model is 0.052 s. Quantitatively, the MSE+DVH+ADV model had the lowest prediction error of 0.038 (conformation), 0.026 (homogeneity), 0.298 (R50), 1.65% (D95), 2.14% (D98), and 2.43% (D99). The MSE model had the worst prediction error of 0.134 (conformation), 0.041 (homogeneity), 0.520 (R50), 3.91% (D95), 4.33% (D98), and 4.60% (D99). For both the mean dose PTV error and the max dose PTV, Body, Bladder and rectum error, the MSE+DVH+ADV outperformed all other models. Regardless of model, all predictions have an average mean and max dose error <2.8% and 4.2%, respectively. Conclusion The MSE+DVH+ADV model performed the best in these categories, illustrating the importance of both human and learned domain knowledge. Expert human domain‐specific knowledge can be the largest driver in the performance improvement, and adversarial learning can be used to further capture nuanced attributes in the data. The real‐time prediction capabilities allow for a physician to quickly navigate the tradeoff space for a patient, and produce a dose distribution as a tangible endpoint for the dosimetrist to use for planning. This is expected to considerably reduce the treatment planning time, allowing for clinicians to focus their efforts on the difficult and demanding cases.

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\begin{matrix} \underset{θ_{N_{D}}}{arg truemin} & L_{A D V_{D}} = \frac{1}{2} {(||, N_{D} ()(, y_{italictrue}) - b)}_{2}^{2} + \frac{1}{2} {(||, N_{D} ()(, N_{G} ()(, x)) - a)}_{2}^{2} \end{matrix}

\begin{matrix} \underset{θ_{N_{G}}}{arg truemin} & L_{A D V_{G}} = \frac{1}{2} {(||, N_{D} ()(, N_{G} ()(, x)) - c)}_{2}^{2} \end{matrix}

where

θ_{N_{D}}

and

θ_{N_{G}}

are the trainable weights parameterizing the discriminator network, N D , and generator network, N G , respectively.

L_{A D V_{D}}

and

L_{A D V_{G}}

are the loss functions to be minimized with respect to

θ_{N_{D}}

and

θ_{N_{G}}

.…”

Section: Methodsmentioning

confidence: 99%

“…The discriminator tries to distinguish

y_{true}

from the data created from the generator. As per suggestion by the LSGAN publication, to minimize the Pearson X 2 divergence, we set a = −1, b = 1, and c = 0.…”

Section: Methodsmentioning

confidence: 99%

Incorporating human and learned domain knowledge into training deep neural networks: A differentiable dose‐volume histogram and adversarial inspired framework for generating Pareto optimal dose distributions in radiation therapy

et al. 2019

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“…According to the original GAN, the generator

G_{italicAB}

and discriminator

D_{B}

can be trained by solving the following min–max problem:

\begin{matrix} \underset{G_{italicAB}}{falsemin} \underset{D_{B}}{falsemax} {scriptL}_{GAN} false(G_{italicAB}, D_{B}, A, B false) \\ = {double-struckE}_{x_{B} \sim P_{B}} false[log D_{B} (x_{B}) false] + {double-struckE}_{x_{A} \sim P_{A}} false[log (1 - D_{B} false(G_{italicAB} (x_{A}) false)) false], \end{matrix}

where

G_{italicAB}

is trained to reduce a noise in the low‐dose CT image

x_{A}

to make it similar to the routine‐dose CT image

x_{B}

, while

D_{B}

is trained to discriminate between the denoised CT image

G_{AB} false(x_{A} false)

and the routine‐dose CT image

x_{B}

. However, we found that the original adversarial loss is unstable during training process; thus, we changed the log‐likelihood function to a least square loss as in the least squares GAN (LSGAN) . Then, the min–max problem can be changed to the two minimization problems as follows:

\underset{G_{italicAB}}{falsemin} {double-struckE}_{x_{A} \sim P_{A}} false[{false(D_{B} (G_{AB} false(x_{A} false)) - 1 false)}^{2} false],

…”

Section: Theorymentioning

confidence: 99%

Cycle‐consistent adversarial denoising network for multiphase coronary CT angiography

et al. 2018

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Purpose In multiphase coronary CT angiography (CTA), a series of CT images are taken at different levels of radiation dose during the examination. Although this reduces the total radiation dose, the image quality during the low‐dose phases is significantly degraded. Recently, deep neural network approaches based on supervised learning technique have demonstrated impressive performance improvement over conventional model‐based iterative methods for low‐dose CT. However, matched low‐ and routine‐dose CT image pairs are difficult to obtain in multiphase CT. To address this problem, we aim at developing a new deep learning framework. Method We propose an unsupervised learning technique that can remove the noise of the CT images in the low‐dose phases by learning from the CT images in the routine dose phases. Although a supervised learning approach is not applicable due to the differences in the underlying heart structure in two phases, the images are closely related in two phases, so we propose a cycle‐consistent adversarial denoising network to learn the mapping between the low‐ and high‐dose cardiac phases. Results Experimental results showed that the proposed method effectively reduces the noise in the low‐dose CT image while preserving detailed texture and edge information. Moreover, thanks to the cyclic consistency and identity loss, the proposed network does not create any artificial features that are not present in the input images. Visual grading and quality evaluation also confirm that the proposed method provides significant improvement in diagnostic quality. Conclusions The proposed network can learn the image distributions from the routine‐dose cardiac phases, which is a big advantage over the existing supervised learning networks that need exactly matched low‐ and routine‐dose CT images. Considering the effectiveness and practicability of the proposed method, we believe that the proposed can be applied for many other CT acquisition protocols.

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“…GANs have been reported to be notoriously hard to train in practice and several techniques have been proposed to alleviate some of the complexities involved in getting them to work including modified objective functions and regularization (Salimans et al, 2016;Mao et al, 2016;Gulrajani et al, 2017). We discuss some of these problems in the following subsection.…”

Section: Generative Adversarial Networkmentioning

confidence: 99%

“…Nowozin et al (2016) show that it is possible to train GANs with a variety of f-divergence measures besides JSD. Wasserstein GANs (WGANs) minimize the earth mover's distance or Wasserstein distance, while Least Squared GANs (LSGANs) (Mao et al, 2016) modifies replaces the log loss with an L2 loss. WGAN-GP (Gulrajani et al, 2017) incorporate a gradient penalty term on the discriminator's loss in the WGAN objective which acts as a regularizer.…”

Section: Generative Adversarial Networkmentioning

confidence: 99%

Proceedings of the 2nd Workshop on Representation Learning for NLP

2017

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Least Squares Generative Adversarial Networks

Cited by 4,382 publications

References 26 publications

Incorporating human and learned domain knowledge into training deep neural networks: A differentiable dose‐volume histogram and adversarial inspired framework for generating Pareto optimal dose distributions in radiation therapy

Incorporating human and learned domain knowledge into training deep neural networks: A differentiable dose‐volume histogram and adversarial inspired framework for generating Pareto optimal dose distributions in radiation therapy

Cycle‐consistent adversarial denoising network for multiphase coronary CT angiography

Proceedings of the 2nd Workshop on Representation Learning for NLP

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