Power-law spectrum-based objective function to train a generative adversarial network with transfer learning for the synthetic breast CT image

Objective. This paper proposes a new objective function to improve the quality of synthesized breast CT images generated by the GAN and compares the GAN performances on transfer learning datasets from different image domains. Approach. The proposed objective function, named beta loss function, is based on the fact that x-ray-based breast images follow the power-law spectrum. Accordingly, the exponent of the power-law spectrum (beta value) for breast CT images is approximately two. The beta loss function is defined in terms of L1 distance between the beta value of synthetic images and validation samples. To compare the GAN performances for transfer learning datasets from different image domains, ImageNet and anatomical noise images are used in the transfer learning dataset. We employ styleGAN2 as the backbone network and add the proposed beta loss function. The patient-derived breast CT dataset is used as the training and validation dataset; 7355 and 212 images are used for network training and validation, respectively. We use the beta value evaluation and Frechet inception distance (FID) score for quantitative evaluation. Main results. For qualitative assessment, we attempt to replicate the images from the validation dataset using the trained GAN. Our results show that the proposed beta loss function achieves a more similar beta value to real images and a lower FID score. Moreover, we observe that the GAN pretrained with anatomical noise images achieves better equality than ImageNet for beta value evaluation and FID score. Finally, the beta loss function with anatomical noise as the transfer learning dataset achieves the lowest FID score. Significance. Overall, the GAN using the proposed beta loss function with anatomical noise images as the transfer learning dataset provides the lowest FID score among all tested cases. Hence, this work has implications for developing GAN-based breast image synthesis methods for medical imaging applications.