L0-Norm-Based CycleGAN for Unpaired Brain CT-to-MR Synthesis

Computed tomography (CT) and magnetic resonance (MR) imaging provide complementary information for the brain, but acquiring both modalities is not always possible. The cycle-consistent adversarial network (CycleGAN) enables unpaired CT-to-MR synthesis, but because the standard L1-norm cycle?consistency penalty grows linearly with the residual magnitude, the network tends to focus on large residuals. This paper introduces an L0-norm-based cycle?consistency term, in which the L0-norm is approximated by a smooth and bounded function. This approximation not only increases sensitivity to small residuals but also effectively suppresses the influence of large residuals. The proposed model and an otherwise identical L1-norm baseline were trained on 102 images and evaluated on 9 test images. The proposed model achieves a lower mean squared error (0.02746 versus 0.03464, a 20.7% reduction), a higher mean peak signal-to-noise ratio (15.80 versus 14.77 dB), and a higher mean structural similarity index (0.5689 versus 0.5407). It also has a lower maximum MSE and higher minimum PSNR and SSIM than the baseline. These results indicate that modifying the cycle-consistency penalty can improve reconstruction accuracy on this dataset.