Table 2.
Quantitative comparisons of low-count PET denoised images using different federated learning methods. Each institution contains three different low-count levels. The best results are marked in bold.
| Evaluation PSNR/NMSE/SSIM | Institution #1 | Institution #2 | Institution #3 | ||||||
|---|---|---|---|---|---|---|---|---|---|
|
| |||||||||
| 5% | 10% | 20% | 2% | 5% | 10% | 2% | 5% | 10% | |
|
| |||||||||
| Original | 20.46/.129/.931 | 23.80/.059/.954 | 27.40/.026/.972 | 19.90/.076/.923 | 23.66/.031/.951 | 26.26/.017/.968 | 20.61/.121/.933 | 24.89/.050/.961 | 27.55/.030/.975 |
| FedAvg | 26.62/.029/.969 | 28.30/.019/.976 | 29.95/.013/.981 | 25.70/.020/.971 | 27.35/.014/.980 | 28.43/.010/.985 | 26.07/.035/.973 | 28.07/.023/.982 | 29.16/.019/.986 |
| FedBN | 26.68/.028/.970 | 28.35/.019/.978 | 30.05/.013/.982 | 25.79/.019/.973 | 27.47/.013/.981 | 28.60/.010/.986 | 26.31/.033/.975 | 28.34/.022/.983 | 29.38/.018/.987 |
| FedProx | 26.64/.028/.969 | 28.32/.018/.977 | 29.99/.013/.981 | 25.75/.020/.972 | 27.39/.014/.981 | 28.50/.010/.985 | 26.13/.034/.974 | 28.17/.023/.983 | 29.23/.019/.986 |
| FedSP | 26.69/.028/.969 | 28.36/.019/.976 | 30.16/.013/.982 | 25.80/.019/.973 | 27.51/.013/.981 | 28.63/.010/.985 | 26.23/.034/.974 | 28.33/.022/.983 | 29.48/.018/.987 |
| FedHyper | 26.88/.027/.971 | 28.56/.018/.978 | 30.33/.012/.983 | 25.85/.019/.974 | 27.49/.013/.982 | 28.65/.010/.986 | 26.44/.033/.976 | 28.52/.022/.983 | 29.73/.018/.987 |
|
| |||||||||
| FedFTN | 27.24/.025/.979 † | 28.96/.017/.983 † | 30.82/.011/.990 † | 26.12/.018/.980 † | 27.80/.013/.989 † | 29.03/.009/.991 † | 26.83/.031/.980 † | 28.91/.021/.990 † | 30.23/.017/.992 † |
|
| |||||||||
| FedFTN + SA | 27.32/.024/.980 † | 28.99/.016/.985 † | 30.83/.011/.991 † | 26.21/.017/.981 † | 27.84/.012/.990 † | 29.05/.009/.992 † | 26.89/.031/.980 † | 28.94/.021/.991 † | 30.25/.017/.992 † |
”†”
indicates that the difference between FedFTN and all compared methods is significant at p < 0.005 based on the non-parametricWilcoxon signed rank test.