Acta Optica Sinica, Volume. 45, Issue 11, 1117001(2025)
UPSU‑Net: an Unsupervised Deep Learning Framework for Photoacoustic Spectral Unmixing
Figures & Tables(17)
Fig. 2. Cross-sectional geometric structures of two numerical phantoms and simulated optical absorption distribution at three wavelengths
Fig. 6. Results and evaluation metrics of spectral unmixing for simulated test samples using different methods. (a) Abundance maps for sample 1; (b) abundance maps for sample 2; (c) evaluation metrics of spectral unmixing for all simulated test samples
Fig. 7. Abundance distribution maps obtained from the unmixing of photoacoustic spectral imaging data for four experimental phantoms
Fig. 8. Evaluation metrics for unmixing results of photoacoustic spectral images of experimental phantoms. (a) Metrics for abundance distribution maps of the inclusions; (b) metrics for abundance distribution maps of the background; (c) statistical results of evaluation metrics for all samples in the phantom test set
Fig. 9. Abundance distribution maps obtained from the unmixing of photoacoustic spectral imaging data collected by scanning the thoracoabdominal region of live mice
Fig. 10. Quantitative evaluation metrics for unmixing results of photoacoustic spectral images of thoracoabdominal regions in live mice. (a) Metrics for abundance distribution maps of HbO2; (b) metrics for abundance distribution maps of Hb; (c) statistical results of evaluation metrics for all samples in the in vivo test set
Fig. 11. Statistical results of evaluation metrics of abundance estimation and endmember estimation for simulation test set under different noise levels. (a) Background; (b) Hb; (c) HbO2; (d) ICG
Fig. 12. Evaluation metrics for spectral unmixing of simulation test set at different numbers of wavelengths. (a) HbO2; (b) Hb; (c) ICG; (d) background
Fig. 13. Spectral unmixing results for simulated test sample using UPSU-Net, CAU, 2DCAU, and De-attention, respectively. (a) Abundance maps; (b) evaluation metrics for abundance maps
Table 1. Optical property parameters of target molecules and background in the numerical phantoms
View tableTable 1. Optical property parameters of target molecules and background in the numerical phantoms
Wavelength /nmHbO2 Hb ICG Background Absorption coefficient /cm-1Scattering coefficient /cm-1 Absorption coefficient /cm-1Scattering coefficient /cm-1 Absorption coefficient /cm-1Scattering coefficient /cm-1 Absorption coefficient /cm-1Scattering coefficient /cm-1 750 0.28 10.44 0.75 10.44 0.37 10.44 0.10 22.10 760 0.31 10.34 0.83 10.34 0.40 10.34 0.13 21.66 770 0.35 10.26 0.70 10.26 0.48 10.26 0.09 21.22 780 0.38 10.17 0.58 10.17 0.62 10.17 0.04 20.80 790 0.40 10.08 0.48 10.08 0.80 10.08 0.04 20.39 800 0.44 10.00 0.41 10.00 0.98 10.00 0.04 20.00 810 0.46 10.82 0.38 10.82 1.02 10.82 0.05 24.06 820 0.49 10.72 0.37 10.72 0.92 10.72 0.07 23.55 830 0.52 9.76 0.37 9.76 0.61 9.76 0.08 18.89 840 0.55 9.68 0.37 9.68 0.33 9.68 0.07 18.54 850 0.57 9.61 0.37 9.61 0.16 9.61 0.06 18.21 860 0.58 9.53 0.37 9.53 0.05 9.53 0.07 17.88 870 0.60 9.46 0.38 9.46 0.01 9.46 0.09 17.56 880 0.62 9.39 0.39 9.39 0 9.39 0.16 17.25 890 0.63 9.32 0.40 9.32 0 9.32 0.31 16.95 900 0.64 9.25 0.41 9.25 0 9.25 0.46 16.66
Table 2. Principles and training hyperparameters of baseline methods
View tableTable 2. Principles and training hyperparameters of baseline methods
Category Method Principle Training scheme and hyperparameter Loss Optimizer Learning rate Batch size Epochs Non-learning ICA Based on the assumption that source components are maximally independent and non-Gaussian， the mixed spectral components are transformed into a set of independent source components and the corresponding mixing matrix by identifying statistically independent endmembers — VCA Assuming that each pixel is a mixture of a finite number of pure endmembers in certain proportions， the data is projected onto an orthogonal subspace， and the pixels with the maximum projection distance are extracted as endmembers — Deep
learning
U-Net The U-Net is employed to extract features by integrating contextual information from multispectral photoacoustic images， predicting the concentration of chromophores Minimize
reconstruction
error （mean
square error）
Adam 0.005 64 300 CAE A dual autoencoder structure， consisting of an initialization network and a demixing network， is used to obtain the optical absorption coefficients of the constituent molecules and the corresponding abundance maps Minimize
reconstruction
error （mean
square error）
Adam 0.001 32 300
Table 3. Design details of ablation experiments
View tableTable 3. Design details of ablation experiments
Experiment No. Design detail Purpose 1 An encoder is constructed using one-dimensional convolutional layers， and the resulting network is named the convolutional autoencoder unmixing （CAU） network The impact of constructing encoders with convolutional layers of different dimensions on the unmixing results is validated 2 An encoder is built using two-dimensional convolutional layers， and the resulting network is named the 2D convolutional autoencoder unmixing （2DCAU） network 3 The attention module is removed The effect of the attention module on the accuracy of spectral unmixing is evaluated
Table 4. Evaluation metrics for spectral unmixing results of simulated imaging data from two numerical phantoms using different methods
View tableTable 4. Evaluation metrics for spectral unmixing results of simulated imaging data from two numerical phantoms using different methods
Metric Tissue component UPSU-Net VCA ICA U-Net CAE Phm. 1 Phm. 2 Phm. 1 Phm. 2 Phm. 1 Phm. 2 Phm. 1 Phm. 2 Phm. 1 Phm. 2 RMSE Hb 0.0823 0.0821 0.1385 0.2386 0.1122 1.1388 0.5229 0.5779 0.5308 0.5313 HbO2 0.0455 0.0666 0.1209 0.3578 0.6372 0.2621 1.5117 0.3084 0.9583 0.3443 ICG 0.0627 0.1223 0.1039 0.6238 1.3340 0.2669 0.9436 1.1357 1.1540 0.9953 Background 0.0227 0.1701 0.3525 0.1859 0.9694 1.0030 0.4556 0.5391 0.4440 0.5968 SAD Hb 0.0785 0.1492 0.1508 0.1518 0.4446 0.1703 0.0923 0.3793 0.2824 0.3815 HbO2 0.0804 0.0746 0.1489 0.0936 0.2356 0.1393 0.3129 0.1088 0.7544 0.1114 ICG 0.1038 0.4256 0.3607 0.4288 0.4391 0.6948 0.1058 0.5316 0.3560 0.5316 Background 0.5854 0.5109 0.5889 0.5899 0.6023 0.5860 0.8597 0.5857 0.7768 0.5879 SID 0.0093 0.0130 0.0102 0.0133 0.2059 0.0699 0.0266 0.0286 0.0857 0.0273
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Jingsai Ai, Zheng Sun, Yingsa Hou, Meichen Sun. UPSU‑Net: an Unsupervised Deep Learning Framework for Photoacoustic Spectral Unmixing[J]. Acta Optica Sinica, 2025, 45(11): 1117001
Paper Information
Category: Medical optics and biotechnology
Received: Dec. 2, 2024
Accepted: Mar. 3, 2025
Published Online: Jun. 24, 2025
The Author Email: Zheng Sun (sunzheng@ncepu.edu.cn)
CSTR:32393.14.AOS241824
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