cs.CVFeb 27, 2026
SavePretty Good Measurement for Radiomics: A Quantum-Inspired Multi-Class Classifier for Lung Cancer Subtyping and Prostate Cancer Risk Stratification
Organizations: Università degli Studi di Cagliari, Via Is Mirrionis 1, Cagliari, 09123, Italy · Institute of Bioimaging and Complex Biological Systems - National Research Council (IBSBC - CNR), Cefalù, 90015, Italy · National Laboratory of South, National Institute for Nuclear Physics(LNS-INFN), Catania, 95125, Italy
Abstract
We investigate a quantum-inspired approach to supervised multi-class classification based on the Pretty Good Measurement (PGM), viewed as an operator-valued decision rule derived from quantum state discrimination. The method associates each class with an encoded mixed state and performs classification through a single POVM construction, thus providing a genuinely multi-class strategy without reduction to pairwise or one-vs-rest schemes. In this perspective, classification is reformulated as the discrimination of a finite ensemble of class-dependent density operators, with performance governed by the geometry induced by the encoding map and by the overlap structure among classes. To assess the practical scope of this framework, we apply the PGM-based classifier to two biomedical radiomics case studies: histopathological subtyping of non-small-cell lung carcinoma (NSCLC) and prostate cancer (PCa) risk stratification. The evaluation is conducted under protocols aligned with previously reported radiomics studies, enabling direct comparison with established classical baselines. The results show that the PGM-based classifier is consistently competitive and, in several settings, improves upon standard methods. In particular, the method performs especially well in the NSCLC binary and three-class tasks, while remaining competitive in the four-class case, where increased class overlap yields a more demanding discrimination geometry. In the PCa study, the PGM classifier remains close to the strongest ensemble baseline and exhibits clinically relevant sensitivity--specificity trade-offs across feature-selection scenarios.
Figures & tables
Figure 1: Representative examples of the imaging modalities underlying the two benchmark datasets. In the first row (NSCLC Case Study) there is an example of CT at the three anatomical planes: sagittal (left), coronal (middle), axial (right). In the second row, there is an example of CT (on the left) and PET/CT (on the right) for the PCa Case Study. PET/CT highlights high metabolic areas, in this case in the liver, kidneys, spleen and a focal spot in the prostate. The figure is included for visual illustration only; the classification analysis is performed on radiomics features extracted from the segmented volumes of interest, as detailed in Section 4 .
| Classification task | Number of classes | Accuracy (Model) |
|---|---|---|
| SCC vs. ADC | 2 | 58.57% (NB) |
| SCC, ADC, LCC | 3 | 52.9% (Ensemble) |
| SCC, ADC, LCC, NOS | 4 | 56.2% (Ensemble) |
Table 1: Best reported classification accuracies from [ 21 ] across NSCLC radiomics tasks of increasing complexity.
| Dataset (Institution) | Modality | Manufacturer & Scanner | Pixel Spacing (x, y) [mm] | Slice Thickness (z) [mm] | Matrix | Acquisition Parameters |
|---|---|---|---|---|---|---|
| NSCLC-Radiomics (MAASTRO Clinic) | CT | Siemens | 0.9765625, 0.9765625 | 3.0 | 512 512 | NA |
| NSCLC-Radiomics (MAASTRO Clinic) | CT | CMS | 0.9770, 0.9770 | 3.0 | 512 512 | NA |
| NSCLC-Radiogenomics (Stanford & Palo Alto VA) | CT | Siemens, GE Medical Systems, Philips | Range: 0.589844 – 0.976562 | Range: 0.625 – 3.0 (median 1.5) | 512 512 | Tube Voltage: 80–140 kVp (mean 120) Tube Current: 124–699 mA (mean 220) |
Table 2: Per-scanner and protocol details for the Non-Small-Cell Lung Carcinoma (NSCLC) cohort.
| Scanner Manufacturer & Model | Modality | Patients ( ) | Matrix Size | Voxel Size (x, y, z) [mm 3 ] | Specific Acquisition Parameters |
|---|---|---|---|---|---|
| General Electric | CT (16 row helical) | 68 | 512 512 | 1.37 1.37 3.75 | Tube Voltage: 140 kVp Tube Current: 800 mAmax |
| Discovery 690FX & MOT | PET ( 18 F-PSMA-1007) | 256 256 | 2.73 2.73 3.27 | Acq. Time: 90 s/bed (7–8 beds) Uptake Time: 120 min Dose: 4 MBq/kg | |
| Siemens | CT (16 row helical) | 75 | 512 512 | 0.98 0.98 3.0 | Tube Voltage: 130 kVp Tube Current: 345 mAmax |
| Biograph Horizon 4R | PET ( 18 F-PSMA-1007) | 512 512 | 1.45 1.45 3.0 | Acq. Time: 90 s/bed (6–7 beds) Uptake Time: 120 min Dose: 4 MBq/kg |
Table 3: Per-scanner and protocol details for the Prostate Cancer (PCa) cohort.
| Encoding | Rescaling | Number of Copies |
| {stereo, amplit} | {0.5, 1, 2, 4, 8, 16} | {1, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60} |
Table 4: Hyperparameter space employed for grid search in the NSCLC (2-class, 3-class, and 4-class) and PCa experiments.
Figure 2: Comparative evaluation of the proposed PGM classifier against conventional baseline models on the NSCLC two-class dataset. (a) Mean test area under the ROC curve (AUC) reported for each class. (b) Macro-averaged accuracy across the two classes.
Figure 3: Comparative evaluation of the proposed PGM classifier against conventional baseline models on the NSCLC three-class dataset. (a) Mean test area under the ROC curve (AUC) reported for each class. (b) Macro-averaged accuracy across the three classes.
Figure 4: Comparative evaluation of the proposed PGM classifier against conventional baseline models on the NSCLC four-class dataset. (a) Mean test area under the ROC curve (AUC) reported for each class. (b) Macro-averaged accuracy across the four classes.
Figure 5: Win–loss heatmap comparing classifiers for each labeling scenario. The three labeling scenarios are: (a) 2 - class labeling – only two disease categories are considered; (b) 3 - class labeling – three distinct categories are distinguished; (c) 4 - class labeling – all four histopathological subtypes are used. For each pair of classifiers, each cell reports the proportion of classes for which the row classifier attains a higher AUC than the column classifier. Values therefore range from 0 to 100 and indicate the fraction of class - wise pairwise wins. Darker cells denote a larger proportion of class - level dominance.
| Accuracy | AUC | Sensitivity | Specificity | Precision | F1-score | |
|---|---|---|---|---|---|---|
| Validation | ||||||
| Test |
Table 5: Performance of the PGM classifier on the NSCLC 2-class dataset (ADC vs. SCC), expressed as mean semi-amplitude of the 95% confidence interval over 10 train/test splits. Results are reported for the adenocarcinoma (ADC) class.
| Class | Accuracy | AUC | Sensitivity | Specificity | Precision | F1-score | |
|---|---|---|---|---|---|---|---|
| ADC | Validation | ||||||
| Test | |||||||
| LCC | Validation | ||||||
| Test | |||||||
| SCC | Validation | ||||||
| Test |
Table 6: Performance of the PGM classifier on the NSCLC 3-class dataset (ADC, LCC, SCC), expressed as mean semi-amplitude of the 95% confidence interval over 10 train/test splits.
| Class | Accuracy | AUC | Sensitivity | Specificity | Precision | F1-score | |
|---|---|---|---|---|---|---|---|
| NOS | Validation | ||||||
| Test | |||||||
| ADC | Validation | ||||||
| Test | |||||||
| LCC | Validation | ||||||
| Test |
Table 7: Performance of the PGM classifier on the NSCLC 4-class dataset (NOS, ADC, LCC, SCC), expressed as mean semi-amplitude of the 95% confidence interval over 10 train/test splits.
Figure 6: Mean confusion matrices (normalized by row) for the NSCLC histopathological subtype classification task, averaged over 10 train/test splits. Each cell reports the mean value and the standard deviation (±std). Panels show the binary classification problem (a) SCC vs. ADC (2-class), (b) the 3-class problem (ADC, LCC, SCC), and (c) the 4-class problem (NOS, ADC, LCC, SCC). ADC: adenocarcinoma; LCC: large cell carcinoma; SCC: squamous cell carcinoma; NOS: not otherwise specified.
Figure 7: Performance analysis of the PGM classifier on the PCa dataset under different feature-selection scenarios.
Figure 8: Heat - map of metric differences (PGM Ensemble) across feature - selection scenarios. Each row corresponds to a feature - set, and each column represents one of the six evaluation metrics Accuracy , AUC , Sensitivity , Specificity , Precision , and F1 - score . Cells are coloured on a diverging blue–red scale centred at zero: A blue hue indicates that the PGM classifier outperforms the ensemble for that metric (positive difference), whereas a red hue denotes inferior performance (negative difference). The colour intensity is proportional to the magnitude of the difference, allowing a rapid visual assessment of where the quantum - inspired PGM model provides gains or losses relative to the traditional ensemble approach.
Figure 9: Mean confusion matrices (normalized by row) for the prostate cancer (PCa) risk stratification task across the 13 feature subsets, averaged over 30 train/test splits. Each cell reports the mean value and the standard deviation (±std). The binary classification distinguishes high-risk from low-risk patients, using [ 18 F]-PSMA-1007 PET/CT radiomic features extracted from the 13 feature subsets defined by their selection frequency threshold (features90 to features0, finetuning, and features7030r).
| Feature Subset | Accuracy | AUC | Sensitivity | Specificity | Precision | F1-score |
|---|---|---|---|---|---|---|
| features90 | 51.35% (49.26–53.57%) | 53.55% (50.61–56.44%) | 38.42% (33.74–43.10%) | 64.29% (59.85–69.21%) | 50.71% (45.37–55.15%) | 43.07% (38.64–46.91%) |
| features80 | 55.67% (53.45–58.00%) | 58.09% (55.43–60.87%) | 49.75% (45.07–54.43%) | 61.58% (56.90–67.24%) | 57.51% (54.00–61.78%) | 52.21% (48.84–55.46%) |
| features70 | 67.98% (64.53–71.18%) | 74.96% (71.02–78.70%) | 65.52% (60.84–70.20%) | 70.44% (66.26–74.63%) | 69.01% (65.52–72.50%) | 66.78% (62.85–70.54%) |
| features60 | 70.94% (67.49–74.38%) | 78.34% (74.91–81.51%) | 71.18% (66.74–75.38%) | 70.69% (66.01–74.88%) | 71.24% (67.77–74.77%) | 70.78% (67.03–74.24%) |
| features50 | 72.02% (69.16–75.00%) | 80.10% (76.95–82.74%) | 70.95% (66.90–74.76%) | 73.10% (69.29–76.67%) | 72.94% (70.04–76.25%) | 71.54% (68.76–74.74%) |
| features40 | 72.62% (70.12–75.12%) | 80.00% (77.53–82.42%) | 72.14% (68.33–75.95%) | 73.10% (69.52–76.43%) | 73.21% (70.44–75.92%) | 72.28% (69.51–74.97%) |
Table 8: Performance of the PGM model across 13 feature subsets (mean and 95% CI over 30 splits). Best values per metric are highlighted in bold .
Appendix figures & tables4 assets
Supplementary material from the paper’s appendix.
Appendix
| Parameter | NSCLC (CT) | PCa ( F PSMA-1007 PET) |
|---|---|---|
| Bin discretization | Bin count = 64 | Bin width = 0.25 |
| Isotropic voxel size | mm 3 | mm 3 |
| Interpolator | sitkLinear | sitkBSpline |
| Wavelet basis | Haar | Coiflet 1 |
| LoG sigma range | 0.5–5.0, step 0.5 | 0.5–5.0, step 0.5 |
| Image normalization | – | Enabled (scale = 1) |
Table 9: PyRadiomics feature extraction configurations of the two reference studies whose feature-selected and harmonized data were used in the present work. The NSCLC (CT) and PCa ( F PSMA-1007 PET) configurations differ in most parameters, reflecting the distinct imaging modalities and the independent protocols established in the respective reference studies. Parameters not listed are left at their PyRadiomics default values. NSCLC configuration adapted from Table A1 of [ 21 ] ; PCa configuration adapted from Table 1 of [ 20 ] .
| Subset name | Selection criterion | Size |
|---|---|---|
| features90 | feature frequency | 1 |
| features80 | feature frequency | 2 |
| features70 | feature frequency | 4 |
| features60 | feature frequency | 5 |
| features50 | feature frequency | 8 |
| features40 | feature frequency | 12 |
Table 10: Specification of the 13 feature subsets used to train the PGM classifier on the PCa dataset. The feature-frequency thresholds and subset sizes follow the construction proposed in [ 20 ] (adapted from Table 4 therein). The features7030r subset is defined as the union of finetuning and features70 .
| Feature | Average PCC | Feature frequency |
|---|---|---|
| log-sigma-4–5-mm-3D-glcm-InverseVariance | 0.3369 | 60.00% |
| log-sigma-0–5-mm-3D-ngtdm-Busyness | 0.2735 | 56.67% |
| log-sigma-3–0-mm-3D-glszm-SmallAreaEmphasis | 0.3756 | 53.33% |
| wavelet-LHL-glcm-MaximumProbability | 0.3758 | 50.00% |
| log-sigma-5–0-mm-3D-glszm-GrayLevelNonUniformityNormalized | 0.3322 | 46.67% |
| log-sigma-2–5-mm-3D-glszm-GrayLevelNonUniformity | 0.0948 | 43.33% |
Table 11: Candidate features for the finetuning subset, i.e., features with a selection frequency in the range. For each feature, the average Pearson Correlation Coefficient (PCC) with respect to the features in the features70 subset (averaged over the 30 iterations of the preliminary pipeline) and the selection frequency are reported. Features in bold are those satisfying and therefore retained in the final finetuning subset. Adapted from Table 5 of [ 20 ] .
| Feature | Selection frequency |
|---|---|
| wavelet-LHH-firstorder-Skewness | 96.67% |
| wavelet-HHL-glszm-SmallAreaEmphasis | 86.67% |
| wavelet-LHL-gldm-DependenceVariance | 76.67% |
| wavelet-HHL-glszm-SmallAreaLowGrayLevelEmphasis | 73.33% |
| log-sigma-4-5-mm-3D-glcm-InverseVariance | 60.00% |
| log-sigma-0-5-mm-3D-ngtdm-Busyness | 56.67% |
Table 12: Selection frequency of all 79 features that were selected at least once across the 30 LASSO iterations of the preliminary pipeline of [ 20 ] . For each feature, the selection frequency is reported as the percentage of iterations in which the feature was retained by LASSO. Features are sorted by decreasing frequency. The eleven frequency-based subsets defined in Table 10 ( features90 , features80 , features70 , …, features5 , features0 ) correspond to the cumulative groups of features whose frequency satisfies the respective threshold; for instance, features70 consists of the four features with frequency (top of the table), and features0 comprises all 79 listed features. Computed by the present authors from the per-split, post-LASSO feature lists made available by the authors of [ 20 ] ; consistent with Figure 4 and Table 4 of [ 20 ] .