H-QDCT: hierarchical quantum DCT for structural-textural feature fusion in medical imaging

Deep learning models for medical image classification typically rely on millions of parameters or extensive pretraining, limiting deployment in resource-constrained settings. We investigate whether a hybrid quantum-classical architecture can achieve competitive diagnostic performance with extreme parameter efficiency and superior stability compared to lightweight classical counterparts.

We propose the hierarchical quantum discrete cosine transform (H-QDCT), a lightweight pipeline combining classical patch-based preprocessing with quantum frequency-domain feature extraction. Images are partitioned into patches, amplitude-embedded into quantum states, and transformed via a quantum DCT that reorganizes information by spatial frequency. A hierarchical variational ansatz processes structural (low-frequency) and textural (high-frequency) components in disjoint qubits subspaces before global fusion. We evaluate H-QDCT on six clinically binarized MedMNIST datasets under grayscale constraints against both heavy and lightweight classical baselines.

H-QDCT achieves competitive performance with only 1726 parameters, exceeding a 99.98% reduction compared to ResNet-18 (11.2M parameters). On PneumoniaMNIST, the model attains an AUC of 0.90, approaching the 0.93 of pretrained ResNet-18. Crucially, H-QDCT demonstrates superior robustness in data-scarce regimes: While the lightweight vision transformer (Tiny-ViT) collapsed to the majority class on DermaMNIST (F1 $=0.00$ ) and BloodMNIST (F1 $=0.06$ ), H-QDCT retained learnability on BloodMNIST (F1 up to 0.22) with stable convergence. Beyond binary screening, the architecture extends natively to multi-class differential diagnosis (from $K=2$ to $K=9$ ) without mode collapse, and on PneumoniaMNIST and PathMNIST its compact encoder surpasses a from-scratch ViT-B/16 ( $\sim$ 86 M parameters) in macro-F1 while using under 1,000 trainable parameters. The architecture operates entirely on grayscale inputs, confirming its reliance on morphological semantics rather than color bias.

H-QDCT demonstrates that quantum spectral feature extraction achieves clinically meaningful classification with orders-of-magnitude parameter reduction. By mitigating the convergence instability inherent in small-scale classical transformers, H-QDCT establishes a robust design principle for compact, frequency-aware medical diagnostics on near-term quantum hardware.