Adaptive Hybrid Quantum Image Representation for Efficient Encoding of Medical and SAR Image

Quantum image representation constitutes a foundational component of quantum image processing; however, its practical deployment on Noisy Intermediate-Scale Quantum (NISQ) hardware is fundamentally constrained by the cost of quantum state preparation. Existing representations such as the Flexible Representation of Quantum Images (FRQI) and the Novel Enhanced Quantum Representation (NEQR) rely on uniform, full-resolution encoding strategies that incur rapidly increasing gate counts and circuit depths, leading to severe decoherence and error accumulation on near-term devices. These limitations are particularly pronounced for heterogeneous and information-sparse modalities such as medical Magnetic Resonance Imaging (MRI) and Synthetic Aperture Radar (SAR), where uniform pixel-wise encoding introduces substantial redundant state preparation. To address these constraints, we propose Adaptive Hybrid Quantum Image Representation (AHQIR), a saliency-driven selective quantum state-preparation framework designed for efficient encoding of medical and SAR imagery under NISQ limitations. AHQIR departs from global encoding by employing a classical adaptive preprocessing stage to identify diagnostically significant regions in MRI and dominant backscatter structures in SAR images using a statistical thresholding criterion, thereby restricting quantum encoding to a salient pixel subset S. The quantum realization of AHQIR integrates Perception-Aided Encoding (PE) and Coherent-Size Encoding (CE) mechanisms, which condition state preparation on salient pixel coordinates and eliminate the requirement for power-of-two image padding. As a result, circuit depth and multi-qubit gate count scale with the number of salient pixels rather than total image size, enabling physically realizable circuits within current coherence limits. This selective and intentionally lossy design sacrifices global pixel-level fidelity in non-salient regions in order to preserve semantic and structural fidelity within regions of interest. AHQIR is evaluated against multiple state-of-the-art quantum image encoding schemes, including FRQI and NEQR, across Brain Tumor MRI and real-world SAR datasets. Experimental results demonstrate substantial reductions in gate count and improved robustness under realistic noise models, while maintaining reconstruction errors below clinically and analytically relevant thresholds for salient regions. These findings indicate that saliency-aware, selective state preparation offers a practical and scalable pathway for quantum.