Self-Supervised, Physics-Driven Sparse-Array XACT Reconstruction Using Sinusoidal Implicit Neural Representation

X-ray induced acoustic computed tomography (XACT) enables high-contrast bone imaging but typically relies on dense and expensive transducer arrays. Sparse array sampling introduces severe streak artifacts and loss of fine structural details in conventional reconstruction. This work aims to establish a robust reconstruction framework that achieves high-fidelity structural imaging under sparse sampling, thereby overcoming hardware density limitations and facilitating low-cost, high-resolution skeletal health assessment. We propose a self-supervised, physics-driven framework based on sinusoidal implicit neural representation. The unknown initial pressure distribution is parameterized as a continuous coordinate-to-pressure function via a sinusoidal representation network, and is coupled end-to-end with a differentiable acoustic forward simulator implemented in j‑Wave. Network optimization is performed by minimizing waveform residuals between measured and predicted signals, eliminating the need for paired ground-truth data. To improve training stability and accelerate convergence, an adjoint-based warm start and total variation regularization are employed. In experiments on simulated hand and femoral bone sparse array datasets, the proposed method consistently outperforms conventional approaches under various sparse sampling conditions. Notably, for an osteoporotic femur imaged with only 64 transducer elements, the method effectively suppresses artifacts and faithfully preserves fine trabecular structures, achieving a peak signal-to-noise ratio of 32.43 dB and a root mean square error of 0.0239, surpassing the structural and quantitative accuracy of traditional reconstruction using a full 256‑element array. These results demonstrate that the framework supports stable XACT reconstruction under sparse array conditions and, with its favorable artifact suppression and microstructural preservation capabilities, offers a practical computational pathway toward low-cost, high-quality XACT imaging.