This study proposes an innovative 3D diffusion-based model called the Cycle-consistency Geometric-integrated X-ray to Computed Tomography Denoising Diffusion Probabilistic Model (X-CBCT-DDPM). The X-CBCT-DDPM is designed to effectively reconstruct volumetric Cone-Beam CBCTs (CBCTs) from a single X-ray projection from any angle, reducing the number of required projections and minimizing patient radiation exposure in acquiring volumetric images. In contrast to the traditional DDPMs, the X-CBCT-DDPM utilizes dual DDPMs: one for generating full-view x-ray projections and another for volumetric CBCT reconstruction. These dual networks synergistically enhance each other's learning capabilities, leading to improved reconstructed CBCT quality with high anatomical accuracy. The proposed patient-specific X-CBCT-DDPM was tested using 4DCBCT data from ten patients, with each patient's dataset comprising ten phases of 3D CBCTs to simulate CBCTs and Cone-Beam X-ray projections. For model training, eight phases of 3D CBCTs from each patient were utilized, with one for validation purposes and the remaining one reserved for final testing. The X-CBCT-DDPM exhibits superior performance to DDPM, conditional Generative Adversarial Networks (GAN), and Vnet, in terms of various metrics, including a Mean Absolute Error (MAE) of 36.36±4.04, Peak Signal-to-Noise Ratio (PSNR) of 32.83±0.98, Structural Similarity Index (SSIM) of 0.91±0.01, and Fréchet Inception Distance (FID) of 0.32±0.02. These results highlight the model's potential for ultra-sparse projection-based CBCT reconstruction.
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