<p>Poisson noise in medical imaging arises from photon counting. Although the deep image prior (DIP) is a promising unsupervised denoising technique, it often suffers from slow convergence, limited structural preservation, and overfitting under Poisson noise. To address these limitations, this study presents an unsupervised denoising model incorporating the generalized Stein's unbiased risk estimator (GSURE) into the DIP framework. The model enables accurate, reference-free risk estimation, allowing the observed noisy image to serve directly as the network input without introducing additional noise priors. This design embeds intrinsic structural information early in the optimization process, which accelerates convergence and enhances denoising accuracy. Furthermore, explicit first- and second-order gradient regularization terms are incorporated into the loss function. The first-order term constrains local intensity variations to preserve fine anatomical details, while the second-order term ensures global smoothness and reduces residual artifacts. These complementary constraints jointly improve noise suppression and mitigate overfitting commonly observed in DIP-based methods. The complex optimization problem is efficiently solved using the alternating direction method of multipliers (ADMM) with fast Fourier transform (FFT) acceleration, thereby reducing computational overhead. Experimental results show that the proposed model achieves an average PSNR improvement of 7.4% and an SSIM increase of 5.1% over the DIP. It reaches the 1000-iteration peak performance of DIP within only 70 iterations. These findings demonstrate the potential of the method to enhance diagnostic reliability and computational efficiency in medical imaging denoising.</p>