Medical image processing plays an important role in the interaction of real world and metaverse for healthcare. Self-supervised denoising based on sparse coding methods, without any prerequisite on large-scale training samples, has been attracting extensive attention for medical image processing. Whereas, existing self-supervised methods suffer from poor performance and low efficiency. In this paper, to achieve state-of-the-art denoising performance on the one hand, we present a self-supervised sparse coding method, named the weighted iterative shrinkage thresholding algorithm (WISTA). It does not rely on noisy-clean ground-truth image pairs to learn from only a single noisy image. On the other hand, to further improve denoising efficiency, we unfold the WISTA to construct a deep neural network (DNN) structured WISTA, named WISTA-Net. Specifically, in WISTA, motivated by the merit of the lp-norm, WISTA-Net has better denoising performance than the classical orthogonal matching pursuit (OMP) algorithm and the ISTA. Moreover, leveraging the high-efficiency of DNN structure in parameter updating, WISTA-Net outperforms the compared methods in denoising efficiency. In detail, for a 256 by 256 noisy image, the running time of WISTA-Net is 4.72 s on the CPU, which is much faster than WISTA, OMP, and ISTA by 32.88 s, 13.06 s, and 6.17 s, respectively.