Correlated and Multi-frequency Diffusion Modeling for Highly Under-sampled MRI Reconstruction

Given the obstacle in accentuating the reconstruction accuracy for diagnostically significant tissues, most existing MRI reconstruction methods perform targeted reconstruction of the entire MR image without considering fine details, especially when dealing with highly under-sampled images. Therefore, a considerable volume of efforts has been directed towards surmounting this challenge, as evidenced by the emergence of numerous methods dedicated to preserving high-frequency content as well as fine textural details in the reconstructed image. In this case, exploring the merits associated with each method of mining high-frequency information and formulating a reasonable principle to maximize the joint utilization of these approaches will be a more effective solution to achieve accurate reconstruction. Specifically, this work constructs an innovative principle named Correlated and Multi-frequency Diffusion Model (CM-DM) for highly under-sampled MRI reconstruction. In essence, the rationale underlying the establishment of such principle lies not in assembling arbitrary models, but in pursuing the effective combinations and replacement of components. It also means that the novel principle focuses on forming a correlated and multi-frequency prior through different high-frequency operators in the diffusion process. Moreover, multi-frequency prior further constraints the noise term closer to the target distribution in the frequency domain, thereby making the diffusion process converge faster. Experimental results verify that the proposed method achieved superior reconstruction accuracy, with a notable enhancement of approximately 2dB in PSNR compared to state-of-the-art methods.