Magnetic resonance imaging (MRI) is a crucial tool for clinical diagnosis while facing the challenge of long scanning time. To reduce the acquisition time, fast MRI reconstruction aims to restore high-quality images from the undersampled k-space. Existing methods typically train deep learning models to map the undersampled data to artifact-free MRI images. However, these studies often overlook the unique properties of k-space and directly apply general networks designed for image processing to k-space recovery, leaving the precise learning of k-space largely underexplored. In this work, we propose a continuous k-space recovery network from a new perspective of implicit neural representation with image domain guidance, which boosts the performance of MRI reconstruction. Specifically, (1) an implicit neural representation based encoder-decoder structure is customized to continuously query unsampled k-values. (2) an image guidance module is designed to mine the semantic information from the low-quality MRI images to further guide the k-space recovery. (3) a multi-stage training strategy is proposed to recover dense k-space progressively. Extensive experiments conducted on CC359, fastMRI, and IXI datasets demonstrate the effectiveness of our method and its superiority over other competitors.

Implicit neural representations have recently demonstrated promising potential in arbitrary-scale Super-Resolution (SR) of images. Most existing methods predict the pixel in the SR image based on the queried coordinate and ensemble nearby features, overlooking the importance of incorporating high-frequency prior information in images, which results in limited performance in reconstructing high-frequency texture details in images. To address this issue, we propose the Local Implicit Wavelet Transformer (LIWT) to enhance the restoration of high-frequency texture details. Specifically, we decompose the features extracted by an encoder into four sub-bands containing different frequency information using Discrete Wavelet Transform (DWT). We then introduce the Wavelet Enhanced Residual Module (WERM) to transform these four sub-bands into high-frequency priors, followed by utilizing the Wavelet Mutual Projected Fusion (WMPF) and the Wavelet-aware Implicit Attention (WIA) to fully exploit the high-frequency prior information for recovering high-frequency details in images. We conducted extensive experiments on benchmark datasets to validate the effectiveness of LIWT. Both qualitative and quantitative results demonstrate that LIWT achieves promising performance in arbitrary-scale SR tasks, outperforming other state-of-the-art methods. The code is available at https://github.com/dmhdmhdmh/LIWT.