Medical grayscale images often suffer from insufficient global brightness information and resolution due to the computational resource limitations of clinical imaging devices and specific clinical needs. To enhance resolution and global luminance information in medical images with low complexity, this paper proposes SparWR, a novel lightweight super-resolution model for medical grayscale images. SparWR can adapt to various imaging modalities, ensuring that the reconstructed image closely matches the original in luminance distribution and characteristics while keeping model parameters and computational costs low and maintaining super-resolution quality, thereby significantly reducing training and inference times. Specifically, considering the sparse characteristics of single-channel grayscale medical images, our method employs sparse coding, which effectively preserves the high-frequency information in all directions of the image through dictionary training and sparse reconstruction. Furthermore, by leveraging the multi-resolution property of the wavelet transform, we apply the transform directly to the full image to enhance the signal’s sparse representation and capture information across different frequency bands without extra inter-channel coupling. To maintain the network’s lightweight design, the model consists of only a single residual block with a residual scaling factor. Finally, experimental results on public datasets across three modalities demonstrate SparWR’s excellent performance, confirming that this approach improves clinical image quality.