MFSR: Multi-fractal Feature for Super-resolution Reconstruction with Fine Details Recovery

Fractal features can capture the rich details of both micro and macro texture structures in an image. We propose MFSR, a diffusion model-based super-resolution method that incorporates multi-fractal features of low-resolution images as texture priors to enhance fine detail recovery. MFSR consists of three key components: (1) a Multi-Fractal Feature Extraction Block (MFB) that approximates fractal features through convolution-based soft assignment, where the Density Estimation Block (DEB) computes local density maps following power-law distributions, the Similar Feature Grouping Block (SFGB) performs soft clustering to partition features into texture-coherent subsets, the Grouped Processing Block (GPB) extracts hierarchical representations via multi-scale grouped convolutions, and the Feature Aggregation Block (FAB) fuses features via $3\times 3$ convolution for integration into the denoiser; (2) a modified U-Net denoiser that integrates multi-fractal features as reinforcement conditions; and (3) an attention-based sub-denoiser using Fast Fourier Transform (FFT) to suppress high-frequency noise during upsampling. Experiments demonstrate that MFSR achieves superior performance: on FFHQ 4×, MFSR attains PSNR of 26.94 dB and SSIM of 0.833, surpassing ResDiff by 0.21 dB in PSNR and 0.015 in SSIM; on DIV2K 4×, it reaches PSNR of 28.16 dB, outperforming ResDiff by 0.22 dB; on Urban100 4×, MFSR achieves PSNR of 27.66 dB with a 0.23 dB gain over ResDiff. Ablation studies further confirm that incorporating multi-fractal features consistently improves SR3, SRDiff, and ResDiff by up to 0.15 dB, demonstrating the generalizability of the proposed texture prior.