SLRCNN: Integrating sparse and low-rank with a CNN denoiser for hyperspectral and multispectral image fusion

Fusion of hyperspectral image (HSI) and multispectral image (MSI) is a prevalent scheme to generate a HSI with enhanced spatial resolution. Current methods often fail to sufficiently leverage the effective spectral and spatial priors existing in the observed HSI and MSI to further enhance the fusion performance. To address this limitation, this paper proposes a novel HSI-MSI fusion approach, which integrates Sparse and Low Rank with a CNN denoiser (SLRCNN) while considering spectral dictionary optimization. Firstly, an initialized spectral dictionary is derived from the HSI. Next, the spatial coefficients optimization model is established by incorporating the sparse prior, local low-rank prior, and plugged image prior simultaneously, where the $l_1$ norm is imposed to promote the sparse prior, and the super-pixel segmentation strategy is conducted on the MSI to impose the local low-rank prior while a well-trained CNN denoiser is plugged in to enforce the image prior. Then, the spectral dictionary optimization model is constructed to refine the initial spectral dictionary, capturing more detailed spectral characteristics to further improve the fusion results. Finally, the optimization process involves applying the split-augmented Lagrangian shrinkage method and the alternating direction method of multipliers. Experimental results on simulated and real datasets, namely the Pavia University dataset, the Indian Pines dataset, and the EO-1 dataset, indicate that SLRCNN outperforms existing state-of-the-art approaches at 4x, 5x, and 6x resolutions in both qualitative and quantitative evaluation results. Specifically, the peak signal-to-noise ratio (PSNR) of SLRCNN is improved by more than 0.9 dB, 0.9 dB, and 0.2 dB while the spectral angle mapper (SAM) is decreased by more than 0.1, 0.2, and 0.2 in degree compared to other state-of-the-art methods across three datasets, respectively, which underscores the effectiveness of SLRCNN in leveraging both spatial detail reconstruction and spectral preservation.