Frequency-Domain Super-Resolution With Reconstruction Using Compressed Representation (FDSR-RCR) Algorithm for Remote Sensing Satellite Images

In remote sensing image processing for Earth and environmental applications, super-resolution (SR) is a crucial technique for enhancing the resolution of low-resolution (LR) images. In this study, we proposed a novel algorithm of frequency-domain super-resolution with reconstruction from compressed representation. The algorithm follows a multistep procedure: first, an LR image in the space domain is transformed to the frequency domain using a Fourier transform. The frequency-domain representation is then expanded to the desired size (number of pixels) of a high-resolution (HR) image. This expanded frequency-domain image is subsequently inverse Fourier transformed back to the spatial domain, yielding an initial HR image. A final HR image is then reconstructed from the initial HR image using a low-rank regularization model that incorporates a nonlocal smoothed rank function (SRF). We evaluated the performance of the new algorithm by comparing the reconstructed HR images with those generated by several commonly used SR algorithms, including: 1) bicubic interpolation; 2) sparse representation; 3) adaptive sparse domain selection and adaptive regularization; 4) fuzzy-rule-based (FRB) algorithm; 5) SR convolutional neural networks (SRCNNs); 6) fast SR convolutional neural networks (FSRCNNs); 7) practical degradation model for deep blind image SR; 8) the frequency separation for real-world SR (FSSR); and 9) the enhanced SR generative adversarial networks (ESRGANs). The algorithms were tested on Landsat-8 and Moderate Resolution Imaging Spectroradiometer (MODIS) multiresolution images over various locations, as well as on images with artificially added noise to assess the robustness of each algorithm. Results show that: 1) the proposed new algorithm outperforms the others in terms of the peak signal-to-noise ratio, structure similarity, and root-mean-square error and 2) it effectively suppresses noise during HR reconstruction from noisy low-resolution (LR) images, overcoming a key limitation of existing SR methods.