U-Fresh: An Fri-Based Single Image Super Resolution Algorithm and An Application in Image Compression

Learning based single image super resolution (SISR) methods have achieved notable results, however, they require large datasets for training, and may struggle when there is a mismatch between the testing and training data. To overcome these drawbacks, we propose an approach, named U - FRESH, which only requires a small dataset but can achieve state-of-the-art performance also in the presence of training and testing mismatches. We accomplish this by leveraging a method called FRESH, which enhances the image resolution using FRI theory. We start upscaling from the FRESH generated low resolution image. To minimize the reconstruction error, we propose a new regression selection technique to make the mapping more reliable and robust, and a wavelet based back projection technique to improve the quality of the reconstructed image. Based on U - FRESH, we also propose a new framework based on JPEG 2000 for image compression. Numerical results show that our U-FRESH method achieves state-of-the-art performance in SISR and provides better compression results than JPEG 2000.