This work aims to advance the field of SR by exploring wavelet-based networks. Unfortunately, this technique has received less attention despite its significant potential. We seek to provide a fresh perspective and revive research by re-evaluating these approaches. Discrete Wavelet Transformation (DWT) enables an efficient image representation without losing information compared to its naive spatial representation, i.e., traditional RGB format. It does so by separating high-frequency details in distinct channels and reducing the spatial area of input image representation by a factor of 4. Therefore, a smaller receptive field is required to capture the input during feature extraction. Using DWT, like in DWSR and MWCNN, reduces the overall model size and computational costs while performing similarly to state-of-the-art image SR architectures.
This work introduces a new Differential Wavelet Amplifier (DWA) module inspired by differential amplifiers from electrical engineering. Differential amplifiers increase the difference between two input signals and suppress the common voltage shared by the two inputs, called Common Mode Rejection (CMR). In other words, it mitigates the impact of noise (e.g., electromagnetic interference, vibrations, or thermal noise) affecting both source inputs while retaining valuable information and improving the integrity of the measured input signal. Our proposed DWA layer adapts this idea to deep learning and can be used as a drop-in module to existing SR models. This work shows its effectiveness as exemplary for wavelet-based SR approaches. DWA leverages the difference between two convolutional filters with a stride difference to enhance relevant feature extraction in the wavelet domain, emphasizing local contrasts and suppressing common noise in the input signals. We demonstrate the effectiveness of DWA through extensive experiments and evaluations, showing improved performance compared to existing wavelet-based SR models without DWA: DWSR with DWA shows overall better performance w.r.t. PSNR and SSIM, and MWCNN with DWA achieves better SSIM scores with comparable PSNR values on the testing datasets Set5, Set14, and BSDS100.
Our experimental analysis shows that DWA enables a direct application of DWSR and MWCNN to the input space by avoiding the DWT on the input image, which is an exciting property. This application reduces the input channel-wise to 3 instead of 12 channels for RGB images while keeping the spatial reduction benefit of DWT.
Our comprehensive evaluation demonstrates the improved performance on popular SR datasets such as Set5, Set14, and BSDS100 by adding DWA to existing wavelet-based SR models: DWSR and MWCNN.
Lastly, visual examinations showcase that DWSR with the DWA module captures better distinct edges and finer details closer to the ground truth residuals.
In conclusion, we presented a novel Differential Wavelet Amplifier (DWA) module, which can be used as a drop-in module to existing wavelet-based SR models. We showed experimentally on Set5, Set14, and BSDS100 for scaling factors 2, 3, and 4 that it improves the reconstruction quality of the SR models DWSR and MWCNN while enabling an application of them to the input image space directly without harm to performance. This module captures more distinct edges and finer details, which are closer to the ground truth residuals, which wavelet-based SR models usually learn. This work is an opportunity to seek further advancements for SR based on frequency-based representations.