Zafran Hussain Shah ^1* Marcel Müller ² Wolfgang Hübner ² Henning Ortkrass ² Barbara Hammer ³ Thomas Huser ² Wolfram Schenck ¹

• ¹ Bielefeld University of Applied Sciences, Bielefeld, Germany
• ² Faculty of Physics, University of Bielefeld, Bielefeld, North Rhine-Westphalia, Germany
• ³ Center of Cognitive Interaction Technology, Bielefeld University, Bielefeld, North Rhine-Westphalia, Germany

Real-valued convolutional neural networks (RV-CNNs) have outperformed classical approaches in many image restoration tasks such as image denoising and super-resolution. Recently, complex-valued convolutional neural networks (CV-CNNs) have shown remarkable performance in several computer vision tasks such as image classification and segmentation. However, the potential of CV-CNNs for image restoration problems in the frequency domain has not been fully investigated. Here, we first aim to explore the potential of CV-CNNs for image denoising and super-resolution in the frequency domain. Second, we propose two novel CV-CNN based models equipped with complexvalued attention gates for denoising and super-resolution problems. Third, we demonstrate that our CV-CNN based models outperform their real-valued counterparts for denoising super-resolution structured illumination microscopy (SR-SIM) and conventional image datasets. Additionally, the experimental results reveal that our proposed CV-CNN based models preserve the frequency spectrum better than their real-valued counterparts. Based on these findings we conclude that CV-CNN based methods provide a plausible and beneficial deep learning approach for image restoration in the frequency domain.