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• New CNN design with complex-valued operations. • Practical complex-valued CNN for image denoising. • Proposed CNN is effective for handling unseen noises. • State-of-the-art results are achieved. While complex-valued transforms have been widely used in image processing and have their deep connections to biological vision systems, complex-valued convolutional neural networks (CNNs) have not seen their applications in image recovery. This paper aims at investigating the potentials of complex-valued CNNs for image denoising. A CNN is developed for image denoising with its key mathematical operations defined in the complex number field to exploit the merits of complex-valued operations, including the compactness of convolution given by the tensor product of 1D complex-valued filters, the nonlinear activation on phase, and the noise robustness of residual blocks. The experimental results show that, the proposed complex-valued denoising CNN performs competitively against existing state-of-the-art real-valued denoising CNNs, with better robustness to possible inconsistencies of noise models between training samples and test images. The results also suggest that complex-valued CNNs provide another promising deep-learning-based approach to image denoising and other image recovery tasks. [ABSTRACT FROM AUTHOR]