Frequency-aware quaternion neural network for high-fidelity color imaging through scattering media

Deep learning enables multi-wavelength speckle imaging over a scattering medium. However, the achieved fidelity in both color correlation and information retrieval is still limited, because the RGB channels are treated as independent and parallel scalar feature maps processed in parallel in the existing deep neural network (DNN). Herein, we propose a frequency-aware quaternion DNN (FQN) that leverages the vectorial process capability of the quaternion, where color images are modeled as vectors within a four-dimensional hypercomplex space. Therefore, the FQN can achieve explicit structural coupling among the RGB channels during quaternion convolution operations, where luminance and chrominance relationships among different color channels can be attracted. Concurrently, a discrete wavelet transform (DWT) is further integrated to explicitly preserve high-frequency texture details, preventing them from being filtered out during training and inference. Experimental results on a natural scene images dataset demonstrate high-fidelity color imaging retrieval over a scattering medium, where both color and information fidelity can be boosted compared to conventional real-valued CNNs. The proposed approach is general and can be generalized to related fields of computational imaging.