Although complex-valued (CV) neural networks have shown better classification results compared to their realvalued (RV) counterparts for polarimetric synthetic aperture radar (PolSAR) classification, the extension of pixel-level RV networks to the complex domain has not yet thoroughly examined. This paper presents a novel complex-valued deep fully convolutional neural network (CV-FCN) designed for PolSAR image classification. Specifically, CV-FCN uses PolSAR CV data that includes the phase information and utilizes the deep FCN architecture that performs pixel-level labeling. It integrates the feature extraction module and the classification module in a united framework. Technically, for the particularity of PolSAR data, a dedicated complex-valued weight initialization scheme is defined to initialize CV-FCN. It considers the distribution of polarization data to conduct CV-FCN training from scratch in an efficient and fast manner. CV-FCN employs a complex downsampling-then-upsampling scheme to extract dense features. To enrich discriminative information, multi-level CV features that retain more polarization information are extracted via the complex downsampling scheme. Then, a complex upsampling scheme is proposed to predict dense CV labeling. It employs complex max-unpooling layers to greatly capture more spatial information for better robustness to speckle noise. In addition, to achieve faster convergence and obtain more precise classification results, a novel average cross-entropy loss function is derived for CV-FCN optimization. Experiments on real PolSAR datasets demonstrate that CV-FCN achieves better classification performance than other state-of-art methods.Index Terms-Complex-valued deep fully convolutional neural network (CV-FCN), polarimetric synthetic aperture radar (Pol-SAR) image classification, pixel-level labeling.

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