Following the great success of deep convolutional neural networks (CNNs) in computer vision, this paper proposes a complex-valued CNN (CV-CNN) sp ally for synthetic aperture radar (SAR) image interpretation. It utilizes both amplitude and phase information of complex SAR imagery. All elements of CNN including input–output layer, convolution layer, activation function, and pooling layer are extended to the complex domain. Moreover, a complex backpropagation algorithm based on stochastic gradient descent is derived for CV-CNN training. The proposed CV-CNN is then tested on the typical polarimetric SAR image classification task which classifies each pixel into known terrain types via supervised training. Experiments with the benchmark data sets of Flevoland and Oberpfaffenhofen show that the classification error can be further reduced if employing CV-CNN instead of conventional real-valued CNN with the same degrees of freedom. The performance of CV-CNN is comparable to that of existing state-of-the-art methods in terms of overall classification accuracy.
The feature extractor is often handcrafted with statistical or physical characteristics to make a good representation of different types of targets. However, such paradigm has been revolutionized by CNN which automatically learns hierarchical representations from the data, and it demonstrated superior performances over conventional approaches by a significant margin.
Problem:Nevertheless, these studies directly applied real-valued neural networks to the amplitude of SAR image (usually converted to dB scale), while neglecting phase information.

POLSAR images are acquired by the polarimetric radar
system, and each resolution cell of the basic SLC format is expressed by a 2 × 2 complex scattering matrix.
CNN has achieved great success in computer vision areas.This study aims to apply CNN to SAR image processing. In order to take advantage of phase information, we present the CV-CNN which extends RV-CNN to complex domain. Both neurons and weights are represented by complex numbers. A complex version of backpropagation is also proposed, which can effectively train deep CV-CNN with massive complex SAR images. A novel POLSAR image classification scheme based on CV-CNN is then proposed and evaluated with real SAR data. Results show that a significant improvement in terms of classification accuracy can be achieved by converting RV-CNN to CV-CNN. It opens up a wide range of applications for CV-CNN in SAR image interpretation.
Notation:The text is orginated from 《Complex-Valued Convolutional Neural Network and Its Application in Polarimetric SAR Image Classification》