Enhanced Millimeter-Wave 3-D Imaging via Complex-Valued Fully Convolutional Neural Network

Abstract

To solve the problems of high computational complexity and unstable image quality inherent in the compressive sensing (CS) method, we propose a complex-valued fully convolutional neural network (CVFCNN)-based method for near-field enhanced millimeter-wave (MMW) three-dimensional (3-D) imaging. A generalized form of the complex parametric rectified linear unit (CPReLU) activation function with independent and learnable parameters is presented to improve the performance of CVFCNN. The CVFCNN structure is designed, and the formulas of the complex-valued back-propagation algorithm are derived in detail, in response to the lack of a machine learning library for a complex-valued neural network (CVNN). Compared with a real-valued fully convolutional neural network (RVFCNN), the proposed CVFCNN offers better performance while needing fewer parameters. In addition, it outperforms the CVFCNN that was used in radar imaging with different activation functions. Numerical simulations and experiments are provided to verify the efficacy of the proposed network, in comparison with state-of-the-art networks and the CS method for enhanced MMW imaging.

3-D Super-Resolution of Coded Aperture Millimeter-Wave Images Using Complex-Valued Convolutional Neural Network

“…Similarly, there are other models also that make use of complex-valued data to solve computer vision problems [52]- [57]. However, as far as the problem of SR is concerned, [46] and [47] are the only two models developed in the literature that uses complexvalued neural network. In [46], four complex convolutional layers, each paired with a complex parametric ReLU activation function were used along with a deconvolutional layer at the end to retrieve the output image.…”

“…However, as far as the problem of SR is concerned, [46] and [47] are the only two models developed in the literature that uses complexvalued neural network. In [46], four complex convolutional layers, each paired with a complex parametric ReLU activation function were used along with a deconvolutional layer at the end to retrieve the output image. This model used large filter sizes of 11 × 11, 9 × 9, 7 × 7 as well as 5 × 5 for mapping the input images to output images.…”

“…As we have developed our model using 3D complex-valued data, our model has the ability to address the SR problem in both the cross-range as well as the range plane. Not only that, the model architecture is simple as compared to [46] and [47] in the sense that it uses smaller filter sizes of 3 × 3 × 3, 2 × 2 × 2, and 1 × 1 × 1, as well as fewer layers. In this paper, a performance comparison was drawn between our architecture with these two previously developed complex-valued networks [46], [47] available in the literature for SR problems.…”

“…As a final test of our architecture, we have performed a comparative study with two previously developed complexvalued CNN architectures, exactly as shown in [46] and [47]. The same training as well as test datasets, as the ones used in this paper, were used to perform these comparisons.…”

“…The same training as well as test datasets, as the ones used in this paper, were used to perform these comparisons. To accommodate the complex-valued data in the networks given in [46] and [47], the convolutional and the activation functions have been changed to the complex-valued convolutional and activation functions mentioned in this paper. The number of layers in the networks as well as the number of layers are kept the same as mentioned in the papers.…”