A Deep Network Based on Wavelet Transform for Image Compressed Sensing

Most conventional compressed sensing (CS) algorithms are impaired by the fact that the optimization of image reconstruction suffers from the need for multiple iterative calculations. Recently, deep learning-based CS algorithms have been proposed and they dramatically achieve efficient reconstruction and fast computing speed with fewer sampling measurements than traditional iterative optimization-based algorithms. However, the sampling process of common deep learning-based CS and traditional CS generally cannot sufficiently exploit the structural sparsity of image sequences to effectively conduct CS research. Motivated by the fact that a sparser signal is easier to reconstruct accurately, in this paper, we propose two novel algorithms called the WCS-Nets (WCS-Net and WCS-Net+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^+$$\end{document}), which synthesize the advantages of a sampling network based on sparse representation and a deep elastic reconstruction network. WCS-Net is an improvement in DR2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^2$$\end{document}-Net, and its primary innovation focuses on combining the sym8 wavelet transform with a sampling network. Moreover, considering that multi-scale residual learning has better reconstruction efficiency, an enhanced version, called WCS-Net+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^+$$\end{document}, is designed in the deep elastic reconstruction network and further improves the reconstruction accuracy. Experimental results demonstrate that the proposed methods achieve better results when compared with other state-of-the-art deep learning-based and traditional CS algorithms in terms of reconstruction quality, runtime and robustness to noise.