结合梯度投影稀疏重构和复数小波的图像重构  

Image reconstruction based on gradient projection for sparse representation and complex wavelet

作　　者：高彦彦[1] 李莉[1] 张晶[1] 贾英茜[1] GAO Yanyan;LI Li;ZHANG Jing;JIA Yingqian(College of Mechanical and Electrical Engineering,Shijiazhuang University,Shijiazhuang Hebei 050035,China)

机构地区：[1]石家庄学院机电学院

出　　处：《计算机应用》2020年第2期486-490,共5页journal of Computer Applications

基　　金：河北省高等学校科学技术研究项目(QN2017411);河北省重点研发计划自筹项目(18210910)~~

摘　　要：压缩感知主要包括随机投影和重构两部分。针对迭代收缩算法收敛速度较慢,普通二维小波变换缺少方向性表示的缺点,利用置乱离散余弦变换(PDCT)实现随机投影,重构时采用梯度投影算法,在简化计算的基础上,通过迭代的方式完善图像在双树复数小波域的变换系数,最后经反变换后得到重构图像。在同一重构算法下,比较了利用双树复数小波变换和双正交小波变换的重构结果,结果表明前者重构后的图像在细节和平滑度上优于后者,在峰值信噪比(PSNR)上平均高出约1.5 dB;同一稀疏域中,梯度投影算法的收敛速度优于迭代收缩算法;相同稀疏域和重构算法下,PDCT与结构随机矩阵相比在PSNR上略高。Compressed sensing mainly contains random projection and reconstruction.Because of lower convergence speed of iterative shrinkage algorithm and the lacking of direction of traditional 2-dimensional wavelet transform,random projection was implemented by using Permute Discrete Cosine Transform(PDCT),and the gradient projection was used for reconstruction.Based on the simplification of computation complexity,the transformation coefficients in the dual-tree complex wavelet domain were improved by iteration.Finally,the reconstructed image was obtained by the inverse transform.In the experiments,the reconstruction results of DT CWT(Dual-Tree Complex Wavelet Transform)and bi-orthogonal wavelet were compared with the same reconstruction algorithm,and the former is better than the latter in image detail and smoothness with higher Peak Signal-to-Noise Ratio(PSNR)of 1.5 dB.In the same sparse domain,gradient projection converges faster than iterative shrinkage algorithm.And in the same sparse domain and random projection,PDCT has a slightly higher PSNR than the structural random matrix.

关 键 词：压缩感知 图像重构 随机投影 稀疏表示 双树复数小波 置乱离散余弦变换 梯度投影 

分 类 号：TP391.4[自动化与计算机技术—计算机应用技术]