基于非下采样contourlet变换的压缩感知图像重建

受传统采样定理限制,直接从信号采集系统得到高分辨率图像较困难,且信号获取过程会导致大量的采样数据.压缩感知理论指出可用特定测量矩阵将高维信号投影到低维空间上,求解数值优化问题准确重构原始信号,突破了传统采样定理的限制.传统压缩感知图像重建算法对所有系数测量,需进行多层小波变换保证图像质量,且小波捕捉方向信息有限,重建图像质量较差.故此提出采用非下采样contourlet变换(NSCT)做信号稀疏变换,并针对变换系数的特点,选择性的对系数测量,利用正交匹配追踪算法进行重构.实验结果表明,仅用单层NSCT变换可重建出高质量图像,克服传统算法需进行多层小波变换的缺点,降低采样和存储的数据量且重建的图像质量得到极大提升.

Compressed sensing based on nonsubsampled contourlet transform for image reconstruction

Constrained by traditional sampling theory,it’s difficult to obtain high resolution images from signal acquisition systems and great amounts of date occur as a result.The theory of compressed sensing broke through the Nyquist sampling theory by combining sampling and compressing together under the assumption that the signal is compressible or sparse in a certain sparse transform domain.Traditional image reconstruction algorithms based on the compressed sensing theory measure all the coefficients,which needs multi-layer wavelet transform to ensure image quality.Since the wavelet can only capture limited direction information,the reconstructed image is consequently of low resolution.Nonsubsampled contourlet transform was thus introduced as the sparse transform.According to the properties of coefficients,only the high-pass coefficients were measured,then the original image was reconstructed using the orthogonal matching pursuit method.Compared with the original algorithm,simulation results show that high resolution images can be obtained with only one layer nonsubsampled contourlet transform,thus reducing the sampling and storage data and greatly improving the quality of the reconstruction image.