基于单层小波变换的自适应压缩感知图像处理

文章在未知二维图像的稀疏度的情况下,提出了基于单层小波变换的自适应压缩感知算法,保留其中的低频系数,只针对高频系数进行测量。在小波变换把二维图像分成低低、低高、高低和高高的4块之后,利用稀疏度自适应匹配追踪算法,分别对其中包含在低高块中的列、高低块中的行、高高块整体中的那些高频系数进行恢复,再进行小波逆变换重构图像。仿真结果表明,与原来的单层小波变换的非自适应压缩感知算法相比,该算法解决了稀疏度未知情况下的图像恢复问题,而且重构图像质量也得到很好的保证,例如在相同的采样率下,新算法与原算法之间的PSNR相差不过2dB。

Adaptive compressed sensing based on single layer wavelet transform for image processing

Without the assumption of the known sparsity of the two dimensional images,an improved adaptive compressed sensing algorithm based on the single layer wavelet transform is proposed,which only measures the high-pass wavelet coefficients but not the low-pass wavelet coefficients.After such a wavelet transform separates the two-dimensional image into four wavelet coefficient blocks,i.e.low-low,low-high,high-low and high-high,the sparsity adaptive matching pursuit(SAMP) algorithm is used to recover the high-pass information included separately in the columns of the low-high clock,in the rows of the high-low block and in the total high-high block,then the image is reconstructed by the inverse wavelet transform.The simulation results demonstrate that comparing to the original compressed sensing algorithm based on the single layer wavelet transform,the proposed algorithm solves the problem of recovering the images without knowing its sparsity as well as guarantees the good enough quality of the image.For example,at the same sampling rate,the PSNR difference between the new algorithm and the old one is not greater than 2 dB.