基于非下采样轮廓波的MRI图像的压缩感知重构

Compressed Sensing Reconstruction of MRI Images Based on Nonsubsampled Contourlet Transform

压缩感知是一种全新的信息采集与处理的理论框架,借助信号内在的稀疏性或可压缩性,可从小规模的线性、非自适应的测量值中通过非线性优化的方法精确重构信号。压缩感知以远低于奈奎斯特频率的采样频率,在压缩成像系统、医学图像处理等领域有着广阔的应用前景。提出算法采用非下采样轮廓波变换稀疏表达原始图像,通过傅立叶矩阵进行测量,最后采用迭代软阈值算法实现医学MRI图像的压缩感知重构。以峰值信噪比、互信息、伪影功率为评价指标,比较小波变换、频率局部化轮廓波变换以及非下采样轮廓波变换三者的压缩感知重构效果。实验结果表明,无论采样率设置如何变化,提出算法在峰值信噪比、原始信息保留比例以及重构精度等方面均具有明显优势,在快速医学成像领域具有广阔的应用前景。

Compressed sensing is a newly developed theoretical framework for information acquisition and processing. Using the non-linear optimization methods, the signals can be recovered accurately from fewer linear and non-adaptive measurements by taking advantages of the sparsity or compressibility inherent in real world signals. Compressed sensing represents compressible signals at a sampling rate significantly below the Nyquist rate, and it has been applied in com- pressive imaging and medical image processing. The flow chart of our algorithm is as follows. The nonsubsampled con- tourlet transform is applied to sparsely represent the original image, then the iterative soft-thresholding algorithm is used to reconstruct the medical MRI images based on Fourier matrix as the measurement matrix. The peak signal to noise rate （PSNR）,mutual information （MI） and artifacts power （AP） are used to compare the reconstruction effects of wavelet transform（WT）,sharp frequency localization contourlet transform （SFLCT） and nonsubsampled contourlet transform （NSCT）. Experimental results demonstrate that our method is superior to the other two methods in PSNR, remained proportion of original information and reconstruction precision. Our algorithm can be extended and widely used in rapid medical imaging technology.