近年来,压缩感知已广泛用于合成孔径雷达(SAR)图像、医学图像重建和磁共振成像等图像处理领域。传统平滑l0范数(SL0)重建方法通过引入平滑函数,很好地将求解最小l0范数这个NP-hard问题转化成求解平滑函数极值的凸优化问题,但SL0方法使用最速下降法搜索最优解,存在锯齿效应、收敛速度不理想的问题。为了解决上述问题,文中首先定义了一种新的混合共轭梯度;然后,在研究SL0 方法的基础上,提出了一种新的基于混合共轭梯度的改进SL0压缩感知重建方法。实验表明:文中所提方法收敛速度快,对噪声不敏感,具有较好的稳健性;在相同实验条件下,对SAR图像的重建性能优于SL0和其他同类方法,重建质量更好。

Compressed sensing has been widely used in image processing in recent years, such as synthetic aperture radar (SAR) images, medical image, single-pixel imaging and so on. Traditional SL0 reconstruction algorithm approaches l0 norm by introducing Gaussian function family, and transforms the NP-hard problem of minimum l0 norm into convex optimization problem of smooth function. But the SL0 algorithm has sawtooth effect and slow convergence speed because it is solved by steepest descent method. In order to solve this problem, the proposed algorithm in this paper introduced a mixed conjugate gradient method. The improved SL0 algorithm does not need to predict the signal sparsity, and is insensitive to noise, so it has good reconstruction effect. Experimental results show that the performance of the proposed compressed sensing reconstruction algorithm in the paper is better than SL0 and other similar algorithms under the same test conditions, and is feasible and effective for SAR image reconstruction.

TN957.51;TP391