新的似零范数的分块压缩感知图像重构

New Image Reconstruction Algorithm for Block Compressed Sensing with Approximate l_0 Norm

针对提高压缩感知图像重构精度的问题,提出新的近似l0范数的函数,并结合牛顿算法实现图像重构.首先选用冗余脊波变换矩阵作为稀疏表示图像的基函数,利用正交匹配追踪算法对图像进行稀疏化.重构过程基于压缩感知理论,结合似零范数算法思想,用一个简单的分式函数来近似估计l0范数,并通过牛顿迭代算法求得稀疏解,从而实现了二维图像重构,融合了似零范数算法快速收敛和牛顿迭代法高精度的优点.仿真实验结果表明,在相同的条件下,相比于现有的其他同类算法,该算法重构的图像精度更高,有效地提高了压缩感知图像重构的质量.

For the problem of improving quality of image reconstruction, a new function is proposed to approximate/0norm. Firstly, or- thogonal matching pursuit algorithm is chosen to represent image sparsely based on ridgelet redundant dictionary. Then, the Newton iterative algorithm determines the optimal sparse solution based on compressed sensing. A simple fractional function is used to approximate l0 norm. Fast convergence of approximate l0norm algorithm and the advantage in accuracy of Newton iterative algorithm are combined. Finally, simulation results show that compared to other similar algorithms, the proposed algorithm can effectively improve image quality and precision in compressed sensing, while providing the same conditions.