基于近似l_0范数的稀疏信号重构

A Sparse Signal Reconstruction Algorithm Based on Approximate l_0 Norm

信号重构算法是压缩感知的关键.基于近似l_0范数的信号重构选取一个连续函数近似估计l_0范数,从而将l_0范数最小化问题转化为平滑函数的优化问题.该算法的关键在于选择合适的平滑函数和优化算法.为了提高压缩感知中稀疏信号恢复的精度,在之前工作的基础上,提出用一个简单的分式函数的和来近似估计l_0范数.然后通过牛顿迭代算法求解该函数的无约束优化问题的稀疏解,整合了似零范数算法快速收敛和牛顿迭代法精度高的优点.这样就可以在较少的时间内平滑且有效地近似l_0范数的最小化问题.仿真实验测试了所提算法在不同的压缩比、稀疏度及噪声水平情况下的性能,并与现有的同类算法进行了比较.结果表明:所提算法比现有的同类算法性能更好,重建信号的精度有了较大的提升,这有效地提高了在同等条件下压缩感知信号的恢复质量.

The signal reconstruction algorithm is the key to compressed sensing.Signal reconstruction based on approximate l_0 norm chooses a continuous function to estimate l_0 norm,thus the minimization problem of l_0 norm is transformed into an optimization problem of a smooth function.It is critical for the signal reconstruction algorithm to select the appropriate smooth function and optimization algorithm.To improve the accuracy of the sparse signal recovered in the compression sense,the sum of a simple fractional function is proposed to approximate l_0 norm on the basis of previous work in the paper.Then the sparse solution of an unconstrained optimization problem of the function is solved by Newton iterative algorithm,which effectively integrated the advantages of the fast convergence of approximate l_0 norm algorithm and the high precision of Newton iteration algorithm.Thus,the minimization of l_0 norm is approximated smoothly and efficiently within less time.The performance of the proposed algorithm is tested and compared with some existing similar algorithms in the case of different compression ratio,sparseness and noise levels in the simulation experiments.Simulation results show that the performance of the proposed algorithm is better than the existing similar algorithms,and the precision of reconstructed signal is greatly improved,which improves the signal recovery quality in compressed sensing effectively under the same conditions.