Abstract: The sparse decomposition algorithm is an important problem in the signal sparse decomposition, and is related to the factual application. The smoothed [l0] norm approximation algorithm based on the Quasi-Newton direction is proposed, and on the algorithm the Quasi-Newton direction is used instead of the steepest ascent direction when maximizing the approximation function of [l0] norm. The experimental results show that the proposed algorithm is efficient to the signal sparse decomposition and has the better ability to anti-noise-jamming, the decomposition coefficient is more accurate and the signal-to-noise is bigger with the algorithm.

Key words: smoothed [l0]approximation algorithm, Quasi-Newton direction, steepest ascent direction, sparse decomposition

摘要： 稀疏分解算法是信号稀疏分解领域的一个重点问题，关系到稀疏分解在实际中的应用。在分析平滑[l0]算法的基础上，提出了基于拟牛顿方向的平滑[l0]算法。该算法在求解[l0]范数的近似函数最优解时，取代平滑[l0]算法中的最速上升方法，以拟牛顿方向作为迭代搜索方向。仿真结果表明，利用基于拟牛顿方向的平滑[l0]算法对信号进行稀疏分解，得到的稀疏分解系数精确度更高，与真实系数之间的误差更小，信噪比更大，抗噪声能力更强。

关键词: 平滑[l0]算法, 拟牛顿方向, 最速上升方向, 稀疏分解