采用改进Levenberg-Marquardt法的快速弹性运动估计

弹性运动估计是近年来出现的一种有效的时间维视频预测编码技术，但其基于高斯-牛顿法的优化求解仍存在计算量高、收敛不稳定的问题.为此提出一种基于改进Levenberg-Marquardt（L-M）法的弹性运动估计算法.首先，根据弹性基函数和黑塞矩阵的数值对称性，给出了L-M黑塞矩阵的快速计算方法，将其计算量降低了62.5%.其次，通过理论和实验分析发现，L-M对角矩阵阻尼系数的更新因子对弹性运动估计性能有明显影响，进而采用最近2次迭代的搜索步长的平方商自适应地确定更新因子，并对该阻尼系数进行正、负交替更新.实验结果表明，对于具有不同空间分辨率和场景特点的视频序列，算法始终能够保持较高的估计精度，运动补偿的平均峰值信噪比较之基于块平移模型的全搜索和基于改进高斯-牛顿法的弹性运动估计分别提高2.54dB、1.77dB.并且，所提算法收敛速度快，一般只需1~2次迭代就能取得高于传统弹性运动估计和块平移全搜索的峰值信噪比.

Fast Elastic Motion Estimation Using Improved Levenberg-Marquardt Method

Elastic motion estimation is an effective temporal predictive coding technique of video proposed in recent years. But its optimization solution based on Gauss-Newton method still exhibits the problem of high computational complexity and unstable convergence yet. Thus an elastic motion estimation algorithm is addressed based on an improved Levenberg-Marquardt (L-M) method. First, a fast implementation of the L-M Hessian matrix is designed according to the numerical symmetry of elastic basis function and the Hessian matrix, which reduces its computational complexity by 62.5%. Second, it is found that the update factor of L-M diagonal matrix''s damping coefficient has obvious influence on the performance of elastic motion estimation through theoretical and experimental analyses. The squared ratio of the step size in the latest two iterations is used to adaptively determine the update factor, by which the damping coefficient is updated positively and negatively in turn. Experimental results show that the proposed algorithm is able to obtain stable performance for the video sequences with various spatial resolution and scene characteristics. It gains 2.54 dB and 1.77 dB higher average motion-compensated peak signal-to-noise ratio (PSNR) than those of the full search based on block-wise translational model and the elastic motion estimation based on modified Gauss-Newton method, respectively. Furthermore, the proposed algorithm converges fast. Only 1~2 iterations are needed before it achieves higher PSNR than the conventional elastic motion estimation and the block-wise translational full search.