中文摘要：

基于位场数据在离散余弦变换域的稀疏性,利用lp（0≤p〈1）范数代替l1范数作为模型参数稀疏性的度量.引入lp范数稀疏约束正则化方法,借用迭代再加权最小二乘算法思想求解得到稀疏约束优化问题的解.分析不同p值的lp范数稀疏约束正则化方法的数据重构能力.将该算法应用于实际位场数据重构试验中获得了较理想的结果,通过边界外延加大计算区域的方法减少了边界数据的重构误差,提高了数据重构质量.

英文摘要：

The lp-norm （0≤p〈1） was used to replace the dl-norm to measure the model parameters sparsity based on the sparseness of the potential field data in the discrete cosine transform domain. The regularization method with lp-norm sparsity constraints was introduced. Then the iteratively re-weighted least squares algorithm was used to get the analytic expression of the corresponding optimization problem. The reconstruction ability of regularization method for different lp-norm sparsity constraints was analyzed. The algorithm was applied to actual potential field data reconstruction and the ideal result was obtained. The reconstruction error of boundary data was reduced by expanding the calculated area via boundary extension, and the quality of the reconstructed data was improved.