基于准范数与零范数的矩阵恢复

针对高维度矩阵的低秩恢复问题中核范数与l1范数过惩罚导致的结果偏差,提出一种矩阵恢复方法。使用准范数代替低秩恢复问题中常用的核范数约束,使用零范数代替l1范数约束。对于准范数的求解问题,采用与准范数等价的Frobenius/核混合范数进行替代,提出基于交替近似的线性最小化方法对目标函数进行求解。在合成数据与真实数据上的实验结果表明,该算法在主观视觉效果与客观数值比较上都能获得更好的结果。

Matrix recovery based on quasi-norm and zero norm

Since the nuclear norm and the l1 norm over-penalize large entries and result in a biased solution for low rank recovery problem of high-dimensional matrices,a matrix recovery method was proposed.Quasi-norm and l0 norm were used to replace nuclear norm and l1 norm prevalently adopted in previous work.Because of the equivalence relation between the quasi-norm and the Frobenius/nuclear hybrid norm,solving quasi-norm was equivalent to solving the Frobenius/nuclear norm.Based on this,an efficient proximal alternating linearized minimization algorithm was designed for solving matrix recovery problems.Experimental results on synthetic data and real-word data show that the proposed algorithm is more accurate than existing matrix recovery algorithms.