Estimation of haplotype sequences from DNA sequencing samples is a challenging task whose mathematical formulation leads to an NP-hard problem. Also, accuracy of the estimates plays an essential role in providing the required information for personalized medicine. In order to fully incorporate the available quality of measurements with higher accuracy into the estimates, in this paper, we propose a new optimization design using a weighted version of the well-established matrix completion approach. This is performed by penalizing the difference between the measurements and the desired matrix using some weights, which are used to form an optimization constraint. Accordingly, we derive the corresponding error bound for the desired matrix, which shows that a larger noise power increases the estimation error with a factor proportional to the inverse of the mentioned weights. This leads to devising a new algorithm called the Haplotype reconstruction using nuclear norm minimization with Weighted Constraint (HapWeC). Computer simulations show the outperformance of the HapWeC compared to some recent algorithms in terms of the normalized reconstruction error and reconstruction rate.

从DNA测序样品中估算单倍型序列是一项艰巨的任务，其数学公式会导致NP难题。同样，估计的准确性在提供个性化医疗所需的信息方面也起着至关重要的作用。为了将更高准确度的可用测量质量完全纳入估算中，在本文中，我们提出了一种使用行之有效的矩阵完成方法的加权版本的新优化设计。这是通过使用一些权重对度量与所需矩阵之间的差异进行惩罚来实现的，这些权重用于形成优化约束。因此，我们得出所需矩阵的相应误差范围，这表明较大的噪声功率会以与上述权重的倒数成正比的因数增加估计误差。这导致设计了一种新算法，称为单倍型重构，该算法使用具有加权约束的核规范最小化（HapWeC）。计算机仿真显示，与标准化算法的重构误差和重构速率相比，HapWeC的性能优于某些最新算法。