Partial Sum Minimization of Singular Values (PSSV) is a powerful tool for image denoising, matrix completion and recovering underlying low-rank structure from the corrupted data via Partial Sum Minimization of Singular Values. However, the performance of PSSV degenerates remarkably when data is incomplete or some data is corrupted completely, which is usually faced in real applications especial for video sequence analysis. To handle this problem, we impose the variance regularization in PSSV by analyzing PSSV and truncated nuclear norm. Our proposed model benefits from 1) the robustness of principal components to outliers and missing values. 2) It can guarantee the compactness of the learned clean data. 3) It can recover the missing sample data from the data matrix. Experimental results on background extraction from the incomplete videos and data, image denoising, and clustering illustrate the effectiveness of the proposed approach.

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奇异值部分和最小化 (PSSV) 是一种强大的工具，用于图像去噪、矩阵补全以及通过奇异值部分和最小化从损坏的数据中恢复底层低秩结构。然而，当数据不完整或某些数据完全损坏时，PSSV的性能会显着下降，这在实际应用尤其是视频序列分析中经常遇到。为了解决这个问题，我们通过分析 PSSV 和截断核范数对 PSSV 进行方差正则化。我们提出的模型受益于 1) 主成分对异常值和缺失值的稳健性。 2）能够保证学习到的干净数据的紧凑性。 3）可以从数据矩阵中恢复丢失的样本数据。从不完整的视频和数据中提取背景、图像去噪和聚类的实验结果说明了该方法的有效性。