Nonconvex plus quadratic penalized low-rank and sparse decomposition for noisy image alignment

针对含噪图像对准问题的非凸加二次罚项约束的低秩和稀疏分解方法

Abstract

This paper proposes a general method for dealing with the problem of recovering the low-rank structure, in which the data can be deformed by some unknown transformations and corrupted by sparse or nonsparse noises. Nonconvex penalization method is used to remedy the drawbacks of existing convex penalization method and a quadratic penalty is further used to better tackle the nonsparse noises in the data. We exploits the local linear approximation (LLA) method for turning the resulting nonconvex penalization problem into a series of weighted convex penalization problems and these subproblems are efficiently solved via the augmented Lagrange multiplier (ALM). Besides comparing with the method of robust alignment by sparse and low-rank decomposition for linearly correlated images (RASL), we also propose a nonconvex penalized lowrank and sparse decomposition (NLSD) model as comparison. Numerical experiments are conducted on both controlled and uncontrolled data to demonstrate the outperformance of the proposed method over RASL and NLSD.

摘要

创新点

本工作的主要创新之处可以概括为以下三点:

  1. (1)

    针对采用 L1 范数进行凸优化时带来的较大偏差问题, 本文提出采用非凸优化的方式来减小偏差并获得了较好的对准效果。

  2. (2)

    实际应用中的数据存在稀疏噪声的同时也经常存在一些非稀疏噪声, 本文提出增加一项二次惩罚函数来对非稀疏噪声部分进行估计。

  3. (3)

    本文提出了一种 LLA-ALM 算法, 来求解一系列非凸优化子问题的局部最优解。

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Correspondence to Zhi Han.

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Chen, X., Han, Z., Wang, Y. et al. Nonconvex plus quadratic penalized low-rank and sparse decomposition for noisy image alignment. Sci. China Inf. Sci. 59, 052107 (2016). https://doi.org/10.1007/s11432-015-5419-2

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Keywords

  • low-rank decomposition
  • nonconvex relaxation
  • quadratic penalized
  • batch image alignment
  • sparse or nonsparse noise

关键词

  • 低秩分解
  • 非凸优化
  • 二次惩罚项
  • 批量图像对准
  • 稀疏或非稀疏噪声