سابِق|تال

Sparse and low-rank abundance estimation with internal variability

  • role： First author第一作者
  • Affiliation：

    Department of Electrical and Engineering, Tsinghua University, Beijing 100084, China

    Institute of Disaster Prevertion, Langfang 065201, China

  • Email：yuanjing20110824@sina.com
  • Introduction：袁静，1981年生，女，博士研究生，研究方向为高光谱解混。E-mail：yuanjing20110824@sina.com
YUAN Jing12,  
  • Affiliation：

    Department of Electrical and Engineering, Tsinghua University, Beijing 100084, China

ZHANG Yujin1

ملخص

Abundance estimation (AE) plays an important role in the processing and analysis of hyperspectral images. Constrained linear regression is usually developed to estimate abundance matrix due to its simplicity and mathematical tractability. However, this approach only focuses on the fitness between the estimated and ground-truth data without considering the internal variability such as the similarity among the first-order gradients and among the second-order gradients. To improve the accuracy of the AE, a novel method of adding internal variability to sparse low-rank AE was proposed. First, first- and second-order gradient constraint terms were used to modify the traditional mathematical model of sparse and low-rank AE. Second, norm inequality and optimization theory were applied to demonstrate the validity of the novel model. The model has been proven applicable to other related fields under constraint conditions. Third, auxiliary variables were utilized to transform the mathematic model to the enhanced Lagrange function (ELF). Finally, the ELF was solved by the alternating direction method of multipliers to estimate the abundance of hyperspectral images. In general, the traditional method of sparse and low-rank AE is the alternating direction sparse and low-rank unmixing (ADSpLRU). In this study, ADSpLRU-FOG refers to the method that adds the first-order gradient to the sparse and low-rank AE, whereas ADSpLRU-FSOG refers to the method that adds first- and second-order gradients to the sparse and low-rank AE. Experiment carried on the USUG library showed that, (1) in the convergent experiment, ADSpLRU-FOG and ADSpLRU-FSOG algorithms converged to a slightly lower NMSE than ADSpLRU. ADSpLRU-FSOG algorithm converged to the lowest NMSE among the three methods. (2) In the robust experiment, ADSpLRU-FOG and ADSpLRU-FSOG algorithms reached higher estimation accuracy than ADSpLRU in terms of SRE under white and colored noises. Among them, ADSpLRU-FSOG achieved remarkably higher SRE value than the other methods. (3) In the visual experiment, ADSpLRU-FOG algorithm could maintain the first-order gradient structure of the data more than ADSpLRU. Meanwhile, the ADSpLRU-FSOG algorithm could preserve the second-order gradient structure of the data better than ADSpLRU-FOG and ADSpLRU algorithms. Experiment based on the Urban and Jasper actual hyperspectral database showed that the accuracy of abundance matrix estimation from ADSpLRU-FSOG was better than those from ADSpLRU and ADSpLRU-FOG. Experimental results suggest that the novel method of adding the internal variability to the abundance matrix estimation can improve convergent behavior, maintain the structure of information of first-order and second-order gradients, obtain comparable estimation accuracy, and enhance robust performance for AE.

مفهوم

abundance estimation;CLR;internal variability;sparse and low-rank;ADMM

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