Robust subspace clustering for image data using clean dictionary estimation and group lasso based matrix completion

In this paper, we consider the problem of subspace clustering for image data under occlusion and gross spatially contiguous noise. The state of the art subspace clustering methods assume that the noise either follows independent Laplacian or Gaussian distributions. However, the realistic noise is much more complicated and exhibits different structures in different scales. To address this issue, we propose a multi scale framework that extracts a clean self-expressive dictionary through an iterative approach and is capable of identifying probable corrupted elements in each sample. Using this information, not only we can estimate parameters of each subspace more accurately but also by optimizing a matrix completion problem based on group sparsity, we can recover corrupted regions more precisely and hence achieve higher clustering accuracy for corrupted samples. Numerical experiments on synthetic and real world data sets demonstrate the efficiency of our proposed framework in presence of occlusion and spatially contiguous noise. (C) 2019 Published by Elsevier Inc.