A Robust Framework For Eigenspace Image Reconstruction

Principal components analysis (PCA) is proved to be a useful tool for many computer vision and signal processing problems. One drawback of traditional PCA is that they are based on least squares estimation techniques and hence fail to account for "outliers" which commonly occurs in realistic training sets. To make PCA more robust to real-world problems such as image reconstruction addressed in this paper, we develop a two-step algorithm that can eliminate the outliers on both frame level and pixel level through the LASSO and RPCA separately. With LASSO optimization method, we may obtain sparse projected coefficients of the original image into the basis image space. According to the sparsity of these coefficients, sample outliers can be recognized automatically. Then, with the use of robust M-estimation, the influence of intra-sample outliers may be overwhelmed to great extent. Additionally, due to orthogonality of the principal components, the soft-threshold estimation can be applied to the LASSO to alleviate the computational costs, hence make our robust PCA method more applicable to large-scale problems. An experiment on object image reconstruction is used to illustrate the advantage of our proposed technique over standard PCA