Low-Rank Latent Pattern Approximation With Applications to Robust Image Classification

This paper develops a novel method to address the structural noise in samples for image classification. Recently, regression-related classification methods have shown promising results when facing the pixelwise noise. However, they become weak in coping with the structural noise due to ignoring of relationships between pixels of noise image. Meanwhile, most of them need to implement the iterative process for computing representation coefficients, which leads to the high time consumption. To overcome these problems, we exploit a latent pattern model called low-rank latent pattern approximation (LLPA) to reconstruct the test image having structural noise. The rank function is applied to characterize the structure of the reconstruction residual between test image and the corresponding latent pattern. Simultaneously, the error between the latent pattern and the reference image is constrained by Frobenius norm to prevent overfitting. LLPA involves a closed-form solution by the virtue of a singular value thresholding operator. The provided theoretic analysis demonstrates that LLPA indeed removes the structural noise during classification task. Additionally, LLPA is further extended to the form of matrix regression by connecting multiple training samples, and alternating direction of multipliers method with Gaussian back substitution algorithm is used to solve the extended LLPA. Experimental results on several popular data sets validate that the proposed methods are more robust to image classification with occlusion and illumination changes, as compared to some existing state-of-the-art reconstruction-based methods and one deep neural network-based method.