Beyond RPCA: Flattening complex noise in the frequency domain

Abstract

Discovering robust low-rank data representations is important in many real-world problems. Traditional robust principal component analysis (RPCA) assumes that the observed data are corrupted by some sparse noise (e.g., Laplacian noise) and utilizes the ℓ1-norm to separate out the noisy component. Nevertheless, as well as simple Gaussian or Laplacian noise, noise in real-world data is often more complex, and thus the ℓ1 and ℓ2-norms are insufficient for noise characterization. This paper presents a more flexible approach to modeling complex noise by investigating their properties in the frequency domain. Although elements of a noise matrix are chaotic in the spatial domain, the absolute values of its alternative coefficients in the frequency domain are constant w.r.t. their variance. Based on this observation, a new robust PCA algorithm is formulated by simultaneously discovering the low-rank and noisy components. Extensive experiments on synthetic data and video background subtraction demonstrate that FRPCA is effective for handles complex noise.