Think big, solve small: Scaling up robust PCA with coupled dictionaries
Recent advances in robust principle component analysis offers a powerful method for solving a wide variety of low-level vision problems. However, if the input data is very large, especially when high-resolution images are involved, it makes RPCA computationally prohibitive for many real applications. To tackle this problem, we propose a fixed-rank RPCA method that uses coupled dictionaries (FRPCA-CD) to handle high-resolution images. FRPCA-CD downsamples high-resolution images into low-resolution images, performs FRPCA on the low-level images to obtain the low-rank matrix, which is reconstructed at original resolution by coupled dictionaries. Comprehensive tests performed on video background recovery, noise reduction in photometric stereo, and image reflection removal problems show that FRPCA-CD can reduce computation time and memory space drastically without sacrificing accuracy.