SVD-Based OMP Algorithms Applying To Face Recognition

Compressed Sensing (CS) is a new sampling theory. The main idea of CS is reconstructing signal with high probability by nonlinear reconstruction algorithm which utilizes the sparsity of signal, while the frequent samples are much less than the Nyquist sampling rate. It caused great attention of scholars as soon as the compressed sensing theory was proposed. Then people began to explore its application in production and daily life. A. y. Yang et al proposed sparse representation-based Classification face recognition algorithm (hereinafter referred to as "SRC"), which gradually becomes the common face recognition algorithm.In this thesis, we introduce the principles of compressed sensing, sufficient conditions and necessary conditions of sparse signal reconstruction, BP and MP reconstruction algorithms represented, and the applicability of compressed sensing to face recognition Combined with SRC, a face recognition algorithm based on singular value decomposition is proposed. This SVD-based face recognition algorithm decomposes the original measurement matrix to form a new measurement matrix by using SVD. The coherence of new measurement matrix is greatly reduced, for the new measurement matrix is a partial orthogonal matrix. According to the theory of compressed sensing, the smaller the coherence of the measurement matrix, the better the reconstruction effect, and the speed of reconstruction will be significantly improved.This thesis focuses on the SVD-based face recognition algorithm. Simulation results shows the reconstruction results of the new algorithm are obviously better than that of SRC algorithm based on OMP. The superiority of the proposed algorithm has been indicated by both theory and experiments.