1. A face recognition method using sparse representation and regularized least squares-based classification on a computing device, the method comprising: obtaining an image to be recognized as a test sample y and a set of training images of certain subjects as training sample matrix T; obtaining a sparse representation of the test sample and the training samples including an initial estimation of a sparse vector a; constructing a new face dictionary comprising training samples with non-zero corresponding coefficients in the sparse vector a for the initial estimation; obtaining new coefficients by solving a regularized least squares problem based on the constructed new face dictionary; and determining a face identity of the test sample based on minimum class residual calculated by using the new coefficients.