Novel sparse representation classification with a closed-form solution

Many face recognition approaches are based on collaborative representation (CR). CR based method represents a test sample using training samples of all classes. To produce a stable and discriminative CR vector, various regularizations on CR vector are employed. With $L _{\mathbf{2}}$-norm there is a closed-form solution of CR vector. A sparse and more discriminative solution of CR vector is obtained if $L _{\mathbf{1}}$-norm is used as regulator, which, however, is computationally expensive. In this paper, we propose a new CR method the solution of which is still closed-form and more sparse than conventional CR methods with $L _{2}$-norm. Compared with state-of-the-art CR-based methods, the proposed method gains promising performance.