Enhancing sparsity via ℓp (0

Abstract

Sparse representation has received an increasing amount of interest in recent years. By representing the testing image as a sparse linear combination of the training samples, sparse representation based classification (SRC) has been successfully applied in face recognition. In SRC, the ℓ1 minimization instead of the ℓ0 minimization is used to seek for the sparse solution for its computational convenience and efficiency. However, ℓ1 minimization does not always yield sufficiently sparse solution in many practical applications. In this paper, we propose a novel SRC method, namely the ℓp (0<p<1) sparse representation based classification (ℓp-SRC), to seek for the optimal sparse representation of a testing image. In ℓp-SRC, the ℓp (0<p<1) minimization is adopted as an alternative to ℓ0 minimization, the solution of which is sparser than that of ℓ1 minimization used in traditional SRC. Furthermore, an iterative algorithm is introduced to efficiently solve the ℓp minimization problem in this paper. The extensive experimental results on publicly available face databases demonstrate the effectiveness of ℓp-SRC for robust face recognition.