Sparse Representation Enables Normal Recognition of N-Class M-Person Faces

This document demonstrates that sparse representation enables effective recognition of M facial images spanning N distinct categories. The core advantage of this approach lies in its ability to represent facial images as sparse vectors, significantly reducing storage requirements and computational overhead. Sparse representation leverages the inherent sparsity in facial image structures and achieves efficient recognition through optimal dictionary selection. From an implementation perspective, this typically involves constructing an overcomplete dictionary using training samples and solving an ℓ1-minimization problem to obtain sparse coefficients for classification. The reconstruction error for each class is then computed using these coefficients, with the test sample assigned to the class yielding minimal error. This methodology enhances both accuracy and efficiency in facial recognition systems, making it suitable for diverse practical applications including security systems and biometric authentication.