Sparse Representation Face Recognition Method with Fidelity Expressed as L2 Norm of Residual

In sparse representation-based face recognition methods, the fidelity of sparse representation is commonly expressed using the L2 norm of the residual term. However, maximum likelihood estimation theory indicates that this formulation implicitly assumes the residuals follow a Gaussian distribution. This assumption often fails in real-world scenarios, especially when test images contain abnormal pixels caused by noise, occlusion, or disguise. Consequently, traditional sparse representation models constructed using conventional fidelity expressions lack sufficient robustness against these challenging conditions.

To address this limitation, the maximum likelihood sparse representation recognition model employs maximum likelihood estimation theory to reformulate the fidelity expression as a maximum likelihood distribution function for the residuals. This approach transforms the maximum likelihood estimation problem into a weighted optimization framework, which significantly enhances the model's robustness when dealing with images containing abnormal pixels. Implementation typically involves iterative reweighting algorithms that adjust penalty weights based on residual magnitudes, effectively downweighting the influence of outliers during sparse coding.