Recent years have witnessed rapid developments of sparse representation in various classification tasks, including face recognition (FR). The success of sparse representation-based classification (SRC) on FR greatly boosts the research of sparsity-based classification techniques. However, many problems are still pending to be further addressed. For example, what is the role of l₀ or l₁ norm sparsity in it? How to design a robust representation fidelity term to handle various outliers? How to extract effective features to improve the accuracy and efficiency of SRC? In this article, we aim to answer these questions via three aspects:

• Role of sparse coefficient: Several works have questioned the role of sparse coefficients. Especially, a collaborative representation-based classification has been proposed for FR, which use l₂-norm to regularize the coding coefficient, with similar accuracy to SRC but much faster speed. However, there is also some work that defends the sparsity of coding coefficients when an appropriate dictionary is used.
• Regularization on the representation residual: Robust models with effective representation terms have been developed to handle various outliers in face images. For instance, by assuming the coding residual and the coding coefficient are respectively independent and identically distributed, regularized robust coding was proposed based on maximum a posterior estimation. Moreover, structured representation models were also proposed to make use of the image structure information.
• Extended sparse representation model: Extended sparse models for FR include misalignment robust models, undersampled models, and multifeature models.

These FR approaches via sparse representation have achieved very promising results.