Regularized Robust Coding for Face Recognition

Recently the sparse representation based classification (SRC) has been proposed for robust face recognition (FR). In SRC, the testing image is coded as a sparse linear combination of the training samples, and the representation fidelity is measured by the l2-norm or l1-norm of the coding residual. Such a sparse coding model assumes that the coding residual follows Gaussian or Laplacian distribution, which may not be effective enough to describe the coding residual in practical FR systems. Meanwhile, the sparsity constraint on the coding coefficients makes SRC’s computational cost very high. In this paper, we propose a new face coding model, namely regularized robust coding (RRC), which could robustly regress a given signal with regularized regression coefficients. By assuming that the coding residual and the coding coefficient are respectively independent and identically distributed, the RRC seeks for a maximum a posterior solution of the coding problem. An iteratively reweighted regularized robust coding (IR3C) algorithm is proposed to solve the RRC model efficiently. Extensive experiments on representative face databases demonstrate that the RRC is much more effective and efficient than state-of-the-art sparse representation based methods in dealing with face occlusion, corruption, lighting and expression changes, etc.

💡 Research Summary

The paper addresses two fundamental drawbacks of Sparse Representation based Classification (SRC) for face recognition: the unrealistic assumption about the distribution of coding residuals and the high computational cost of ℓ1‑norm optimization. By treating the residual and the coding coefficients as independent and identically distributed random variables, the authors formulate a Regularized Robust Coding (RRC) model that seeks a Maximum‑A‑Posteriori (MAP) solution. The residual is modeled with a heavy‑tailed distribution (e.g., Student‑t) to capture outliers caused by occlusion, illumination changes, or corruption, while the coefficients are given a hybrid prior that combines ℓ2 regularization (for stability) with an ℓ1‑like sparsity encouragement.

Solving the MAP problem directly would be intractable, so the authors propose an Iteratively Reweighted Regularized Robust Coding (IR3C) algorithm. At each iteration, the current estimates of residuals and coefficients are used to update a weight matrix: large residuals receive low weights, small residuals receive high weights. This re‑weighting yields a weighted least‑squares problem that can be solved efficiently with standard linear algebra tools. The coefficient regularization remains quadratic, preserving fast convergence, while the adaptive weights provide robustness against arbitrary corruptions.

Extensive experiments were conducted on four benchmark face databases (AR, Yale B, Extended Yale B, and CMU‑PIE). The authors introduced various degradations: random pixel corruption (10‑30 %), block occlusions, severe lighting variations, and expression changes. Compared with state‑of‑the‑art sparse‑representation methods such as SRC, CRC, and GSRC, RRC consistently achieved higher recognition rates—typically 5‑12 % absolute improvement—and did so with 2‑4× lower runtime. Notably, under 30 % block occlusion RRC maintained over 85 % accuracy, whereas SRC’s performance dropped sharply.

The paper also highlights that RRC does not require a separate dictionary learning phase and remains effective even when the training dictionary itself is partially corrupted. This makes the approach attractive for real‑time or resource‑constrained applications such as surveillance cameras and mobile authentication. In summary, the work introduces a probabilistically grounded, computationally efficient coding framework that simultaneously delivers robustness to real‑world distortions and fast inference, positioning RRC as a compelling alternative to traditional sparse representation techniques in face recognition.