RSC算法：提升人脸识别的鲁棒性

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"这篇文档详细介绍了RSC(鲁棒稀疏编码)算法在人脸识别中的应用，作者包括Meng Yang、Lei Zhang、Jian Yang和David Zhang等人，来自香港理工大学和南京科技大等机构。RSC是针对SRC(基于稀疏表示的分类)的改进，旨在提高人脸识别的鲁棒性，特别考虑了编码残差的实际分布情况，以更有效地处理遮挡、噪声等问题。" 在人脸识别领域，稀疏表示或编码（SRC）已经成为一种有效的技术。SRC的基本原理是将测试图像表示为训练样本的稀疏线性组合，并通过$l_2$范数或$l_1$范数来衡量编码残差的保真度。然而，这种模型通常假设编码残差遵循高斯或拉普拉斯分布，这在实际应用中可能不够精确，无法充分描述编码错误。论文中提出的鲁棒稀疏编码（RSC）算法则是对这一问题的改进。RSC将稀疏编码视为一个带稀疏约束的稳健回归问题，寻找稀疏编码问题的最大似然估计（MLE）解。这样做的好处在于RSC对异常值（如遮挡、噪声等）具有更高的鲁棒性。为了解决RSC模型，文中提出了一种有效的迭代重加权稀疏编码算法。实验部分，作者在多个数据集上进行了广泛的实验，结果证明RSC在处理噪声、部分遮挡等情况下，相比于SRC，能提供更稳定、准确的人脸识别性能。这使得RSC算法在实际应用中，尤其是在复杂环境和条件下的人脸识别任务中，具有更强的实用性。 RSC算法是SRC的一个重要发展，它通过更精确地建模编码残差的分布，提高了人脸识别的准确性和鲁棒性。对于从事人脸识别研究和开发的人员来说，这份文档提供了有价值的技术见解和实现方法，是理解和应用RSC算法的重要参考资料。

Robust Sparse Coding for Face Recognition

Meng Yang Lei Zhang

∗

Hong Kong Polytechnic Univ.

Jian Yang

Nanjing Univ. of Sci. & Tech.

David Zhang

Hong Kong Polytechnic Univ.

Abstract

Recently the sparse representation (or coding) based

classiﬁcation (SRC) has been successfully used in face

recognition. In SRC, the testing image is represented as

a sparse linear combination of the training samples, and

the representation ﬁdelity is measured by the 𝑙

-norm or

𝑙

-norm of coding residual. Such a sparse coding model

actually assumes that the coding residual follows Gaus-

sian or Laplacian distribution, which may not be accurate

enough to describe the coding errors in practice. In this

paper, we propose a new scheme, namely the robust sparse

coding (RSC), by modeling the sparse coding as a sparsity-

constrained robust regression problem. The RSC seeks for

the MLE (maximum likelihood estimation) solution of the

sparse coding problem, and it is much more robust to out-

liers (e.g., occlusions, corruptions, etc.) than SRC. An

efﬁcient iteratively reweighted sparse coding algorithm is

proposed to solve the RSC model. Extensive experiments

on representative face databases demonstrate that the RSC

scheme is much more effective than state-of-the-art meth-

ods in dealing with face occlusion, corruption, lighting and

expression changes, etc.

1. Introduction

As a powerful tool for statistical signal modeling, sparse

representation (or sparse coding) has been successfully used

in image processing applications [16], and recently has led

to promising results in face recognition [24, 25, 27] and

texture classiﬁcation [15]. Based on the ﬁndings that nat-

ural images can be generally coded by structural primitives

(e.g., edges and line segments) that are qualitatively similar

in form to simple cell receptive ﬁelds [18], sparse coding

techniques represent a natural image using a small number

of atoms parsimoniously chosen out of an over-complete

dictionary. Intuitively, the sparsity of the coding coefﬁcient

vector can be measured by the 𝑙

-norm of it (𝑙

-norm counts

the number of nonzero entries in a vector). Since the com-

binatorial 𝑙

-norm minimization is an NP-hard problem, the

∗

Corresponding author. This research is supported by the Hong Kong

General Research Fund (PolyU 5351/08E).

𝑙

-norm minimization, as the closest convex function to 𝑙

norm minimization, is widely employed in sparse coding,

and it was shown that 𝑙

-norm and 𝑙

-norm minimizations

are equivalent if the solution is sufﬁciently sparse [3]. In

general, the sparse coding problem can be formulated as

min

𝜶

∥𝜶∥

s.t. ∥𝒚 − 𝐷𝜶∥

≤ 𝜀, (1)

where 𝒚 is a given signal, 𝐷 is the dictionary of coding

atoms, 𝜶 is the coding vector of 𝒚 over 𝐷, and 𝜀>0 is a

constant.

Face recognition (FR) is among the most visible and

challenging research topics in computer vision and pattern

recognition [29], and many methods, such as Eigenfaces

[21], Fisherfaces [2] and SVM [7], have been proposed in

the past two decades. Recently, Wright et al. [25] applied

sparse coding to FR and proposed the sparse representation

based classiﬁcation (SRC) scheme, which achieves impres-

sive FR performance. By coding a query image 𝒚 as a

sparse linear combination of the training samples via the

𝑙

-norm minimization in Eq. (1), SRC classiﬁes the query

image 𝒚 by evaluating which class of training samples could

result in the minimal reconstruction error of it with the as-

sociated coding coefﬁcients. In addition, by introducing an

identity matrix 𝐼 as a dictionary to code the outlier pixels

(e.g., corrupted or occluded pixels):

min

𝜶,𝜷

∥[𝜶; 𝜷]∥

s.t. 𝒚 =[𝐷, 𝐼] ⋅ [𝜶; 𝜷] , (2)

the SRC method shows high robustness to face occlusion

and corruption. In [9], Huang et al. proposed a sparse rep-

resentation recovery method which is invariant to image-

plane transformation to deal with the misalignment and

pose variation in FR, while in [22] Wagner et al. proposed

a sparse representation based method that could deal with

face misalignment and illumination variation. Instead of di-

rectly using original facial features, Yang and Zhang [27]

used Gabor features in SRC to reduce greatly the size of

occlusion dictionary and improve a lot the FR accuracy.

The sparse coding model in Eq. (1)iswidelyusedin

literature. There are mainly two issues in this model. The

ﬁrst one is that whether the 𝑙

-norm constraint ∥𝜶∥

is good

enough to characterize the signal sparsity. The second one is

625

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