  The robustness to noise and outliers is an important issue in linear
representation in real applications. We focus on the problem that samples are
grossly corrupted, which is also the 'sample specific' corruptions problem. A
reasonable assumption is that corrupted samples cannot be represented by the
dictionary while clean samples can be well represented. This assumption is
enforced in this paper by investigating the coefficients of corrupted samples.
Concretely, we require the coefficients of corrupted samples be zero. In this
way, the representation quality of clean data can be assured without the effect
of corrupted data. At last, a robust dictionary based data representation
approach and its sparse representation version are proposed, which have
directive significance for future applications.
