Density Corrected Sparse Recovery when R.I.P. Condition Is Broken

Traditional methods which the features form cluster structures, as can be seen in often rely on R.I.P or its relaxed variants. However, many machine learning [Lehiste, 1976] and computer vision in real applications, features are often correlated problems [Lan et al., 2013; Lowe, 2004]. Due to the fact that to each other, which makes these assumptions many features extractors are similar to each others and they too strong to be useful. In this paper, we reflect the characteristics of the same image, vision features study the sparse recovery problem in which the feature are often correlated and have cluster structures. This correlation matrix is strictly non-R.I.P.. We prove that is even stronger in those systems that have thousands when features exhibit cluster structures, which often to millions of features [Lan et al., 2013; Gan et al., 2015a; happens in real applications, we are able to recover 2015b].