Improving detection performance of compressed sensing by orthogonal projection

Many real-world signals have a sparse expansion in terms of a particular basis or frame. A distinguishable representation of this small number of coefficients can be achieved by low-dimension vectors instead of vectors resulting from Nyquist sampling. This is the basic idea of Compressed Sensing. A quantification about the related representative matrix is the restricted isometry property (RIP). However, if the signal and the corresponding reference matrix fail to obey the RIP, which would happen by strong sub-sampling, successful signal recovery seems to be impossible. In this paper, we introduce a new method, called Orthogonal projection, to improve recovery when the RIP condition was not held.