MSE Analysis Based on Nearly-Oracle Estimation for SCoSaMP Algorithm

For the reconstruction of signals acquired with Sub-Nyquist sampling system based on redundant Gabor frames, SCoSaMP (Signal space-based CoSaMP) algorithm has excellent performance. However, there's still no analysis about the MSE analysis under Gaussian noise and it is hard to estimate SCoSaMP algorithm reconstruction performance from a theoretical point of view. This paper presents an MSE analysis method based on nearly-oracle estimation to assess the error generated by Gaussain noise. With the proposed method, the upper bound of the MSE (Mean Square Estimate) is calculated, which shows how to improve the algorithm more quickly.