Modulated wideband converter (MWC) is a multi-branch structure for sub-Nyquist sampling the signals which spectra are sparse. With several band-limited sampling sequences, MWC can recover the signals by compressed sensing (CS) reconstruction algorithms. However, for hardware-implemented MWC, the hardware scale and imperfection of the physical devices lead to strong column correlations of the sensing matrix which may invalidate the classic CS algorithms. Combined with the characteristics of the sensing matrix of the CS receiver, this paper proposes the double screening orthogonal matching pursuit algorithm (DSOMP) to solve this problem. DSOMP updates the support based on the distance from the residual to the column vector subspace of the sensing matrix and adds a secondary screening mechanism to remove strong interference terms. With the strong column correlation sensing matrix of the CS receiver, DSOMP exhibits an excellent support set recovery rate.