Focused on the problem that the signal sparsity is difficult to be predicted accurately in actual electromagnetic environment, we propose a distributed modulated wideband converter (DMWC) reconstruction algorithm based on regularized weak correlation, which does not rely on the sparsity as convergence condition. First, the atoms that satisfy the weak correlation are added to the index set. Then, the index set is regularized and the newly selected atoms are added to the support set. When the residual energy reaches the threshold condition, the iteration is stopped. Finally, the support set out-of-bounds condition is set, and the invalid atoms with less correlation are deleted to obtain the final support set. Simulation results show that the proposed algorithm can greatly improve the tolerance of DMWC to signal transmission attenuation. In addition, under the same conditions, the recovery performance of this algorithm is better than orthogonal matching pursuit (OMP) algorithm.