Exact CS Reconstruction Condition of Undersampled Spectrum-Sparse Signals - Ying Luo; Qun Zhang; Guozheng Wang; Youqing Bai (Journal of Applied Mathematics)
Compressive sensing (CS) reconstruction of a spectrum-sparse signal from undersampled data is, in fact, an ill-posed problem. In this paper, we mathematically prove that, in certain cases, the exact CS reconstruction of a spectrum-sparse signal from undersampled data is impossible. Then we present the exact CS reconstruction condition of undersampled spectrum-sparse signals, which is valuable for digital signal compression.