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Exact CS reconstruction condition of undersampled spectrum-sparse signals. (English) Zbl 1397.94020

Summary: 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.

MSC:

94A12 Signal theory (characterization, reconstruction, filtering, etc.)
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