The L0/L1 norm can have surprising benefits under certain assumptions. If you know (or assume) your signal is sparse (or mostly zero) in some domain, you're jus

The L0/L1 norm can have surprising benefits under certain assumptions. If you know (or assume) your signal is sparse (or mostly zero) in some domain, you're just trying to minimize the nonzero terms with the L0 norm.... But that's hard so we use the L1 norm (which still guarantees exact recovery even under Nyquist). Look up the 2004 paper by Candes and Tao for more info (titled "Exact recovery ... undersampled ...")