Recent results show that a relatively small number of random projections of a signal can contain most of its salient information. It follows that if a signal is compressible in some orthonormal basis, then a very accurate reconstruction can be obtained from random projections. We extend this type of result to show that compressible signals can be accurately recovered from random projections contaminated with noise. We also propose a practical iterative algorithm for signal reconstruction, and briefly discuss potential applications to coding, A/D conversion, and remote wireless sensing.
Haupt et al. REF showed that signal information can be obtained from several random Fourier projections.
Signal Reconstruction From Noisy Random Projections
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Computer Science