Signal reconstruction from noisy randomized projections with applications to wireless sensing

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 projections of the signal onto random basis elements. We extend this type of result to show that compressible signals can be accurately recovered from random projections contaminated with noise, in many cases much more accurately than is possible using an equivalent number of conventional point samples. We also investigate the application of this new sampling and reconstruction procedure to remote wireless sensing.