Framework of Compressive Sampling with Its Applications to One- and Two-Dimensional Signals

摘要

Compressive sampling emerged as a very useful random protocol and has become an active research area for almost a decade. Compressive sampling allows us to sample a signal below Shannon Nyquist rate and assures its successful reconstruction with some limitations on signal, that is, signal should be sparse in some domain. In this paper, we have used compressive sampling for an arbitrary one-dimensional signal and two-dimensional image signal compression and successfully reconstructed them by solving L1-norm optimization problems. We also have showed that compressive sampling can be implemented if a signal is sparse and incoherent through simulations. Further, we have analyzed the effect of noise on the recovery.