  Compressive sensing (CS) is a new methodology to capture signals at lower
rate than the Nyquist sampling rate when the signals are sparse or sparse in
some domain. The performance of CS estimators is analyzed in this paper using
tools from statistical mechanics, especially called replica method. This method
has been used to analyze communication systems like Code Division Multiple
Access (CDMA) and multiple input multi- ple output (MIMO) systems with large
size. Replica analysis, now days rigorously proved, is an efficient tool to
analyze large systems in general. Specifically, we analyze the performance of
some of the estimators used in CS like LASSO (the Least Absolute Shrinkage and
Selection Operator) estimator and Zero-Norm regularizing estimator as a special
case of maximum a posteriori (MAP) estimator by using Bayesian framework to
connect the CS estimators and replica method. We use both replica symmetric
(RS) ansatz and one-step replica symmetry breaking (1RSB) ansatz, clamming the
latter is efficient when the problem is not convex. This work is more
analytical in its form. It is deferred for next step to focus on the numerical
results.
