  A new signal processing framework based on making orthogonal Projections onto
the Epigraph Set of a Convex cost function (PESC) is developed. In this way it
is possible to solve convex optimization problems using the well-known
Projections onto Convex Set (POCS) approach. In this algorithm, the dimension
of the minimization problem is lifted by one and a convex set corresponding to
the epigraph of the cost function is defined. If the cost function is a convex
function in $R^N$, the corresponding epigraph set is also a convex set in
R^{N+1}. The PESC method provides globally optimal solutions for
total-variation (TV), filtered variation (FV), L_1, L_2, and entropic cost
function based convex optimization problems. In this article, the PESC based
denoising and compressive sensing algorithms are developed. Simulation examples
are presented.
