Highly Nonlinear Approximations for Sparse Signal Representation
(or counting measure) which is defined as:
Thus, is equal to the number of nonzero coefficients in (29). However, sice minimization of is numerically intractable, the minimization of for has been considered . Because the minimization of does not lead to a convex optimization problem, the most popular norm to minimize, when a sparse solution is required, is the 1-norm . Minimization of the 1-norm is considered the best convex approximant to the minimizer of [17,18]. In the context of signals splitting already stated, we are not particularly concerned about convexity so we have considered the minimization of , allowing for uncertainty in the available data . This was implemented by a recursive process for incorporating constrains, which is equivalent to the procedure introduced in  and applied in .