We present a theoretical study of the recovery of an unknown vector x ∈ IR (a signal, an image) from noisy data y ∈ IR by minimizing with respect to x a regularized cost-function F(x, y) = Ψ(x, y) + αΦ(x), where Ψ is a data-fidelity term, Φ is a smooth regularization term and α > 0 is a parameter. Typically, Ψ(x, y) = ‖Ax − y‖ where A is a linear operator. The data-fidelity terms Ψ involved in ...

The main reason for introducing smooth structures was to enable us to define smooth functions on manifolds and smooth maps between manifolds. In this chapter we carry out that project. We begin by defining smooth real-valued and vector-valued functions, and then generalize this to smooth maps between manifolds. We then focus our attention for a while on the special case of diffeomorphisms, whic...

Consider a piecewise smooth function for which the (pseudo-)spectral coefficients are given. It is well known that while spectral partial sums yield exponentially convergent approximations for smooth functions, the results for piecewise smooth functions are poor, with spurious oscillations developing near the discontinuities and a much reduced overall convergence rate. This behavior, known as t...

In practice, obtaining the global optimum for the economic dispatch {bf (ED)}problem with ramp rate limits and prohibited operating zones is presents difficulties. This paper presents a new andefficient method for solving the economic dispatch problem with non-smooth cost functions using aFuzzy Adaptive Genetic Algorithm (FAGA). The proposed algorithm  deals  with the issue ofcontrolling the ex...