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A new approach based on d.c. (difference of convex functions) is presented for signal (1-D) and (2-D) restoration problems. It consists in applying d.c. algorithms (DCA) to suitable d.c. programs. Some choices of starting points for DCA have been discussed. Finally computational results are reported which prove the globality of sought solutions, the robustness and the efficiency of our method with respect to the Graduated NonConvexity algorithm (GNC).

We present a numerical method for solving the d.c. programming problem $$c^* = \min \{ \langle c,x\rangle s.t. f_i (x) \leqslant 0, i = 1,...,m, x \in D\} $$ wherefi, i=1,...,m are d.c. (difference of two convex functions) and D is a convex set in ℝn. An (ɛ, η)-solutionx(ɛ, η) satisfying $$x(\varepsilon ,\eta ) \in D, \langle c,x(\varepsilon ,\eta )\rangle \leqslant c^* + \varepsilon , f_i (x(\varepsilon ,\eta )) \leqslant \eta , i = 1,...,m,$$ can be found after a finite number of iterations. This algorithm combines an outer approximation procedure for solving a system of d.c. inequalities with a simple general scheme for minimizing a linear function over a compact set. As an application we discuss the numerical solution of a fuel mixture problem (encountered in the oil industry).