An improved signal restoration method using frequency domain information

This paper addresses the problem of using frequency domain information for improved signal restoration. Specifically we want to estimate the underlying signal from degraded measurements when we are given (i) the distribution of the frequency components (ii) the bounds on the signal spectrum. We also asume that the energy of the noise is bounded by a known constant. The first problem is formulated as a constrained minimization of the windowed power in the frequency domain where the prior information is injected by the choice of window. The second problem is formulated as finding the feasible region which is the intersection of ellipsoids which are determined from the bounds on the signal spectrum and noise energy. This formulation is computationally very involved and we avoid this difficulty by finding an ellipsoid which will tightly bound the intersection. The geometric center of the resulting ellipsoid provides a good estimate of the underlying signal.