Graph approximation and generalized Tikhonov regularization for signal deblurring
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Given a compact linear operator , the (pseudo) inverse ^† is usually substituted by a family of regularizing operators _α which depends on itself. Naturally, in the actual computation we are forced to approximate the true continuous operator with a discrete operator ^(n) characterized by a finesses discretization parameter n, and obtaining then a discretized family of regularizing operators _α^(n). In general, the numerical scheme applied to discretize does not preserve, asymptotically, the full spectrum of . In the context of a generalized Tikhonov-type regularization, we show that a graph-based approximation scheme that guarantees, asymptotically, a zero maximum relative spectral error can significantly improve the approximated solutions given by _α^(n). This approach is combined with a graph based regularization technique with respect to the penalty term.
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