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Restoration of Nonlinearly Distorted Audio by Histogram Equalization
Restoration of degraded speech which has been captured on audio tape often relies on linear adaptive-filtering procedures or their hardware embodiments such as the Rockwell ADAP. If the speech degradation can be modeled by a linear process, then liner adaptive filtering can provide suitable restoration. If, however, a nonlinear phenomenon, such as soft saturation, has been a contributor to the degradation, then the linear adaptive filter is no longer adequate. Linear adaptive filters consist of one or more transversal and/or recursive sections whose tap weights or gains are linear and whose values are adjusted so that the filter minimizes a performance criterion in some prescribed sense, such as minimum mean-squared error. A more general form of adaptive filter is proposed, one in which the gain at each tap location is a function of the signal at that tap. Next, this new filter is approximated by an alternating sequence of short linear adaptive filters which perform frequency-domain equalization, and nonlinear amplitude correctors which perform amplitude-domain equalization. Preliminary experiments have been performed using the nonlinear corrector portion of this new class of adaptive filter. Histogram equalization is used to define the nonlinear-gain strategy. The training to obtain the reference histogram for histogram equalization is remarkably speaker invariant when proper techniques are used for modeling. Sample audio tapes will be played to demonstrate the results which have been obtained by this technique.
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