A causal regularizing deconvolution filter for optimal waveform reconstruction

A causal regularizing filter is described for selecting an optimal reconstruction of a signal from a deconvolution of its measured data and the measurement instrument's impulse response. Measurement noise and uncertainties in the instrument's response can cause the deconvolution (or inverse problem) to be ill-posed, thereby precluding accurate signal restoration. Nevertheless, close approximations to the signal may be obtained by using reconstruction techniques that alter the problem so that it becomes numerically solvable. A regularizing reconstruction technique is implemented that automatically selects the optimal reconstruction via an adjustable parameter and a specific stopping criterion, which is also described. Waveforms reconstructed using this filter do not exhibit large oscillations near transients as observed in other regularized reconstructions. Furthermore, convergence to the optimal solution is rapid.<
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