Deconvolution and model-based restoration of clipped ultrasonic signals

This paper presents a simple and general approach for deconvolving ultrasonic signals for which some of the samples have been clipped at the maximum and minimum saturation levels of the analog-to-digital converter. Furthermore, it shows how the deconvolution results can be used to restore the clipped amplitudes. By using the presented methods, the artifacts that typically arise when applying standard deconvolution methods on clipped data can be avoided. The deconvolution problem is stated as maximum a posteriori estimation of the reflection sequence under an assumption of uncorrelated Gaussian measurement noise and with the signal clipping explicitly taken into account in the signal generation model. Apart from the exact solution, two simplified approximate solutions are considered. The first approximation leads to solving a quadratic programming problem with inequality constraints and the second yields a simple closed form linear solution. A comparison under varying noise and clipping distortion conditions shows that the exact solution consistently yields the best performance, but the accuracies of both the approximative solutions are almost as good as the exact solution for low clipping distortion levels. At larger distortion levels, only the first approximative solution can compete in accuracy with the exact solution. Signal restoration results using real ultrasonic data further verify the above conclusions.