Normal priors with unknown variance (NUV) have long been known to promote sparsity and to blend well with parameter learning by expectation maximization (EM). In this paper, we advocate this approach for linear state space models for applications such as the estimation of impulsive signals, the detection of localized events, smoothing with occasional jumps in the state space, and the detection and removal of outliers.The actual computations boil down to multivariate-Gaussian message passing algorithms that are closely related to Kalman smoothing. We give improved tables of Gaussian-message computations from which such algorithms are easily synthesized, and we point out two preferred such algorithms.

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Novel applications of transcranial Doppler (TCD) ultrasonography, such as the assessment of cerebral vessel narrowing/occlusion or the non-invasive estimation of intracranial pressure (ICP), require high-quality maximal flow velocity waveforms. However, due to the low signal-to-noise ratio of TCD spectrograms, measuring the maximal flow velocity is challenging. In this work, we propose a calibration-free algorithm for estimating maximal flow velocities from TCD spectrograms and present a pertaining beat-by-beat signal quality index. Methods: Our algorithm performs multiple binary segmentations of the TCD spectrogram and then extracts the pertaining envelopes (maximal flow velocity waveforms) via an edge-following step that incorporates physiological constraints. The candidate maximal flow velocity waveform with the highest signal quality index is finally selected. Results: We evaluated the algorithm on 32 TCD recordings from the middle cerebral and internal carotid arteries in 6 healthy and 12 neurocritical care patients. Compared to manual spectrogram tracings, we obtained a relative error of −1.5%, when considering the whole waveform, and a relative error of −3.3% for the peak systolic velocity. Conclusion: The feedback loop between the signal quality assessment and the binary segmentation yields a robust algorithm for maximal flow velocity estimation. Clinical Impact: The algorithm has already been used in our ICP estimation pipeline. By making the code and the data publicly available, we hope that the algorithm will be a useful building block for the development of novel TCD applications that require high-quality flow velocity waveforms.

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