Federico Wadehn

On sparsity by NUV-EM, Gaussian message passing, and Kalman smoothing

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.

Estimation of heart rate and heart rate variability from pulse oximeter recordings using localized model fitting

Heart rate variability is one of the key parameters for assessing the health status of a subjects cardiovascular system. This paper presents a local model fitting algorithm used for finding single heart beats in photoplethysmogram recordings. The local fit of exponentially decaying cosines of frequencies within the physiological range is used to detect the presence of a heart beat. Using 42 subjects from the CapnoBase database, the average heart rate error was 0.16 BPM and the standard deviation of the absolute estimation error was 0.24 BPM.

A multiscale, model-based analysis of the multi-tissue interplay underlying blood glucose regulation in type I diabetes

A multiscale model for blood glucose regulation in diabetes type I patients is constructed by integrating detailed metabolic network models for fat, liver and muscle cells into a whole body physiologically-based pharmacokinetic/pharmacodynamic (pBPK/PD) model. The blood glucose regulation PBPK/PD model simulates the distribution and metabolization of glucose, insulin and glucagon on an organ and whole body level. The genome-scale metabolic networks in contrast describe intracellular reactions. The developed multiscale model is fitted to insulin, glucagon and glucose measurements of a 48h clinical trial featuring 6 subjects and is subsequently used to simulate (in silico) the influence of geneknockouts and drug-induced enzyme inhibitions on whole body blood glucose levels. Simulations of diabetes associated gene knockouts and impaired cellular glucose metabolism, resulted in elevated whole body blood-glucose levels, but also in a metabolic shift within the cells reaction network. Such multiscale models have the potential to be employed in the exploration of novel drug-targets or to be integrated into control algorithms for artificial pancreas systems.

Heart rate estimation in photoplethysmogram signals using nonlinear model-based preprocessing

We propose a frequency domain algorithm for heart rate estimation from photoplethysmographic signals (PPG) recorded during intense physical activity. Starting from the Beer-Lambert law we model the effect of movement artifacts on the PPG signal as an amplitude modulation. Using tri-axis accelerometer recordings to demodulate the PPG signal, we are able to extract the heart rate even when motion artifacts are within the frequency band of interest. The average heart rate error using two-channel PPG recordings from 12 subjects was 1:6 BPM with a standard deviation of 3 BPM.

Outlier-insensitive Kalman smoothing and marginal message passing

We propose a new approach to outlier-insensitive Kalman smoothing based on normal priors with unknown variance (NUV). In contrast to prior work, the actual computations amount essentially to iterations of a standard Kalman smoother (with few extra computations). The proposed approach is easily extended to nonlinear estimation problems by combining the outlier detection with an extended Kalman smoother. For the Kalman smoothing, we consider both a Modified Bryson-Frasier smoother and the recently proposed Backward Information Filter Forward Marginal smoother, neither of which requires matrix inversions.

New square-root and diagonalized Kalman smoothers

Naive implementations of Kalman filters and smoothers often suffer from numerical problems. In this paper, we consider two Kalman smoothers that were proposed recently: (i) the adaptation of the MBF (Modified-Bryson Frazier) for input estimation and (ii) the BIFM (backward information filter, forward marginal) smoother. Even naive implementations of these smoothers are numerically rather robust because these smoothers require no matrix inversion. Nonetheless, additional measures are sometimes required. We present square-root versions for both these smoothers as well as state reparametrizations for improved numerical stability. The main novelty in this paper is the square-root version of the BIFM smoother, which can be used in numerically critical smoothing problems, as exemplified in a force estimation problem using a multi-mass resonator model of an industrial milling machine.

Motion sensitivity analysis of retinal ganglion cells in mouse retina using natural visual stimuli

One of the major objectives in functional studies of the retina is the understanding of neural circuits and identification of the function of involved nerve cells. Instead of stimulating the retina with light patterns of simple geometrical shapes, we analyze the response of retinal ganglion cells of mouse retina to a black and white movie containing a natural scenery. By correlating measured spike trains with a metric for the velocity of a visual scene, PV0 cells were found to be direction selective, whereas PV5 cells did not show any sensitivity to motion.