2020, Wildhaber, Reto, Ren, Elizabeth, Waldmann, Frederic, Loeliger, Hans-Andrea

Local polynomial approximations represent a versatile feature space for time-domain signal analysis. The parameters of such polynomial approximations can be computed by efficient recursions using autonomous linear state space models and often allow analytical solutions for quantities of interest. The approach is illustrated by practical examples including the estimation of the delay difference between two acoustic signals and template matching in electrocardiogram signals with local variations in amplitude and time scale.

2017, Wildhaber, Reto, Zalmai, Nour, Jacomet, Marcel, Loeliger, Hans-Andrea

We introduce a model-based approach for computationally efficient signal detection and discrimination, which is relevant for biological signals. Due to its low computational complexity and low memory need, this approach is well-suited for low power designs, as required for medical devices and implants. We use linear state space models to gain recursive, efficient computation rules and obtain the model parameters by minimizing the squared error on discrete-time observations. Furthermore we combine multiple models of different time-scales to match superpositions of signals of variable length. To give immediate access to our method, we highlight the use in several practical examples on standard and on esophageal ECG signals. This method was adapted and improved as part of a research and development project for medical devices.

2018, Wildhaber, Reto, Zalmai, Nour, Jacomet, Marcel, Loeliger, Hans-Andrea

This paper introduces a toolbox for model-based detection, separation, and reconstruction of signals that is especially suited for biomedical signals, such as electrocardiograms (ECGs) or electromyograms (EMGs). The modeling is based on autonomous linear state space models (LSSMs), which are localized with flexible windows. The models are fit to observations by minimizing the squared error while the use of LSSMs leads to efficient recursive error computations and minimizations. Multisection windows enable complex models, and per-sample weights enable multistage processing or adaptive smoothing. This paper is motivated by, and intended for, practical applications, for which several examples and tabulated cost computations are given.

2017, Zalmai, Nour, Wildhaber, Reto, Loeliger, Hans-Andrea

The paper addresses the problem of fitting, at any given time, a parameterized signal generated by an autonomous linear state space model (LSSM) to discrete-time observations. When the cost function is the squared error, the fitting can be accomplished based on efficient recursions. In this paper, the squared error cost is generalized to more advanced cost functions while preserving recursive computations: first, the standard sample-wise squared error is augmented with a sampledependent polynomial error; second, the sample-wise errors are localized by a window function that is itself described by an autonomous LSSM. It is further demonstrated how such a signal estimation can be extended to handle unknown additive and/or multiplicative interference. All these results rely on two facts: first, the correlation function between a given discrete-time signal and a LSSM signal can be computed by efficient recursions; second, the set of LSSM signals is a ring.

2018, Wildhaber, Reto, Bruegger, Dominik, Zalmai, Nour, Malmberg, Hampus, Goette, Josef, Jacomet, Marcel, Tanner, Hildegard, Haeberlin, Andreas, Loeliger, Hans-Andrea

The rapid progress of invasive therapeutic options for cardiac arrhythmias increases the need for accurate diagnostics. The surface electrocardiogram (ECG) is still the standard of noninvasive diagnostics but lacks atrial signal resolution. By contrast, esophageal electrocardiography (EECG) yields atrial signals of high amplitude and with a high signal-to-noise ratio. Esophageal electrocardiography has become fast and safe, but the mechanical constraints of esophageal measuring catheters and the “random” motion of the catheter inside the subject's esophagus limit the spatial resolution of EECG signals. In this paper, we propose a method to estimate the electrical field projected onto the esophagus with an increased spatial resolution, using commonly available esophageal catheters. In a first step, we estimate the time-varying catheter position, and in a second step, we estimate the projected electrical field with enhanced spatial resolution. The proposed algorithm comprises several consecutive optimization steps, where each intermediate step produces not just a single point estimate, but a cost function over multiple solutions, which reduces the information loss at each processing step. We conclude with examples from a clinical trial, where the fields of cardiac arrhythmias are presented as two-dimensional contour plots.

2016, Zalmai, Nour, Wildhaber, Reto, Clausen, Desiree, Loeliger, Hans-Andrea

Cell depolarization runs essentially in a uniform motion along the muscular tissue, which creates transient electrical potential differences measurable by nearby electrodes. Inferring the depolarization speed and direction from measurements is of great interest for physicians. In cardiology, this is part of the inverse ECG problem which often requires a large number of electrodes and intense computational power even if the simple common model of the single equivalent moving dipole (SEMD) is applied. In this paper, we model a depolarization process as a straight-line movement of a SEMD. We provide an efficient algorithm based on linear state space models that infers the SEMD movement using only 3 measurement channels from a tetrahedral electrode and with the presence of interferences. Our algorithm is tested both on simulated and experimental data.