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Accurate and reliable estimation of the heart rate using wearable devices, especially during physical exercise, must deal with noisy signals that contain motion artifacts. We present an approach that is based on photoplethysmographic (PPG) signals which are measured with two wrist-type pulse oximeters. The heart rate is related to intensity changes of the reflected light. Our proposed method suppresses the motion artifacts by adaptively estimating the transfer functions of each of the three-axis acceleration signals that produce the artifacts in the PPG signals. We combined the output of the six adaptive filters into a single enhanced time-frequency domain signal based on which we track the heart rate with a high accuracy. Our approach is real-time capable, computationally efficient and real data results for a benchmark data set illustrate the superior performance compared to a recently proposed approach.

The role of cardiopulmonary signals in the dynamics of wavefront aberrations in the eye has been examined. Synchronous measurement of the eye's wavefront aberrations, cardiac function, blood pulse, and respiration signals were taken for a group of young, healthy subjects. Two focusing stimuli, three breathing patterns, as well as natural and cycloplegic eye conditions were examined. A set of tools, including time-frequency coherence and its metrics, has been proposed to acquire a detailed picture of the interactions of the cardiopulmonary system with the eye's wavefront aberrations. The results showed that the coherence of the blood pulse and its harmonics with the eye's aberrations was, on average, weak ( 0.4+/-0.15), while the coherence of the respiration signal with eye's aberrations was, on average, moderate ( 0.53+/-0.14). It was also revealed that there were significant intervals during which high coherence occurred. On average, the coherence was high ( > 0.75) during 16% of the recorded time, for the blood pulse, and 34% of the time for the respiration signal. A statistically significant decrease in average coherence was noted for the eye's aberrations with respiration in the case of fast controlled breathing (0.5 Hz). The coherence between the blood pulse and the defocus was significantly larger for the far target than for the near target condition. After cycloplegia, the coherence of defocus with the blood pulse significantly decreased, while this was not the case for the other aberrations. There was also a noticeable, but not statistically significant, increase in the coherence of the comatic term and respiration in that case. By using nonstationary measures of signal coherence, a more detailed picture of interactions between the cardiopulmonary signals and eye's wavefront aberrations has emerged.

We derive a new Bayesian Information Criterion (BIC) by formulating the problem of estimating the number of clusters in an observed data set as maximization of the posterior probability of the candidate models. Given that some mild assumptions are satisfied, we provide a general BIC expression for a broad class of data distributions. This serves as a starting point when deriving the BIC for specific distributions. Along this line, we provide a closed-form BIC expression for multivariate Gaussian distributed variables. We show that incorporating the data structure of the clustering problem into the derivation of the BIC results in an expression whose penalty term is different from that of the original BIC. We propose a two-step cluster enumeration algorithm. First, a model-based unsupervised learning algorithm partitions the data according to a given set of candidate models. Subsequently, the number of clusters is determined as the one associated with the model for which the proposed BIC is maximal. The performance of the proposed two-step algorithm is tested using synthetic and real data sets.