Semiparametric curve alignment and shift density estimation for biological data

Assume that we observe a large number of curves, all of them with identical, although unknown, shape, but with a different random shift. The objective is to estimate the individual time shifts and their distribution. Such an objective appears in several biological applications like neuroscience or ECG signal processing, in which the estimation of the distribution of the elapsed time between repetitive pulses with a possibly low signal-noise ratio, and without a knowledge of the pulse shape is of interest. We suggest an M-estimator leading to a three-stage algorithm: we split our data set in blocks, on which the estimation of the shifts is done by minimizing a cost criterion based on a functional of the periodogram; the estimated shifts are then plugged into a standard density estimator. We show that under mild regularity assumptions the density estimate converges weakly to the true shift distribution. The theory is applied both to simulations and to alignment of real ECG signals. The estimator of the shift distribution performs well, even in the case of low signal-to-noise ratio, and is shown to outperform the standard methods for curve alignment.Comment: 30 pages ; v5 : minor changes and correction in the proof of Proposition 3.

Semiparametric Curve Alignment and Shift Density Estimation: ECG Data Processing Revisited

We address in this contribution a problem stemming from functional data analysis. Assuming that we dispose of a large number of shifted recorded curves with identical shape, the objective is to estimate the time shifts as well as their distribution. Such an objective appears in several biological applications, for example in ECG signal processing. We are interested in the estimation of the distribution of elapsed durations between repetitive pulses, but wish to estimate it with a possibly low signal-to-noise ratio, or without any knowledge of the pulse shape. This problem is solved within a semiparametric framework, that is without any knowledge of the shape. We suggest an M-estimator leading to two different algorithms whose main steps are as follows: we split our dataset in blocks, on which the estimation of the shifts is done by minimizing a cost criterion, based on a functional of the periodogram. The estimated shifts are then plugged into a standard density estimator. Some theoretical insights are presented, which show that under mild assumptions the alignment can be done efficiently. Results are presented on simulations, as well as on real data for the alignment of ECG signals, and these algorithms are compared to the methods used by practitioners in this framework. It is shown in the results that the presented method outperforms the standard ones, thus leading to a more accurate estimation of the average heart pulse and of the distribution of elapsed times between heart pulses, even in the case of low Signal-to- Noise Ratio (SNR)

Sparse regression algorithm for activity estimation in γ\gamma spectrometry

We consider the counting rate estimation of an unknown radioactive source, which emits photons at times modeled by an homogeneous Poisson process. A spectrometer converts the energy of incoming photons into electrical pulses, whose number provides a rough estimate of the intensity of the Poisson process. When the activity of the source is high, a physical phenomenon known as pileup effect distorts direct measurements, resulting in a significant bias to the standard estimators of the source activities used so far in the field. We show in this paper that the problem of counting rate estimation can be interpreted as a sparse regression problem. We suggest a post-processed, non-negative, version of the Least Absolute Shrinkage and Selection Operator (LASSO) to estimate the photon arrival times. The main difficulty in this problem is that no theoretical conditions can guarantee consistency in sparsity of LASSO, because the dictionary is not ideal and the signal is sampled. We therefore derive theoretical conditions and bounds which illustrate that the proposed method can none the less provide a good, close to the best attainable, estimate of the counting rate activity. The good performances of the proposed approach are studied on simulations and real datasets

Fast Digital Filtering of Spectrometric Data for Pile-up Correction

International audienceThis paper considers a problem stemming from the analysis of spectrometric data. When performing experiments on highly radioactive matter, electrical pulses recorded by the spectrometer tend to overlap, thus yielding severe distortions when computing the histogram of the pulses' energies. In this paper, we propose a fast recursive algorithm which estimates efficiently this histogram from measurements of the duration and energies of overlapping pulses. Its good performances are shown both on simulations and real data. Furthermore, its lower algorithmic complexity makes it more fitting for real-time implementation