Compressive Parameter Estimation for Sparse Translation-Invariant Signals Using Polar Interpolation

We propose new compressive parameter estimation algorithms that make use of polar interpolation to improve the estimator precision. Our work extends previous approaches involving polar interpolation for compressive parameter estimation in two aspects: (i) we extend the formulation from real non-negative amplitude parameters to arbitrary complex ones, and (ii) we allow for mismatch between the manifold described by the parameters and its polar approximation. To quantify the improvements afforded by the proposed extensions, we evaluate six algorithms for estimation of parameters in sparse translation-invariant signals, exemplified with the time delay estimation problem. The evaluation is based on three performance metrics: estimator precision, sampling rate and computational complexity. We use compressive sensing with all the algorithms to lower the necessary sampling rate and show that it is still possible to attain good estimation precision and keep the computational complexity low. Our numerical experiments show that the proposed algorithms outperform existing approaches that either leverage polynomial interpolation or are based on a conversion to a frequency-estimation problem followed by a super-resolution algorithm. The algorithms studied here provide various tradeoffs between computational complexity, estimation precision, and necessary sampling rate. The work shows that compressive sensing for the class of sparse translation-invariant signals allows for a decrease in sampling rate and that the use of polar interpolation increases the estimation precision.Comment: 13 pages, 5 figures, to appear in IEEE Transactions on Signal Processing; minor edits and correction

Towards the sequential assimilation of SAR-derived water stages into hydraulic models using the Particle Filter : proof of concept

With the onset of new satellite radar constellations (e.g. Sentinel-1) and advances in computational science (e.g. grid computing) enabling the supply and processing of multimission satellite data at a temporal frequency that is compatible with real-time flood forecasting requirements, this study presents a new concept for the sequential assimilation of Synthetic Aperture Radar (SAR)-derived water stages into coupled hydrologic-hydraulic models. The proposed methodology consists of adjusting storages and fluxes simulated by a coupled hydrologic-hydraulic model using a Particle Filterbased data assimilation scheme. Synthetic observations of water levels, representing satellite measurements, are assimilated into the coupled model in order to investigate the performance of the proposed assimilation scheme as a function of both accuracy and frequency of water level observations. The use of the Particle Filter provides flexibility regarding the form of the probability densities of both model simulations and remote sensing observations. We illustrate the potential of the proposed methodology using a twin experiment over a widely studied river reach located in the Grand-Duchy of Luxembourg. The study demonstrates that the Particle Filter algorithm leads to significant uncertainty reduction of water level and discharge at the time step of assimilation. However, updating the storages of the model only improves the model forecast over a very short time horizon. A more effective way of updating thus consists in adjusting both states and inputs. The proposed methodology, which consists in updating the biased forcing of the hydraulic model using information on model errors that is inferred from satellite observations, enables persistent model improvement. The present schedule of satellite radar missions is such that it is likely that there will be continuity for SAR-based operational water management services. This research contributes to evolve reactive flood management into systematic or quasi-systematic SAR-based flood monitoring services

An Empirical-Mathematical Approach for Calibration and Fitting Cell-Electrode Electrical Models in Bioimpedance Tests

This paper proposes a new yet efficient method allowing a significant improvement in the on-line analysis of biological cell growing and evolution. The procedure is based on an empirical-mathematical approach for calibration and fitting of any cell-electrode electrical model. It is valid and can be extrapolated for any type of cellular line used in electrical cell-substrate impedance spectroscopy (ECIS) tests. Parameters of the bioimpedance model, acquired from ECIS experiments, vary for each cell line, which makes obtaining results difficult and—to some extent-renders them inaccurate. We propose a fitting method based on the cell line initial characterization,and carry out subsequent experiments with the same line to approach the percentage of well filling and the cell density (or cell number in the well). To perform our calibration technique, the so-called oscillation-based test (OBT) approach is employed for each cell density. Calibration results are validated by performing other experiments with different concentrations on the same cell line with the same measurement technique. Accordingly, a bioimpedance electrical model of each cell line is determined, which is valid for any further experiment and leading to a more precise electrical model of the electrode-cell system. Furthermore, the model parameters calculated can be also used by any other measurement techniques. Promising experimental outcomes for three different cell-lines have been achieved, supporting the usefulness of this technique

Compressive Measurement Designs for Estimating Structured Signals in Structured Clutter: A Bayesian Experimental Design Approach

This work considers an estimation task in compressive sensing, where the goal is to estimate an unknown signal from compressive measurements that are corrupted by additive pre-measurement noise (interference, or clutter) as well as post-measurement noise, in the specific setting where some (perhaps limited) prior knowledge on the signal, interference, and noise is available. The specific aim here is to devise a strategy for incorporating this prior information into the design of an appropriate compressive measurement strategy. Here, the prior information is interpreted as statistics of a prior distribution on the relevant quantities, and an approach based on Bayesian Experimental Design is proposed. Experimental results on synthetic data demonstrate that the proposed approach outperforms traditional random compressive measurement designs, which are agnostic to the prior information, as well as several other knowledge-enhanced sensing matrix designs based on more heuristic notions.Comment: 5 pages, 4 figures. Accepted for publication at The Asilomar Conference on Signals, Systems, and Computers 201