Vector-FRI Recovery of Multi-Sensor Measurements

Thanks to lowering costs, sensors of all kinds have increasingly been used in a wide variety of disciplines and fields, facilitating the rapid development of new technologies and applications. The information of interest (e.g. source location, refractive index, etc.) gets encoded in the measured sensor data, and the key problem is then to decode this information from the sensor measurements. In many cases, sensor data exhibit sparse features - 'innovations' - that typically take the form of a finite sum of sinusoids. In practice, the robust retrieval of such encoded information from multi-sensors data (array or network) is difficult due to the non-uniformity of instrument precision and noise (i.e. different across sensors). This motivates the development of a joint sparse ('vector Finite Rate of Innovation') recovery strategy for multi-sensor data: by fitting the data to a joint parametric model, an accurate sparse recovery can be achieved, even if the noise of the sensors is non-homogenous and correlated. Although developed for one-dimensional sensor data, we show that our method is easily extended to multi-dimensional sensor measurements, e.g. direction-of-arrival data of 2D planar array and interference fringes of underwater acoustics, which provides a generic solution to these applications. A very robust and efficient algorithm is proposed, which we validate in various conditions (simulations, multiple types of real data).