Source term estimation using convex optimization

A computationally efficient, grid-based estimation method is presented for multiple source identification from distributed sensor data. Under the assumption that the sources are located on a grid over the region of interest, the solution to the problem of multiple source identification, that is, estimation of the number, locations, and intensities of the sources, is represented by a large sparse vector (whose size is greater than that of the observation vector) and is obtained by solving a convex optimization problem using the ℓ₁ minimization method. The method can exactly and efficiently recover the true source parameters in the absence of source representation error and measurement noise and can efficiently identify the areas of the true sources with the clusters of grid points in the more realistic scenarios when the source locations do not coincide with the grid points and the sensor data are contaminated by noise.