The inverse source method with the sparse recovery of equivalent currents is proposed for the case where a small antenna is embedded in a larger body, such as in the case of 5G devices with small antenna chips. The proposed sparse recovery method based on the L1-norm regularization and a convex optimization algorithm called the fast iterative shrinkage-thresholding algorithm recovers the equivalent electromagnetic current sparsely on a surface covering the whole body of the device. The method improves accuracy for reconstructing the incident power density, a metric of human exposure above 6 GHz, in close proximity to the device under test.