Abstract: A method for reconstructing a signal from a subset of the full signal is disclosed. In one embodiment, the method includes receiving a plurality of randomly sampled multichannel radio-frequency or in-phase and quadrature signals acquired from a physical environment including a transmitter, a propagation medium and a receiver; modelling the full signal as a matrix comprising a plurality of vector signals wherein the full signal is expressed as a matrix product of a first matrix and a second matrix; updating the second matrix based on an objective function to produce an updated second matrix; determining a convergence parameter in dependence upon the evaluated objective function; and modifying the updated second matrix in dependence upon the convergence parameter.