A method for estimating a full signal X from a subset B of the full signal, the method comprising: receiving a plurality of randomly sampled multichannel radio-frequency or in-phase and quadrature signals acquired from a physical environment comprising a transmitter , the transmitter comprising one or more transmitting elements (10 1 , 10 2 , 10 3 , 10 4 , 10s, 10 6 ) for emitting ultrasound excitation pressure waves, a propagation medium containing non-uniformities capable of reflecting said pressure waves, and a receiver for receiving the full signal, wherein the receiver comprises a plurality of receiver elements (14 1 , 14 2 ); modelling the full signal X as a matrix comprising a plurality of vector signals, each vector signal corresponding to the full signal incident on a corresponding receiver element (14 1 , 14 2 ), wherein each vector signal comprises a plurality of samples representing the full signal sampled from a corresponding receiver element (14 1 , 14 2 ), wherein each sample comprises a weighted sum of complex sinusoids, wherein the full signal X is expressed as a matrix product of a first matrix Y and a second matrix D; wherein the complex sinusoids have a finite number k of distinct frequencies, wherein each weighted sum comprises sinusoids at the same k distinct frequencies, wherein the first matrix Y comprises the set of complex sinusoids, wherein the second matrix D comprises, for each vector signal, a set of k coefficients corresponding to the complex sinusoids; updating the second matrix D based on an objective function, wherein the objective function is configured to estimate the second matrix D based on the randomly sampled signals, to produce an updated second matrix D1; determining a convergence parameter in dependence upon the evaluated objective function; and modifying the updated second matrix D1 in dependence upon the convergence parameter, wherein modifying the updated second matrix D1 in dependence upon the convergence parameter comprises comparing the convergence parameter with a predetermined threshold value, and, further comprising, if the convergence parameter is greater than the predetermined threshold value, repeating the step of evaluating the objective function for the modified first trial matrix. wherein the complex sinusoids have a finite number k of distinct frequencies, wherein each weighted sum comprises sinusoids at the same k distinct frequencies, wherein the first matrix Y comprises the set of complex sinusoids, wherein the second matrix D comprises, for each vector signal, a set of k coefficients corresponding to the complex sinusoids; updating the second matrix D based on an objective function, wherein the objective function is configured to estimate the second matrix D based on the randomly sampled signals, to produce an updated second matrix D1; determining a convergence parameter in dependence upon the evaluated objective function; and modifying the updated second matrix D1 in dependence upon the convergence parameter, wherein modifying the updated second matrix D1 in dependence upon the convergence parameter comprises comparing the convergence parameter with a predetermined threshold value, and, updating the second matrix D based on an objective function, wherein the objective function is configured to estimate the second matrix D based on the randomly sampled signals, to produce an updated second matrix D1; determining a convergence parameter in dependence upon the evaluated objective function; and modifying the updated second matrix D1 in dependence upon the convergence parameter, wherein modifying the updated second matrix D1 in dependence upon the convergence parameter comprises comparing the convergence parameter with a predetermined threshold value, and, further comprising, if the convergence parameter is greater than the predetermined threshold value, repeating the step of evaluating the objective function for the modified first trial matrix. <EOS>