Reconstruction system and method

An apparatus for performing ultrasound measurements of a propagation medium containing non-uniformities, the apparatus comprising:

• an ultrasound transducer configured to emit ultrasound excitation pressure waves;
• a receiver comprising one or more elements for receiving a full signal X resulting from reflection of said excitation pressure waves by the non-uniformities;
• and
• a processor configured to receive a set of random samples B of the full signal X or of a demodulated full signal X and to estimate the full signal X from the set of random samples, wherein the processor is configured to perform the steps of:
• 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, wherein each vector signal comprises a plurality of samples representing the full signal sampled from a corresponding receiver element, 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;
• 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 Dl;
• determining a convergence parameter in dependence upon the evaluated objective function;
• and
• modifying the updated second matrix Dl in dependence upon the convergence parameter.