Reconstruction using approximate message passing methods

The present invention is notably directed to a computer-implemented method for image reconstruction. The method comprises: accessing elements that respectively correspond to measurement values, which can be respectively mapped to measurement nodes; and performing message passing estimator operations to obtain estimates of random variables associated with variable nodes, according to a message passing method in a bipartite factor graph. In this message passing method: the measurement values are, each, expressed as a term that comprises linear combinations of the random variables; each message exchanged between any of the measurement nodes and any of the variable nodes is parameterized by parameters of a distribution of the random variables; and performing the message passing estimator operations further comprises randomly mapping measurement values to the measurement nodes, at one or more iterations of the message passing method. Finally, image data are obtained from the obtained estimates of the random variables, which image data are adapted to reconstruct an image. The present invention is further directed to related systems and methods using the above image reconstruction method.