A method of reconstructing an MRI or ultrasound biomedical image, based on compressed sensing and comprising the steps of acquiring several sets of image data from said generated signals, each data set being acquired in a different undersampling scheme and/or a different acquisition mode such as to make expected and unavoidable artifacts incoherent. Each of the acquired image data set is multiplied by a correction matrix Δ, which is calculated from a mathematical model of expected artifacts according to prior knowledge, for adjusting fidelity of the reconstructed image to the corrected acquired image data. For each iteration of said nonlinear iterative algorithm the data sets are processed to generate a combination image which will therefore be faithful to the acquired data but not to the incoherent artifacts.
