A method of reconstructing an MRI or ultrasound biomedical image, based on compressed sensing includes exciting a body under examination； acquiring image data from the generated signals, wherein the signals are acquired by pseudo-random undersampling； reconstructing the image using a nonlinear iterative algorithm for minimizing an optimization function containing one or more terms for image data sparsity in one or more predetermined domains with a data fidelity constraint term ensuring fidelity to the acquired image data； wherein two or more sets of image data are acquired from the 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.
