1. A method that produces images, comprising: acquiring a k-space data set of an imaged object; collecting a portion of the k-space data set according to a data collecting pattern, the data collecting pattern having a degree of incoherence incorporated into the data collecting pattern by a process comprising rotating the entire data collecting pattern along an axis containing a trajectory plane of the data collecting pattern, the rotating introducing a pseudo-random shift into the trajectory plane; and reconstructing an image from the collected portion of the k-space data set according to a convex optimization model, wherein the reconstructing of the image according to the convex optimization model includes generating image data using an iterative process, the iterative process including updating a value of a norm weighting factor to prevent penalizing of discontinuities in the reconstructed image, and wherein the acquiring, the collecting, and the reconstructing are performed by one or more processors.