Abstract: A method for image reconstruction that utilizes a generalization of compressed sensing is provided. More particularly, a method for homotopic l0 minimization is provided, in which a series of subproblems that asymptotically approach a solution to the l0 minimization are iteratively solved. These subproblems include utilizing concave metric prior functionals in the traditional compressed sensing framework. Substantially undersampled image data is acquired from a subject, for example, with a medical imaging system, such as a magnetic resonance imaging (“MRI”) system or a computed tomography (“CT”) system. Using the provided method, undersampling on the order of around 96 percent can be achieved while still producing clinically acceptable images.