1. A computerized method for transforming a signal representative of image information, the signal being a sparse signal, the method comprising: obtaining the signal; using the signal to learn a dictionary of basis functions that represent at least part of the signal based on the signal, wherein learning the dictionary of basis functions includes estimating a representation of the signal and using parameters determined from the signal, wherein the dictionary is learned using a Beta process, wherein the basis functions represent at least part of the signal, wherein the parameters include at least one of a number of basis functions in the dictionary of basis functions; and using the learned dictionary of basis functions to transform the signal, wherein the transformed signal based on the learned dictionary of basis functions, wherein transforming the signal includes performing at least one of denoising, inpainting, and compressive sensing on the signal.