1. A method for training a system for reconstructing a magnetic resonance (MR) image from signals collected by an MR scanner, the method comprising: under-sampling respective image data from each of a plurality of fully-sampled images; inputting the under-sampled image data to a multi-scale neural network comprising a plurality of sequentially connected layers, each layer having a respective input for receiving a respective array of input image data and an output for outputting reconstructed image data, each layer performing a recursive process comprising: decomposing the array of input image data received at the input of the layer; applying a thresholding function to the decomposed image data, to form a shrunk data, the thresholding function outputting a non-zero value asymptotically approaching one in the case where the thresholding function receives an input having a magnitude greater than a first value, reconstructing the shrunk data for combining with a reconstructed image data output by another one of the plurality of layers to form updated reconstructed image data, and machine-learning at least one parameter of the decomposing, the thresholding function, or the reconstructing based on the fully sampled images and the updated reconstructed image data.