1. A method to process medical raw data, comprising: operating a medical imaging apparatus to acquire medical data in a compressively sampled data acquisition procedure wherein said medical data are undersampled at a sampling rate that does not obey Shannon's Theorem, thereby producing compressively sampled raw data, and providing said compressively sampled raw data to a processor; in said processor, controlling storage of the compressively sampled raw data in a memory; in said processor, in addition to the compressively sampled raw data, controlling storage of processing data configured to operate on the compressively sampled raw data to generate output data, in an output data file, with the compressively sampled raw data and the processing data being stored in a file in said memory having a file size that is less than a file size of said output data file; and making said output data file available at an output of said processor in electronic form.