1. A method to process medical image data acquired at an imaging modality serving as a data source, for transfer to a cloud system for processing at the cloud system, said method comprising: prior to transferring said medical image data, incrementally compressing said medical image data separately in each of a plurality of compression stages of a compressor, to produce a set of incrementally compressed medical image data from each compression stage; transferring the sets of incrementally compressed medical image data in parallel from the data source to the cloud system; in the cloud system, incrementally decompressing the individual sets of incrementally compressed medical image data separately in parallel in each of a plurality of decompression stages of a decompressor, said decompression stages operating respectively with different degrees of decompression so as to produce a plurality of decompressed medical image data sets each having a different degree of compression that remains after said different degrees of decompression; processing the sets of decompressed medical image data respectively in parallel in different processing units of a processor in the cloud system, thereby generating a plurality of different processed images that differ in visual contact from each other due to the different degrees of decompression of the respective decompressed medical image data sets; transferring the processing results together from the cloud system to a recipient selected from the group consisting of the data source and an additional computer-based entity; and at said recipient, allowing a display selection to be made among said plurality of different processed images dependent on the respective different visual content of each processed image.