Compressed Sensing Techniques Applied to the Reconstruction of Magnetic Resonance Images

Magnetic resonance Imaging (MRI) is nowadays a central technique in medical diagnostics but, in order to acquire a high resolution image of the human body, long acquisition times are still needed. MRI scanners have traditionally been limited to imaging static structures over a short period, and the patient has been instructed to hold his or her breath. However, the image can now be treated as a sparse signal in space and time, and MRI scanners have begun to overcome the previous limitations and produce images, for example, of a beating heart. Compressive sensing, and more generally the possibility of efficiently capturing sparse and compressible signals, using a relatively small number of measurements, paves the way for a number of possible applications. New physical sampling devices may be designed that directly record discrete low-rate incoherent measurements of the analog signal, which is needed for the completeness of the signal itself. This should be especially useful in situations where large collections of samples may be costly, difficult or impossible to obtain. A digital camera newly developed by Richard Baraniuk and Kevin Kelly at Rice University (see dsp. rice. edu/cs/cscamera) provides a particularly interesting example of successful implementation of compressive sensing methodology. In the detector array of a conventional digital camera, each pixel performs an analog-to-digital conversion; for example, the detector on a 5-megapixel camera produces 5 million bits for each image. This large amount of data is then dramatically reduced through a compression algorithm (using wavelet or other techniques), so as not to overburden typical storage and transfer capacities. Rather than collect 5 million pixels for an image, the new camera samples only 200,000 single-pixels that provide an immediate 25-fold savings in data collected compared with 5 megapixels. However, CS-MRI is still in its infancy, and many crucial issues remain unsettled. These include: optimizing sampling trajectories, developing improved sparse transforms that are incoherent to the sampling operator, studying reconstruction quality in terms of clinical significance improving the speed of reconstruction algorithms Therefore, there are still fascinating theoretical and practical research problems, promising substantial payoffs in improved medical care. In conclusion, a lot of work is still waiting ahead, but signal acquisition and processing field are finally off the constrictions imposed by previous theoretical and practical limits.