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The process of forming images from measured data using computational algorithms is referred to as computational imaging. Rapid advances in computational hardware and signal processing algorithms have resulted in a flurry of activity in computational imaging in several application areas, including medicine, biology, remote sensing, and seismic imaging. Medical imaging has witnessed extensive research in computational imaging, beginning with computed tomography (CT), which relies on algorithms to construct a 3D volume from X-ray measurements taken from X-ray projections at different angles; this work received the 1979 Nobel Prize in Medicine. Most of the current medical-imaging modalities [e.g., magnetic resonance imaging (MRI), CT, positron emission tomography] employ computational imaging in one form or another.
Advances in computational MRI were primarily driven in the last decade by parallel image acquisition using multiple receiver coils and compressed sensing (CS). The ability of these approaches to break the classical Nyquist sampling limit has been exploited to considerably reduce the acquisition time in static imaging applications and to significantly improve the spatial and temporal resolution in dynamic imaging applications. Extensive research in this area has facilitated developments of efficient transforms, novel regularization priors, smart acquisition strategies, fast optimization algorithms, and computational toolboxes. The recent U.S. Food and Drug Administration approval of CS products for clinical scans makes MRI one of the main benefactors of CS algorithms.
While the application of CS-based algorithms in medical imaging is maturing, the recent research in this area has initiated a new computational way of thinking. The main focus of this special issue of IEEE Signal Processing Magazine (SPM), entitled Computational MRI: Compressive Sensing and Beyond in Jan. 2020, is on recent developments in computational MRI. These developments are pushing the frontier of computational imaging beyond CS. Similar to CS, most of these algorithms rely on image representation in one form or another. However, the common recent thread is the departure from handcrafted image representations (e.g., sparse wavelet model) to learning-based image representations. These learned representations are seamlessly combined with clever measurement strategies to significantly advance the state of the art in a number of areas. Several exciting applications including significantly improved spatial and temporal resolution, a considerable reduction in scan time, measurement of biophysical parameters directly from highly undersampled data, and direct measurement of very high-dimensional data are reviewed in this special issue of SPM.
This describes key ideas underlying the computational approaches used in MRI. These approaches range from CS algorithms that rely on fixed transforms or dictionaries, to adaptive or shallow-learning algorithms that adapt the image representation to the data (e.g., low-rank and dictionary-based methods), to recent deep-learning methods that learn a highly nonlinear representation from exemplar data. The articles provide insight into the capabilities of the current algorithms, their limitations, and their utility in challenging MRI problems. While the focus of this special issue is on medical imaging and in particular MRI, most of the problems, and hence solutions, are easily translatable to signal recovery applications in other areas.
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