Gauss Prize-2018 : Prof. David Donoho (Stanford University, USA)

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Magnetic Resonance Imaging (MRI) and Computerized Tomography (CT) are popular imaging techniques, which allow doctors to identify abnormalities, present inside human bodies non-destructively and non-invasively. Typically, an MRI scan lasts for almost an hour letting the patient lie inside a cramped tube. In CT, however, the X-ray dosage given to the patient could be harmful. Consequently, any reduction in scanning time or dosage administered possesses great value in healthcare domain.

The contributions of Prof. David Donoho led to a new mathematical area, popularly known as Compressed Sensing (CS).  Prof. Donoho was one of the first researchers who developed math describing signals that are sparse. The mathematical analyses of Prof. Donoho and his collaborators showed clearly that, for data that can be sparsely generated, one can obtain good reconstructions from reduced number of measurements – thereby compressing the sensing process rather than the traditionally sensed data. Such clear mathematical understanding was transformational, and inspired rapid progress, in MRI research, and elsewhere. In particular, the CS based algorithms help in realizing scanning process 10 times faster in MRI and reducing X-ray dosage in CT significantly.

A full rank matrix Φ of size m by n (with m < < n) generates an underdetermined system of linear equations Φ x=y possessing infinitely many solutions. Among all solutions, the CS based algorithms pick the sparsest solution (the solution with smallest number of nonzero components) through the following convex relaxation:

provided Φ satisfies some sparse recovery properties. Prof. Donoho and his collaborators established mathematical guarantees for convex relaxation of original problem and provided faster algorithms for solving afore-stated optimization problem.

For his outstanding mathematical contributions in fields like Harmonic Analysis, Wavelets and Compressed Sensing, Prof. Donoho has been awarded the prestigious Gauss prize in ICM-2018 held recently in Brazil.  

Author: C. S. Sastry, IIT Hyderabad 

Posted By : ScienceIndia Administrator

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