He has been the Ph.D. advisor of at least 20 doctoral students, including Emmanuel Candès.
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Around 2004, Emmanuel Candès, Terence Tao, and David Donoho proved that given knowledge about a signal's sparsity, the signal may be reconstructed with fewer samples than the Nyquist-Shannon theorem requires.
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The results found by Emmanuel Candès, Justin Romberg, Terence Tao and David Donoho, showed that the number of these compressive measurements can be small and still contain nearly all the useful information.