History
Several scientific fields used L1 techniques. In statistics, the least-squares method was complemented by the -norm, which was introduced by Laplace. Following the introduction of linear programming and Dantzig's simplex algorithm, the -norm was used in computational statistics. In statistical theory, the -norm was used by George W. Brown and later writers on median-unbiased estimators. It was used by Peter Huber and others working on robust statistics. The -norm was also used in signal processing, for example, in the 1970s, when seismologists constructed images of reflective layers within the earth based on data that did not seem to satisfy the Nyquist–Shannon criterion. It was used in matching pursuit in 1993, the LASSO estimator by Robert Tibshirani in 1996 and basis pursuit in 1998. There were theoretical results describing when these algorithms recovered sparse solutions, but the required type and number of measurements were sub-optimal and subsequently greatly improved by compressed sensing.
Around 2004 Emmanuel Candès, Terence Tao and David Donoho discovered important results on the minimum amount of data needed to reconstruct an image even though the amount of data would be deemed insufficient by the Nyquist–Shannon criterion. This work is the basis of compressed sensing as currently studied.
Read more about this topic: Compressed Sensing
Famous quotes containing the word history:
“The basic idea which runs right through modern history and modern liberalism is that the public has got to be marginalized. The general public are viewed as no more than ignorant and meddlesome outsiders, a bewildered herd.”
—Noam Chomsky (b. 1928)
“Don’t you realize that this is a new empire? Why, folks, there’s never been anything like this since creation. Creation, huh, that took six days, this was done in one. History made in an hour. Why it’s a miracle out of the Old Testament!”
—Howard Estabrook (1884–1978)
“Regarding History as the slaughter-bench at which the happiness of peoples, the wisdom of States, and the virtue of individuals have been victimized—the question involuntarily arises—to what principle, to what final aim these enormous sacrifices have been offered.”
—Georg Wilhelm Friedrich Hegel (1770–1831)