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:
“... that there is no other way,
That the history of creation proceeds according to
Stringent laws, and that things
Do get done in this way, but never the things
We set out to accomplish and wanted so desperately
To see come into being.”
—John Ashbery (b. 1927)
“A people without history
Is not redeemed from time, for history is a pattern
Of timeless moments.”
—T.S. (Thomas Stearns)
“The history of this country was made largely by people who wanted to be left alone. Those who could not thrive when left to themselves never felt at ease in America.”
—Eric Hoffer (1902–1983)