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:
“As History stands, it is a sort of Chinese Play, without end and without lesson.”
—Henry Brooks Adams (1838–1918)
“The history of work has been, in part, the history of the worker’s body. Production depended on what the body could accomplish with strength and skill. Techniques that improve output have been driven by a general desire to decrease the pain of labor as well as by employers’ intentions to escape dependency upon that knowledge which only the sentient laboring body could provide.”
—Shoshana Zuboff (b. 1951)
“The history of a soldier’s wound beguiles the pain of it.”
—Laurence Sterne (1713–1768)