Basic pursuit

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Pursuit base ( BP ) is a mathematical optimization problem of the form

${\displaystyle \min _{x}\|x\|_{1}\quad {\mbox{mit}}\quad y=Ax}$,

where is the solution vector, the observation vector of the measurement and a transformation matrix (often also called measurement matrix). The following applies here , whereby the linear system of equations is underdetermined. ${\displaystyle x\in \mathbb {C} ^{n}}$ ${\displaystyle y\in \mathbb {C} ^{m}}$ ${\displaystyle A\in \mathbb {C} ^{m\times n}}$ ${\displaystyle m<n}$ ${\displaystyle y=Ax}$

Among the solutions to the equation , the one with the minimum value of the norm (sum of the coordinate amounts, see Manhattan metric ) is sought. ${\displaystyle x}$ ${\displaystyle y=Ax}$ ${\displaystyle L_{1}}$

literature

• Stephen Boyd, Lieven Vandenbergh: Convex Optimization , Cambridge University Press, 2004, ISBN 9780521833783 , pp. 337-337
• Simon Foucart, Holger Rauhut: A Mathematical Introduction to Compressive Sensing . Springer, 2013, ISBN 9780817649487 , pp. 77-110

Web links

• Shaobing Chen, David Donoho: Basic Pursuit
• Terence Tao : Compressed Sensing . Mahler Lecture Series (slides)